Designing spatio-spectral-controllable optics

Abstract

Designing a spatio-spectral-controllable optic includes: defining a first spatially varying complex electric field at a first location; numerically back-propagating the first spatially varying complex electric field to a second location, defining a second spatially varying complex electric field at the second location; defining a basis set of phase-versus-wavelength curves, each phase-versus-wavelength curve corresponding to a category; determining a root-mean-squared error value for each pixel of the second spatially varying complex electric field relative to each curve of the basis set, generating a plurality of root-mean-squared error values for each pixel; assigning a category to each pixel based on which curve of the basis set corresponds to the lowest root-mean-squared error value of the pixel; and defining an achievable optic by selecting a physical structure for each category based on the assigned categories of the pixels.

Description

DESIGNING SPATIO-SPECTRAL-CONTROLLABLE OPTICSSTATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0001] This invention was made with United States Government support from the National Institute of Standards and Technology (NIST), an agency of the United States Department of Commerce. The Government has certain rights in this invention.CROSS REFERENCE

[0002] This application claims the benefit of U.S. Provisional Patent Application Serial No. 63 / 697,840 (filed 9 / 23 / 2024), which is herein incorporated by reference in its entirety.BACKGROUND

[0003] The present invention generally relates to the field of designing optics, and more particularly to techniques for controlling the spatio-spectral profile of output beams by manipulating the spatial profile of spectral components, including wavelength, polarization, and incidence angle.

[0004] Optics play a crucial role in manipulating light for a wide range of applications, including imaging, spectroscopy, lithography, and communications. Traditional refractive optics, based on lenses, are often limited in their ability to handle short wavelengths, such as those found in the short-wavelength light (SWL) region of the electromagnetic spectrum including extreme ultraviolet (EUV), vacuum ultraviolet (VUV), and soft x-ray (SXR). Diffractive optics, on the other hand, use diffraction phenomena to manipulate light and offer advantages for these shorter wavelengths. Zoneplates, a type of diffractive optic, have been used for focusing and imaging in these spectral ranges.

[0005] However, conventional diffractive optics suffer from several significant limitations. Chromatic aberration, wherein the focal length of the optic varies with wavelength, limits their effectiveness for broadband light sources or for applications requiring precise focusing of multiple wavelengths. Diffraction efficiency, which determines the fraction of light directed into the desired order or focal spot, can be wavelength-dependent, further reducing performance for broadband light. Additionally, alignment of diffractive optics, particularly for short wavelengths, can be challenging and time-consuming, often requiring specialized equipment and expertise.

[0006] These limitations have hindered the development of compact, efficient, and versatile beam lines for SWL applications. The need for multiple optics to address chromatic aberration, low diffraction efficiency, and alignment challenges increases beamline complexity and cost. Furthermore, the sensitivity of these wavelengths to environmental factors like air absorption necessitates operation in vacuum, further complicating alignment procedures and experimental setups.

[0007] It is therefore an objective of the present invention to provide a new process for designing optics that control the spatio-spectral profile of output beams by manipulating the spatial profile of spectral components, including wavelength, polarization, and incidence angle, thereby overcoming the above-mentioned disadvantages of the prior art at least in part. Accordingly, methods and equipment for designing optics capable of manipulating light across a broad range of wavelengths and polarizations would be advantageous and would be favorably received in the art.BRIEF DESCRIPTION

[0008] One aspect of the present invention relates to designing a multi-beam spatio-spectral-controllable optic. A multi-beam spatio-spectral-controllable optic can be understood as an optic that can manipulate light to produce one or multiple output beams, where the properties of those beams, such as their wavelength, polarization, shape and direction, can be individually controlled.

[0009] It can be provided that the method defines a first spatially varying complex electric field at a first location. A spatially varying complex electric field refersto a description of light that includes both its amplitude and phase, which can vary across space. This arrangement provides the precise definition of the desired light pattern at a target location, such as a sample in a microscopy experiment or a detector in a spectroscopy setup. One advantage of this arrangement is the flexibility to tailor the light distribution to the specific requirements of an application, potentially providing new imaging, sensing, or processing capabilities.

[0010] It can be provided that the method numerically back-propagates the first spatially varying complex electric field to a second location, thereby defining a second spatially varying complex electric field at the second location. Back- propagation is a mathematical technique used to calculate the light field at an earlier point in its path, based on knowledge of the field at a later point. This allows for the determination of the light distribution required at the optic to produce the desired field at the first location. One advantage of this arrangement is the ability to account for the propagation of light and ensure that the optic will generate the desired output, mitigating potential issues like diffraction or spreading of the beam.

[0011] It can be provided that the method defines a basis set of phase- versus-wavelength curves, each phase-versus-wavelength curve corresponding to a category. A basis set is a collection of functions that can be combined to represent other, more complex functions. In this context, each curve in the basis set captures a specific way in which the phase of light can vary with wavelength. This arrangement facilitates the design of optics that can control the behavior of light over a broad range of wavelengths, an aspect for achieving achromatic or spectrally selective performance. One advantage of this arrangement is the ability to represent a wide variety of spectral responses with a limited number of curves, leading to more efficient computation, and data storage.

[0012] It can be provided that the method determines a root-mean-squared error value for each pixel of the second spatially varying complex electric field relative to each curve of the basis set, thereby generating a plurality of root-mean-squared error values for each pixel. The root-mean-squared error quantifies the difference between the desired phase-versus-wavelength behavior at each pixel and the behavior represented by each basis curve. This provides the selection of the most suitable basis curve for each pixel, ensuring an accurate representation of the desiredspectral response across the entire optic. One advantage of this arrangement is the quantitative basis for selecting categories, leading to a more robust and optimized design.

[0013] It can be provided that the method assigns a category to each pixel based on which curve of the basis set corresponds to the lowest root-mean-squared error value of the pixel. This step effectively classifies each pixel according to its desired spectral behavior, grouping similar pixels together. One advantage of this arrangement is the reduction of the complex, continuous light field into a discrete set of categories, facilitating the subsequent selection of physical structures for the optic.

[0014] It can be provided that the method defines an achievable optic by selecting a physical structure for each category based on the assigned categories of the pixels. This bridges the gap between a desired abstract design and the tangible optic, translating the calculated light field into a realizable device. By selecting appropriate physical structures, such as multilayer coatings or precisely etched features, the optic can impart the desired phase shifts or amplitude changes and achieve the targeted spatio-spectral control. One advantage of this arrangement is the ability to translate the complex, multifaceted design into a manufacturable optic, providing practical realization of the targeted light manipulation capabilities.

[0015] One aspect of the present invention relates to a diagnostic optic configured to produce a plurality of images of an incident beam of light. A diagnostic optic can be understood as an optic that provides information about the characteristics of a light beam, such as its intensity profile, spatial distribution, or spectral content.

[0016] It can be provided that the optic comprises a substrate. A substrate is a supporting structure upon which optical elements can be fabricated. One advantage of this arrangement is the provision of mechanical stability and a base upon which to build the diffractive structures, providing precise control over the optic’s properties.

[0017] It can be provided that the optic comprises a first diffractive structure on the substrate, the first diffractive structure configured to produce a focused image of at least one spectral component of the incident beam of light. A diffractive structure refers to a pattern of features, can etched or deposited on a substrate that manipulateslight through diffraction. One advantage of this arrangement is the ability to create a focused image of a specific wavelength or polarization, providing detailed analysis of the light beam’s spectral composition.

[0018] It can be provided that the optic comprises a second diffractive structure on the substrate, the second diffractive structure configured to diffract a portion of the incident beam of light. This arrangement allows for the separation and redirection of a portion of the incident beam, providing simultaneous imaging of multiple spectral components of the beam. One advantage of this arrangement is the possibility to have a reference measurement of the beam’s properties, potentially improving the accuracy and stability of the diagnostic measurements.

[0019] It can be provided that the first or second diffractive structures are configured to diffract only part of the beam, thus leaving a portion of the beam unaltered. This arrangement allows for the separation and redirection of a portion of the incident beam, providing simultaneous imaging of both altered and unaltered portions of the beam. One advantage of this arrangement is the possibility to have a reference measurement of the beam’s properties effectively without the optic, thereby decoupling any effect the optic itself might impose on the measurement and allowing a purer measurement of the beam.

[0020] One aspect of the present invention relates to a multi-layer grating configured to diffract an incident beam of light. A multi-layer grating can be understood as a diffraction grating composed of multiple layers of materials with different optical properties. This layered structure provides precise control over the grating’s behavior, providing for tailored manipulation of light.

[0021] It can be provided that the multi-layer grating comprises a substrate. A substrate, as before, serves as the underlying support for the grating structure. One advantage of this arrangement is the mechanical stability and a base upon which to build the multilayer structure, ensuring precise control over the grating’s dimensions and performance.

[0022] It can be provided that the multi-layer grating comprises a plurality of grating structures disposed on the substrate, each grating structure comprising a stackup of at least two layers of differing material composition. This arrangementallows for the creation of complex phase or amplitude profiles along the grating structure by exploiting the interaction of light with the multiple layers. By selecting the materials and thicknesses of the layers, the grating can be designed to exhibit specific diffraction properties for different wavelengths, polarizations, or angles of incidence. One advantage of this arrangement is the ability to achieve a wider bandwidth for high diffraction efficiency compared to conventional gratings made from a single material, providing more efficient and versatile light manipulation.

[0023] It can be provided that a thickness of at least one layer of the stackup varies along a length of the grating structure, and the grating structure is configured to impart a pre-determined phase shift or amplitude change that varies with at least one spectral component of the incident beam of light. By controlling the thickness of each layer along the grating structure, the phase or amplitude of the diffracted light can be precisely tailored. One advantage of this arrangement is the ability to tailor chromatic aberration, ensuring that different wavelengths are diffracted at desired angles, potentially providing high-resolution spectroscopy or achromatic focusing.

[0024] One aspect of the present invention relates to a dual-grating beamsplitter configured to split an incident beam of light into a primary beam and a reference beam. A dual-grating beamsplitter can be understood as an optical device that uses two diffraction gratings to divide an incoming light beam into two separate beams with specific properties.

[0025] It can be provided that the beamsplitter comprises a first grating configured to diffract the incident beam of light into at least a zeroth order and a first order. A diffraction grating is an optical element with a periodic structure that diffracts light into multiple orders at specific angles. This first grating divides the incident beam into at least two components, one undeflected (zeroth order) and one deflected at a specific angle (first order), based on the grating equation. One advantage of this arrangement is the efficient separation of the incident beam into distinct components, with the potential to control the relative intensity of each order by adjusting the grating’s properties.

[0026] It can be provided that the beamsplitter comprises a second grating configured to diffract at least one order of the diffracted beam of light from the firstgrating. This second grating further manipulates the light that has been diffracted by the first grating. One advantage of this arrangement is the ability to recombine or redirect specific orders, providing precise control over the direction and spectral content of the output beams.

[0027] It can be provided that the first and second gratings are on a substrate. A substrate provides mechanical support and a platform for aligning the two gratings, ensuring their precise relative positioning. One advantage of this arrangement is the stable and reproducible performance of the beamsplitter that can be used for applications requiring accurate and consistent beam splitting.

[0028] One aspect of the present invention relates to a multi-focus optic configured to produce a plurality of focal spots from an incident beam of light. A multifocus optic can be understood as a diffractive optic capable of generating multiple focused beams from a single incident beam. This capability provides parallel processing or simultaneous illumination of multiple points, enhancing the speed and efficiency of various optical techniques.

[0029] It can be provided that the multi-focus optic comprises a substrate. The substrate serves as a supporting structure upon which the diffractive elements are fabricated, providing mechanical stability and facilitating precise control over their placement and alignment. One advantage of this arrangement is the robust construction and reproducible performance of the optic, crucial for applications requiring precise and reliable multi-focus operation.

[0030] It can be provided that the multi-focus optic comprises a plurality of diffractive structures disposed on the substrate, wherein each diffractive structure is configured to focus a portion of the incident beam of light to a different location. A diffractive structure, as before, is a pattern of features that manipulates light through diffraction. One advantage of this arrangement is the ability to create multiple focal points with controlled spacing and intensity, providing tailored illumination patterns for a wide range of applications. For instance, in microscopy, this could provide simultaneous imaging of multiple regions of a sample, potentially increasing throughput and reducing measurement time.

[0031] One aspect of the present invention relates to a multi-focus optic configured to produce a plurality of focal spots with different beam profiles. A multifocus optic, as described previously, can generate multiple focal spots from a single incident beam. In this embodiment, the optic is specifically designed to control the shape and intensity distribution of each focal spot, providing tailored illumination patterns for a wide range of applications.

[0032] It can be provided that the multi-focus optic comprises a substrate. As before, the substrate provides mechanical support for the diffractive structures, ensuring stability and facilitating precise alignment for reliable performance. One advantage of this arrangement is the robust construction and the ability to fabricate complex diffractive structures with high precision, providing the generation of precisely shaped focal spots.

[0033] It can be provided that the multi-focus optic comprises a plurality of diffractive structures disposed on the substrate, wherein each diffractive structure is configured to focus a portion of the incident beam of light to a different location with a different beam profile. A beam profile refers to the spatial distribution of intensity within a beam of light. This arrangement allows for the creation of focal spots with various shapes, such as circular, square, or those with hard or soft edges, as well as controlled intensity distributions within each spot. One advantage of this arrangement is the flexibility to tailor the illumination pattern to the specific requirements of an application. For instance, in lithography, this could provide the creation of complex patterns with high resolution by using focal spots with tailored shapes, potentially improving the efficiency and quality of microfabrication processes.

[0034] One aspect of the present invention relates to a multi-focus optic configured to produce a plurality of focal spots with different orbital angular momentum (0AM) content. A multi-focus optic, as described previously, can generate multiple focal spots from a single incident beam. In this embodiment, the optic is uniquely designed to control the 0AM of each focused beam. 0AM is a property of light associated with its helical wavefront, and beams with different 0AM values can be used for applications like optical trapping, high-resolution microscopy, and quantum information processing.

[0035] It can be provided that the multi-focus optic comprises a substrate. The substrate, as in previous embodiments, provides a stable base for the diffractive structures, ensuring their accurate placement and alignment for consistent and reliable multi-focus operation. One advantage of this arrangement is the robustness and reproducibility of the optic’s performance, crucial for applications sensitive to variations in 0AM.

[0036] It can be provided that the multi-focus optic comprises a plurality of diffractive structures disposed on the substrate, wherein each diffractive structure is configured to focus a portion of the incident beam of light to a different location with a different 0AM value. This arrangement provides the generation of multiple focal spots, each carrying a distinct and precisely defined 0AM. One advantage of this arrangement is the ability to create complex optical fields with spatially varying 0AM for advanced light manipulation techniques. For example, in optical trapping, this could provide the simultaneous manipulation of multiple particles with different rotation properties or the creation of complex trapping geometries, opening new possibilities in biophysics and micromanipulation.

[0037] One aspect of the present invention relates to a multi-focus optic configured to produce a plurality of focal spots with different spectral components. A multi-focus optic, as described in previous embodiments, can generate multiple focal spots from a single incident beam. This embodiment is uniquely designed to control the spectral content of each focal spot, providing for selective focusing of specific wavelengths or polarization states. This capability can be particularly beneficial for applications like multi-wavelength microscopy or polarization-sensitive imaging.

[0038] It can be provided that the multi-focus optic comprises a substrate. The substrate, as in previous embodiments, serves as a stable base for the diffractive structures, ensuring their precise placement and alignment for reliable performance. This is particularly important for spectral control, as slight misalignments could lead to undesired mixing of wavelengths or polarization states at the focal spots. One advantage of this arrangement is the robustness and reproducibility of the optic’s performance, critical for applications requiring precise and consistent spectral separation.

[0039] It can be provided that the multi-focus optic comprises a plurality of diffractive structures disposed on the substrate, wherein each diffractive structure comprises a stackup of at least two layers of differing material composition. This multilayer structure provides fine control over the optic’s spectral response by exploiting the interaction of light with the different layers. One advantage of this arrangement is the ability to engineer the phase or amplitude response of each diffractive structure, providing for selective focusing or diffraction of specific wavelengths or polarization states.

[0040] It can be provided that each diffractive structure is configured to focus a portion of the incident beam of light having a selected spectral component to a different location. This arrangement ensures that different spectral components, such as specific wavelengths or polarization states, are directed to separate focal points. One advantage of this arrangement is the ability to create spatially resolved spectral information, which could be valuable for applications like hyperspectral imaging or spectroscopic microscopy. For example, in biological imaging, this could provide the simultaneous visualization of multiple fluorescent probes emitting at different wavelengths, providing a richer and more detailed view of a sample.

[0041] One aspect of the present invention relates to a discrete-wavelength optic configured to focus a plurality of discrete spectral components of an incident beam of light to different locations. A discrete-wavelength optic can be understood as an optic specifically designed to manipulate a set of distinct wavelengths or polarization states within a light beam. This capability is particularly advantageous for applications requiring precise control over multiple wavelengths, such as multi-color imaging, wavelength-selective excitation, or spectroscopic measurements.

[0042] It can be provided that the discrete-wavelength optic comprises a substrate. The substrate, as in previous embodiments, provides mechanical stability and a platform for precise alignment of the diffractive structures. This stability is crucial for maintaining the accuracy and reproducibility of the optic’s performance, ensuring consistent focusing of the selected spectral components. One advantage of this arrangement is the robust construction and the potential for miniaturization, providing the development of compact and reliable multi-wavelength optical systems.

[0043] It can be provided that the discrete-wavelength optic comprises a plurality of diffractive structures disposed on the substrate, wherein each diffractive structure comprises a stackup of at least two layers of differing material composition. This multilayer design allows for precise tailoring of the optic’s spectral response by controlling the interaction of light with the different layers. By selecting the materials and thicknesses of the layers, each diffractive structure can be optimized to focus a specific wavelength or polarization state to a desired location. One advantage of this arrangement is the ability to achieve high diffraction efficiency for the selected spectral components while minimizing unwanted diffraction of other wavelengths, providing efficient and selective light manipulation.

[0044] It can be provided that each diffractive structure is configured to focus a portion of the incident beam of light having a selected spectral component to a different location. This ensures spatial separation of the different wavelengths or polarization states, providing multi-color imaging or selective excitation of specific regions within a sample. One advantage of this arrangement is the ability to perform multi-wavelength measurements or manipulations without the need for multiple optics or complex beam steering mechanisms, leading to more compact and efficient optical systems.

[0045] One aspect of the present invention relates to an achromatic optic configured to focus an incident beam of light comprising a plurality of spectral components to substantially the same location. An achromatic optic can be understood as an optic that minimizes chromatic aberration, ensuring that different wavelengths within a beam of light are focused to the same point. This capability is crucial for applications requiring high resolution and sharp focusing across a broad range of wavelengths, such as microscopy, spectroscopy, and lithography.

[0046] It can be provided that the achromatic optic comprises a substrate. The substrate, as in previous embodiments, serves as the underlying support structure for the diffractive element, providing mechanical stability and a base upon which to build the multilayer structure. One advantage of this arrangement is the robust construction of the optic, providing precise fabrication and alignment of the diffractive structure for reliable and reproducible performance.

[0047] It can be provided that the achromatic optic comprises a diffractive structure disposed on the substrate, wherein the diffractive structure comprises a stackup of at least two layers of differing material composition. This multilayer design provides precise control over the optic’s spectral response by exploiting the varying optical properties of the different layers. By selecting the materials and thicknesses of the layers, the diffractive structure can be engineered to impart a phase shift that compensates for the chromatic aberration inherent in diffractive optics. One advantage of this arrangement is the ability to achieve a broader operating bandwidth, providing for high-resolution focusing across a wider range of wavelengths than possible with conventional diffractive optics.

[0048] It can be provided that the diffractive structure is configured to impart a phase shift that varies with at least one spectral component of the incident beam of light. This arrangement provides the creation of a phase profile that counteracts the wavelength-dependent phase shifts introduced by diffraction, ensuring that different wavelengths within the incident beam are brought to focus at substantially the same location. One advantage of this arrangement is the improved image quality and resolution for broadband light sources, providing sharper and more detailed imaging or focusing in applications like microscopy, spectroscopy, and lithography.

[0049] One aspect of the present invention relates to a pre-sample dispersive optic configured to focus multiple spectral components of an incident beam of light onto a sample and to spectrally disperse the beam of light after the sample. A pre-sample dispersive optic can be understood as a single optic that performs both focusing and spectral dispersion functions, simplifying spectroscopic measurements by eliminating the need for separate optics for each task.

[0050] It can be provided that the pre-sample dispersive optic comprises a substrate. The substrate, as in previous embodiments, provides mechanical stability and a platform for the precise fabrication and alignment of the focusing and dispersive structures. One advantage of this arrangement is the compact design and robust construction, providing integration of both functionalities within a single optic, simplifying experimental setups and potentially reducing alignment challenges.

[0051] It can be provided that the optic comprises a focusing structure disposed on the substrate, the focusing structure configured to focus the incident beam of light onto the sample. The focusing structure, can a diffractive element like a zoneplate, concentrates the incident light onto a small spot disposed on the sample, providing spatially resolved spectroscopic measurements. One advantage of this arrangement is the ability to perform spectroscopy on specific regions of a sample, potentially revealing variations in composition or properties across the sample.

[0052] It can be provided that the optic comprises a dispersive structure disposed on the substrate, the dispersive structure configured to spectrally disperse the beam of light after it interacts with the sample. The dispersive structure, which can be a grating, separates the different wavelengths within the beam after it passes through or reflects from the sample. This arrangement allows for the analysis of the sample’s spectral response, revealing information about its absorption, transmission, or reflection properties as a function of wavelength. One advantage of this arrangement is the direct measurement of the spectral content of light that has interacted with the sample, providing efficient and sensitive spectroscopic analysis.

[0053] One aspect of the present invention relates to an alignment-assisted optic configured for use with a short-wavelength light (SWL) beam of light. An alignment-assisted optic can be understood as an optic that incorporates features specifically designed to aid in its alignment with an SWL beam, simplifying and accelerating the alignment process. This capability is particularly advantageous for EUV, VUV and SXR optics, which are notoriously difficult to align due to their sensitivity to small misalignments and the need for operation in vacuum.

[0054] It can be provided that the alignment-assisted optic comprises a substrate. The substrate, as in previous embodiments, acts as the underlying support structure, providing mechanical stability and a base upon which to build both the primary diffractive structure for SWL manipulation and the alignment structure. One advantage of this arrangement is the robust construction and the ability to integrate multiple functionalities within a single optic, simplifying fabrication and potentially reducing the number of components required in an optical system.

[0055] It can be provided that the optic comprises a diffractive structure disposed on the substrate, the diffractive structure configured to diffract the SWL beam of light. This diffractive structure, such as a zoneplate or grating, performs the primary function of the optic, manipulating the SWL beam for focusing, imaging, or other desired purposes. One advantage of this arrangement is the integration of the alignment structure directly onto the SWL optic, providing precise relative positioning and ensuring that both structures are aligned simultaneously.

[0056] It can be provided that the optic comprises an alignment structure disposed on the substrate, the alignment structure configured to diffract or reflect a beam of alignment light having a wavelength different from a wavelength of the SWL beam of light, wherein the beam of alignment light is collinear with the SWL beam of light. The alignment structure, which can be a grating or zoneplate designed for visible or infrared light, is used to manipulate a secondary beam of light that travels along the same path as the SWL beam. One advantage of this arrangement is the ability to align the optic using the alignment light, which is easier to detect and manipulate than the SWL beam. By observing the diffraction or reflection pattern of the alignment light, the position and orientation of the optic can be adjusted until the alignment structure is properly aligned, which inherently aligns the diffractive structure for SWL manipulation. This simplifies the alignment process, potentially eliminating the need for specialized SWL detectors and intricate in-vacuum manipulation, saving time, cost, and effort.BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The following description cannot be considered limiting in any way. Various objectives, features, and advantages of the disclosed subject matter can be more fully appreciated with reference to the following detailed description of the disclosed subject matter when considered in connection with the following drawings, in which like reference numerals identify like elements.

[0058] FIG. 1 shows, according to some embodiments, steps in a method for designing a multi-beam spatio-spectral-controllable optic.

[0059] FIG. 2 shows, according to some embodiments, a truth table in a truth table approach for designing a multi-beam spatio-spectral-controllable optic for two distinct wavelengths (A1 and A2).

[0060] FIG. 3 shows, according to some embodiments, the truth table approach for designing a multi-beam spatio-spectral-controllable optic for two distinct wavelengths (A1 and A2).

[0061] FIG. 4 shows, according to some embodiments, a truth table showing the design of a three-level multi-beam spatio-spectral-controllable optic for two wavelengths (A1 and A2)

[0062] FIG. 5 shows, according to some embodiments, a general approach for designing an achromatic zoneplate optic for focusing multiple spectral components across a range of photon energies or wavelengths.

[0063] FIG. 6 shows, according to some embodiments, a method for imparting a phase shift on light using the geometric phase.

[0064] FIG. 7 shows, according to some embodiments, a cross-section of a multilayer structure designed to impart a desired phase shift or amplitude change on reflected light.

[0065] FIG. 8 shows, according to some embodiments, a cross-section of a multilayer structure designed to impart a desired phase shift or amplitude change on reflected light, specifically leveraging the material phase of aluminum (Al) in a certain energy range.

[0066] FIG. 9 shows, according to some embodiments, a multilayer approach for selecting physical structures that impart desired phase shifts on reflected light.

[0067] FIG. 10 shows, according to some embodiments, a graph for the phase shift imparted on reflected light as a function of photon energy for a multilayer structure, as compared to the phase shift achievable using only the geometric phase.

[0068] FIG. 11 shows, according to some embodiments, a cross-section of a grating structure designed to exploit the waveguiding phase or waveguiding amplitude for controlling the reflectivity of light.

[0069] FIG. 12A shows, according to some embodiments, different structures that can be used to impart a desired phase shift or amplitude change on reflected light, including structures for fabrication using multi-step lithography.

[0070] FIG. 12B shows, according to some embodiments, different structures that can be used to impart a desired phase shift or amplitude change on reflected light, including structures for fabrication using multi-step lithography.

[0071] FIG. 13 shows, according to some embodiments, different structures for fabrication using grayscale lithography.

[0072] FIG. 14 shows, according to some embodiments, a plurality of different structures that can impart a desired phase shift or amplitude change on reflected light.

[0073] FIG. 15 shows, according to some embodiments, steps in a process for fabricating a multifunctional optic using an additive technique.

[0074] FIG. 16 shows, according to some embodiments, an atomic force micrograph (AFM) image of a fabricated dual-focus optic made according to the process for FIG. 15.

[0075] FIG. 17 shows, according to some embodiments, an atomic force micrograph (AFM) image of another section of the same dual-focus optic shown in FIG. 16.

[0076] FIG. 18 shows, according to some embodiments, a design process for a diagnostic optic, showing the optic’s pattern, functionality, and resulting focal image.

[0077] FIG. 19 shows, according to some embodiments, use of certain diagnostic optics.

[0078] FIG. 20 shows, according to some embodiments, experimental results obtained using a fabricated diagnostic optic with a grating duty cycle that is not 50%, showing the optic’s ability to produce multiple images of an incident beam with distinct functionalities including a focused beam that is not wavelength-dispersed.

[0079] FIG. 21 shows, according to some embodiments, experimental results obtained using a fabricated diagnostic optic with a grating duty cycle of 50%, showing the optic’s ability to produce multiple images of an incident beam with distinct functionalities.

[0080] FIG. 22 shows, according to some embodiments, an optic with a multi-layer grating.

[0081] FIG. 23 shows, according to some embodiments, a cross-sectional view of a multilayer grating structure designed to provide a controllable phase-versus- wavelength response, indicating tailoring of the spectral characteristics of diffracted light by using multiple materials and varying layer thicknesses.

[0082] FIG. 24 shows, according to some embodiments, a cross-sectional view of a multilayer grating structure designed to provide a controllable phase-versus- wavelength response, indicating the ability to tailor the spectral characteristics of diffracted light using a multilayer structure.

[0083] FIG. 25 shows, according to some embodiments, a cross-sectional view of a multilayer grating designed to provide controllable phase-versus-wavelength response, indicating tailoring of the spectral characteristics of diffracted light by using multiple materials and varying layer thicknesses, and indicating improved precision by using of grayscale lithography.

[0084] FIG. 26 shows, according to some embodiments, various configurations of a dual-grating beamsplitter designed to split an incident beam of light into a primary beam and a reference beam.

[0085] FIG. 27 shows, according to some embodiments, an optimization process for guiding the selection of grating periods to achieve a spectrally collimated reference beam.

[0086] FIG. 28 shows, according to some embodiments, various optics.

[0087] FIG. 29 shows, according to some embodiments, a process for creating a dual-focus zoneplate optic by interfering two zoneplate optics.

[0088] FIG. 30 shows, according to some embodiments, creation of a triplefocus zoneplate optic by interfering three zoneplate optics.

[0089] FIG. 31 shows, according to some embodiments, a process for controlling the relative intensities of two focal spots in a dual-focus zoneplate optic by adjusting the strength of each optic during interference.

[0090] FIG. 32 shows, according to some embodiments, a process for controlling the relative phases of two focal spots in a dual-focus zoneplate optic by adjusting the phase of each optic during interference.

[0091] FIG. 33 shows, according to some embodiments, empirical results of a dual focusing optic that operated in the 72 eV to 50 eV range of photon energies.

[0092] FIG. 34 shows, according to some embodiments, an atomic force micrograph (AFM) image of the dual-focus optic used to acquire the experimental data presented in FIG. 33.

[0093] FIG. 35 shows, according to some embodiments, an AFM image and a corresponding height profile of the dual-focus optic used to acquire the experimental data presented in FIG. 33.

[0094] FIG. 36 shows, according to some embodiments, a process for defining a hard edge to truncate the spatial extent of focal spots in a dual-focus zoneplate optic.

[0095] FIG. 37 shows, according to some embodiments, a process for creating a dual-focus zoneplate optic, where one focal spot is shaped as a square.

[0096] FIG. 38 shows, according to some embodiments, a design of an optic that produces a Gaussian beamlet and an L=1 0AM beamlet.

[0097] FIG. 39 shows, according to some embodiments, a design process for an optic that produces an L=1 0AM beamlet and an L=-1 0AM beamlet.

[0098] FIG. 40 shows, according to some embodiments, a design process for an optic that produces two L=1 0AM beam lets.

[0099] FIG. 41 shows, according to some embodiments, discrete wavelength optics.

[0100] FIG. 42 shows, according to some embodiments, design of a multifocus optic with spectral control, focusing two different wavelengths to controllable locations, using the truth table approach.

[0101] FIG. 43 shows, according to some embodiments, a design process for a multi-focus optic that focuses two different polarizations to controllable locations using the truth table approach.

[0102] FIG. 44 shows, according to some embodiments, a design of a discrete-wavelength optic using the truth table approach to focus multiple discrete spectral components, specifically two wavelengths, to the same location.

[0103] FIG. 45 shows, according to some embodiments, simulations demonstrating the performance of a discrete-wavelength optic designed using the truth table approach.

[0104] FIG. 46 shows, according to some embodiments, discrete wavelength optics.

[0105] FIG. 47 shows, according to some embodiments, a design of a discrete-wavelength grating using the truth table approach.

[0106] FIG. 48 shows, according to some embodiments, achromatic optics.

[0107] FIG. 49 shows, according to some embodiments, a design of an achromatic zoneplate, a diffractive lens that minimizes chromatic aberration by effectively defining a different focal length zoneplate for different wavelengths.

[0108] FIG. 50 shows, according to some embodiments, a design of an achromatic orbital angular momentum (0AM) phase plate that ensures the same 0AM content is imparted onto each spectral component, particularly for different wavelengths.

[0109] FIG. 51 shows, according to some embodiments, achromatic 0AM phase plates.

[0110] FIG. 52 shows, according to some embodiments, a design and function of a spatial-aberration-correcting optic for correcting the spatial aberrations of a secondary optic, using a two-level diffractive optic. This also indicates the interference of multiple such optics to produce multiple beams at the focus.

[0111] FIG. 53 shows, according to some embodiments, a configuration for an aberration correcting optic.

[0112] FIG. 54 shows, according to some embodiments, a design and application of a diverging zoneplate for enhancing the focusing performance of a secondary optic. This also indicates the interference of multiple such optics to produce multiple beams at the focus.

[0113] FIG. 55 shows, according to some embodiments, a design and application of a diverging zoneplate for correcting spatial aberrations and potentially canceling chromatic aberrations. This also indicates the interference of multiple such optics to produce multiple beams at the focus.

[0114] FIG. 56 shows, according to some embodiments, a pre-sample dispersive optic and measurement apparatus for performing spectroscopic measurements.

[0115] FIG. 57 shows, according to some embodiments, a multi-focus spectroscopy beamline designed for high-efficiency, low-noise spectroscopy measurements.

[0116] FIG. 58 shows, according to some embodiments, an alignment- assisted optic incorporating a grating designed for visible light alignment.

[0117] FIG. 59 shows, according to some embodiments, an alignment- assisted optic incorporating a zoneplate designed for visible light alignment.

[0118] FIG. 60 shows, according to some embodiments, a configuration for a beam combiner.DETAILED DESCRIPTION

[0119] A detailed description of one or more embodiments is presented herein by way of exemplification and not limitation.

[0120] Conventional methods for designing optics often focus on optimizing performance for a single wavelength or a narrow range of wavelengths. This approach leads to chromatic aberration when these optics are used with broadband light sources, resulting in blurred images or reduced focusing efficiency. Furthermore, traditional design techniques often rely on simplified models that do not fully capture the complex interaction of light with matter, particularly for multilayer structures or for optics operating at short wavelengths where waveguiding effects become significant. These limitations hinder the development of compact, efficient, and versatile optical systems for applications requiring precise control over the spatio-spectral profile of multiple output beams, such as advanced microscopy, spectroscopy, and lithography.

[0121] The method for designing a multi-beam spatio-spectral-controllable optic described herein overcomes these limitations by providing the design of optics that can manipulate light across a broad range of wavelengths and polarizations while maintaining precise control over the spatio-spectral content of multiple output beams.

[0122] It has been discovered that a method for designing a multi-beam spatio-spectral-controllable optic can be achieved by employing a series of steps that leverage numerical light propagation, basis set decomposition, and category-based structure selection.

[0123] One advantage of the method for designing a multi-beam spatio- spectral-controllable optic is the ability to numerically define a first spatially varying complex electric field at a first location. This provides the precise specification of thedesired light pattern at a target location, such as a sample in a microscopy experiment or a detector in a spectroscopy setup.

[0124] One advantage of the method for designing a multi-beam spatio- spectral-controllable optic is the ability to numerically back-propagate the first spatially varying complex electric field to a second location, thereby defining a second spatially varying complex electric field at the second location. This allows for the determination of the light distribution required at the optic to produce the desired field at the first location.

[0125] One advantage of the method for designing a multi-beam spatio- spectral-controllable optic is the ability to define a basis set of phase-versus- wavelength curves, each phase-versus-wavelength curve corresponding to a category. This facilitates the design of optics that can control the behavior of light over a broad range of wavelengths.

[0126] One advantage of the method for designing a multi-beam spatio- spectral-controllable optic is the ability to determine a root-mean-squared error value for each pixel of the second spatially varying complex electric field relative to each curve of the basis set, thereby generating a plurality of root-mean-squared error values for each pixel. This provides the selection of the most suitable basis curve for each pixel, ensuring an accurate representation of the desired spectral response across the entire optic.

[0127] One advantage of the method for designing a multi-beam spatio- spectral-controllable optic is the ability to assign a category to each pixel based on which curve of the basis set corresponds to the lowest root-mean-squared error value of the pixel. This effectively classifies each pixel according to its desired spectral behavior.

[0128] One advantage of the method for designing a multi-beam spatio- spectral-controllable optic is the ability to define an achievable optic by selecting a physical structure for each category based on the assigned categories of the pixels. This step bridges the gap between the abstract design and the tangible optic, translating the calculated light field into a realizable device.

[0129] This method provides a more accurate and versatile design process, providing for the creation of optics with previously unattainable capabilities in terms of spatio-spectral control. By employing numerical methods, the design process can handle complex multilayer structures and accurately model waveguiding effects, leading to more efficient and predictable optics for advanced optical applications.

[0130] Moreover, multi-beam spatio-spectral-controllable optics provide enhanced metrology techniques used in the fabrication and inspection of semiconductor chips. As semiconductor devices continue to shrink in size and increase in complexity, the demand for high-resolution, high-throughput, and multifunctional metrology tools grows. Conventional metrology techniques often rely on single-wavelength, single-polarization optics or on low-quality multi-wavelength optics, limiting their ability to probe diverse material properties or to perform multiple measurements simultaneously. Multi-beam spatio-spectral-controllable optics address these limitations by enabling the manipulation of multiple wavelengths and polarizations within a single optical system, leading to more versatile, efficient, and precise metrology tools. For instance, a multi-focus optic with spectral control can be used to simultaneously image multiple layers within a semiconductor chip at different wavelengths. By focusing different wavelengths to different depths within the chip, each layer can be selectively imaged, revealing information about its structure, composition, and potential defects. This multi-wavelength imaging capability eliminates the need for mechanical scanning or multiple optics, enhancing throughput and simplifying the metrology setup. Furthermore, polarization-sensitive multi-focus optics can be employed to characterize the stress distribution within a semiconductor chip. The polarization of reflected light from the chip’s surface can be sensitive to stress-induced birefringence, providing a map of stress variations across the chip. By focusing different polarizations to different locations on the chip, a spatially resolved stress map can be obtained, revealing potential areas of stress concentration that could lead to device failure.

[0131] Discrete-wavelength gratings can be integrated into metrology systems for spectral analysis of semiconductor materials. By diffracting different wavelengths at different angles, the grating can spatially separate the spectral components of light reflected or transmitted through the chip, allowing for theidentification and quantification of different materials or dopants within the chip structure. Achromatic zoneplates, by enabling high-resolution focusing across a broad range of wavelengths, can enhance the performance of interferometric metrology techniques. Interferometry relies on the interference of light waves to measure distances, surface profiles, or refractive index variations. The use of achromatic zoneplates can improve the accuracy and sensitivity of these measurements by ensuring that all wavelengths within the incident beam are focused to the same plane, minimizing chromatic aberration and enhancing fringe contrast.

[0132] Alignment-assisted optics, by simplifying the alignment process for SWL wavelengths, can facilitate the development of advanced metrology tools operating at these shorter wavelengths. SWL wavelengths offer higher resolution and sensitivity compared to visible light, enabling the detection of smaller features and more subtle variations in material properties.

[0133] The integration of multi-beam spatio-spectral-controllable optics into semiconductor metrology systems opens up new possibilities for characterization and inspection, enabling higher resolution, enhanced throughput, and the ability to probe a wider range of material properties. These advancements ensure the quality and reliability of future generations of semiconductor devices as they continue to shrink in size and increase in complexity.

[0134] As used herein, extreme ultraviolet light (EUV), unless contextually inconsistent, refers to a wavelength of light sometimes referred to as short wavelength light (SWL), e.g., from .1 nm to 100 nm. Exemplary EUV includes EUV from 9_nm to 60_nm, VUV from 60 to 100_nm, SXR from 1 to 9 nm, and hard x-ray (HXR) from .01 to 1 nm.

[0135] As used herein, the terms “composition” and “material composition” refer to elements present, density, dopants, structural effects like layer thickness, lineedge roughness, surface roughness, and interface roughness, and the like. A change of any of these effects constitutes a change in composition.

[0136] In an embodiment, a computer-implemented method for designing a multi-beam spatio-spectral-controllable optic comprises using a processor to define a first spatially varying complex electric field at a first location, using the processor tonumerically back-propagate the first spatially varying complex electric field to a second location, thereby defining a second spatially varying complex electric field at the second location, using the processor to define a basis set of phase-versus-wavelength curves, each phase-versus-wavelength curve corresponding to a category, using the processor to determine a root-mean-squared error value for each pixel of the second spatially varying complex electric field relative to each curve of the basis set, thereby generating a plurality of root-mean-squared error values for each pixel, using the processor to assign a category to each pixel based on which curve of the basis set corresponds to the lowest root-mean-squared error value of the pixel, and using the processor to define an achievable optic by selecting a physical structure for each category based on the assigned categories of the pixels. In an embodiment, the first spatially varying complex electric field is a focal spot on a sample. In an embodiment, the second location is a surface of the optic. In an embodiment, the phase-versus- wavelength curves include: a phase value for each design spectral component, an amplitude value for each design spectral component, or a combination comprising at least one of the foregoing values. In an embodiment, the basis set of phase-versus- wavelength curves is defined using principal component analysis. In an embodiment, the achievable optic operates in reflection. In an embodiment, the achievable optic operates in transmission. In an embodiment, selecting a physical structure comprises using the geometric phase, wherein structures having different heights impart different phase shifts. In an embodiment, selecting a physical structure comprises using the material phase or amplitude, wherein structures having different material compositions or roughness impart different phase shifts or amplitude changes. In an embodiment, selecting a physical structure comprises using the waveguiding phase or amplitude, wherein structures having different sizes and shapes impart different phase shifts, amplitude changes, or polarization changes. In an embodiment, selecting a physical structure comprises using a combination of the geometric phase, the material phase, the material amplitude, the waveguiding phase, and the waveguiding amplitude.

[0137] It can be appreciated that the terms ‘intensity’ and ‘amplitude’ are related by a square law (amplitudes = intensity). As a result, either can be used in the design and analysis of optics, and they are used interchangeably throughout the document for the most part.

[0138] In an embodiment, a computer-readable, non-transitory medium has stored thereon computer-executable instructions for causing a processor to design a multi-beam spatio-spectral-controllable optic, the instructions comprising: instructions for defining a first spatially varying complex electric field at a first location; instructions for numerically back-propagating the first spatially varying complex electric field to a second location, thereby defining a second spatially varying complex electric field at the second location; instructions for defining an ideal optic for each spectral component by applying a transform to the second spatially varying complex electric field; instructions for grouping pixels of the ideal optics into categories based on a combination of the ideal optics, the categories corresponding to a physical structure; and instructions for defining an achievable optic by applying the physical structures to the ideal optics according to the categories. In an embodiment, the first spatially varying complex electric field is a focal spot on a sample. In an embodiment, the second location is a surface of the optic. In an embodiment, defining an ideal optic comprises dividing the second spatially varying complex electric field into a plurality of regions, wherein each region is associated with a phase value or amplitude value. In an embodiment, defining an ideal optic comprises assigning a phase value or amplitude value to each pixel of the second spatially varying complex electric field, based on the pixel’s phase or amplitude. In an embodiment, grouping pixels comprises creating a truth table, wherein each cell of the truth table corresponds to a combination of phase ranges or amplitude ranges. In an embodiment, the achievable optic operates in reflection. In an embodiment, the achievable optic operates in transmission. In an embodiment, the physical structures impart a phase shift or amplitude change based on a combination of geometric phase, material phase, material amplitude, waveguiding phase, and waveguiding amplitude. In an embodiment, the achievable optic comprises at least one of: a diagnostic optic, a multi-layer grating, a dual-grating beamsplitter, a multi-focus optic, a discrete-wavelength optic, an achromatic optic, a pre-sample dispersive optic, or an alignment-assisted optic.

[0139] Conventional methods for designing optics often struggle to handle the complexities of multi-beam spatio-spectral control, especially when considering a broad range of spectral components. Traditional approaches can focus on single wavelengths or narrow bandwidths, leading to designs that suffer from chromatic aberration and limited efficiency when applied to broadband light sources. Additionally,conventional methods often rely on simplified models that do not fully capture the intricate interaction of light with multilayer structures or the impact of waveguiding effects, particularly for optics operating at short wavelengths. These limitations hinder the development of advanced optical systems for applications like multi-wavelength microscopy, hyperspectral imaging, and polarization-sensitive techniques.

[0140] The method for designing a multi-beam spatio-spectral-controllable optic presented herein addresses these limitations by providing the design of optics that can manipulate light across a broad range of spectral components while precisely controlling the spatio-spectral profile of multiple output beams. It has been discovered that a method for designing a multi-beam spatio-spectral-controllable optic can achieve these results by employing a series of steps that leverage numerical light propagation, basis set decomposition, and category-based structure selection. This approach provides the creation of optics with precisely tailored spatio-spectral responses, potentially unlocking new capabilities in various optical applications.

[0141] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic defines a first spatially varying complex electric field at a first location 202. In the method, a processor, a component of a computer system, executes instructions to perform calculations and manipulate data. In this context, the processor defines the desired light distribution at the target location, such as the focal plane of a microscope or the surface of a detector. This information is represented as a complex-valued matrix, where each element corresponds to a specific point in space and encodes both the amplitude and phase of the electric field, or field, at that point. By manipulating the values within this matrix, the designer can precisely specify the desired light pattern, including the intensity, shape, and phase distribution of the beam. One advantage of this arrangement is the flexibility to create arbitrary light distributions, providing the design of optics for a wide range of applications requiring tailored illumination patterns, such as microscopy, lithography, and optical trapping.

[0142] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic numerically back-propagate the first spatially varying complex electric field to a second location 201 , thereby defining a second spatially varying complex electric field at the second location. Back-propagation is a computational technique used to calculate the light field at an earlier point in its path,based on the known field at a later point. In this instance, the processor uses a numerical algorithm, such as the spectrum of plane waves approach, to simulate the propagation of light from the first location back to the second location, can the surface of the optic. This process takes into account factors like diffraction and interference, ensuring an accurate representation of the light field as it travels through space. The result of this back-propagation is a second complex-valued matrix that defines the light distribution required at the optic to produce the desired field at the first location. One advantage of this arrangement is the ability to account for the physical propagation of light and compensate for any distortions or spreading that might occur, ensuring that the optic will generate the desired output with high fidelity.

[0143] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic defines a basis set of phase-versus-wavelength curves 361 - 364, each phase-versus-wavelength curve corresponding to a category 361 -364. A basis set is a collection of functions that can be combined to represent a wide range of other functions. In this context, each curve in the basis set represents a specific way in which the amplitude or phase of light can vary with wavelength. These curves are selected to capture the typical spectral responses of various material compositions and structural configurations. One common approach for defining the basis set is principal component analysis, a statistical technique that identifies the most significant patterns of variation within a dataset. By applying principal component analysis to a library of simulated or measured phase-versus-wavelength responses, the processor can extract a set of basis curves that effectively captures the range of achievable spectral behaviors. One advantage of this arrangement is the ability to represent a vast space of possible spectral responses with a relatively small number of basis curves, providing efficient computation and storage. This approach also facilitates the design of optics with tailored spectral responses, providing selective manipulation of different wavelengths within a beam of light.

[0144] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic determines a root-mean-squared error value for each pixel of the second spatially varying complex electric field relative to each curve of the basis set, thereby generating a plurality of root-mean-squared error values for each pixel. The root-mean-squared error quantifies the difference between two functions ordatasets. In this context, the processor calculates the root-mean-squared error between the phase-versus-wavelength behavior at each pixel of the back-propagated field and the phase-versus-wavelength behavior represented by each basis curve. This process results in a set of error values for each pixel, one for each basis curve, representing how well each basis curve matches the desired spectral response at that particular point on the optic. One advantage of this arrangement is the quantitative basis for comparing the suitability of different basis curves for each pixel, providing the selection of the most accurate representation of the desired spectral behavior. This approach ensures a precise and efficient design process, maximizing the optic’s performance in terms of spatio-spectral control.

[0145] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic assigns a category to each pixel based on which curve of the basis set corresponds to the lowest root-mean-squared error value of the pixel. This step classifies each pixel according to its desired spectral response, grouping similar pixels together. By selecting the basis curve with the lowest error value for each pixel, the processor effectively segments the optic’s surface into regions with distinct spectral properties. These regions, or categories, represent groups of pixels that should ideally exhibit similar phase-versus-wavelength behavior. One advantage of this arrangement is the reduction of the complex, continuous light field into a discrete set of categories, simplifying the subsequent selection of physical structures for the optic. This categorization process facilitates the translation of the abstract design into a manufacturable optic by defining distinct regions that can be fabricated with specific material compositions or structural configurations. The manufacturable optic is the optic to be manufactured, i.e., the multi-beam spatio-spectral-controllable optic.

[0146] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic uses defines an achievable optic by selecting a physical structure for each category based on the assigned categories of the pixels. This step translates the abstract design into a realizable optic by assigning a specific physical structure to each category. This process involves selecting appropriate materials, layer thicknesses, and structural features for each region of the optic, based on the desired phase-versus-wavelength response for that category. One approach for imparting phase shifts or amplitude changes is to use multilayer coatings with varyingthicknesses and material compositions, exploiting the geometric phase, material phase, material amplitude, waveguiding phase, and waveguiding amplitude introduced by these structures. The processor can access a library of pre-simulated or measured phase-versus-wavelength responses for various multilayer designs and select the structure that most closely matches the desired behavior for each category. One advantage of this arrangement is the ability to translate the complex, multifaceted design into a manufacturable optic with precisely controlled spatio-spectral properties, that is, spatial and spectral properties.

[0147] The method provides the technical advantages of defining a target light distribution, accounting for light propagation through back-propagation, representing diverse spectral responses with a compact basis set, quantitatively comparing the suitability of different spectral behaviors for each pixel, classifying pixels based on their desired spectral properties, and translating the abstract design into a realizable optic with specific physical structures. These advantages synergistically provide the creation of high-performance optics (i.e., the multi-beam spatio-spectral- controllable optics) with tailored spectral responses and precise spatio-spectral control, exceeding the capabilities of conventional design methods.

[0148] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic can use a first spatially varying complex electric field that is a focal spot on a sample 202. The focal spot represents the point or region on the sample where the light is intended to be concentrated. By defining the desired intensity and phase distribution at the focal spot, the designer establishes the target illumination pattern for the optic. One advantage of this arrangement is the ability to tailor the focal spot to the specific requirements of an application, such as achieving a small spot size for high-resolution microscopy or shaping the spot for patterned illumination in lithography.

[0149] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic can include defining a second spatially varying complex electric field on a surface of the optic 201 . The surface of the optic represents the interface where the incident light interacts with the diffractive structure. By back- propagating the desired field from the sample to the optic’s surface, the design process accounts for the propagation of light and ensures that the diffractive structure willgenerate the correct output. One advantage of this arrangement is the accurate representation of the light field at the optic, providing the design of diffractive structures that compensate for diffraction and other propagation effects, ensuring high-fidelity generation of the desired focal spot.

[0150] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic can include defining a basis set of phase-versus- wavelength curves using principal component analysis. Principal component analysis is a statistical technique that identifies the most significant patterns of variation within a dataset. In this context, the processor applies principal component analysis to a library of simulated or measured phase-versus-wavelength responses for various material compositions and structural configurations. This analysis extracts a set of basis curves that can be linearly combined to represent a wide range of spectral responses. One advantage of this arrangement is the compact and efficient representation of the space of possible spectral behaviors, providing faster computation and reduced data storage requirements.

[0151] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic can include defining an achievable optic that operates in either reflection or transmission. An optic operating in reflection manipulates light by reflecting it from a structured surface, while an optic operating in transmission modifies light as it passes through a structured material. The choice between reflection and transmission depends on the specific application and the desired wavelength range. One advantage of reflection-mode optics is their potential for higher diffraction efficiency, particularly for short wavelengths where absorption in transmissive materials can be significant. One advantage of transmission-mode optics is their potential for simpler fabrication, especially for structures with low aspect ratios.

[0152] In an embodiment, a method for designing a multi-beam spatio- spectral-controllable optic can include selecting a physical structure for the achievable optic by using the geometric phase, the material phase, the material amplitude, the waveguiding phase, or the waveguiding amplitude. The geometric phase refers to the phase shift imparted on light upon reflection from or transmission through a structure with a spatially varying topography. The material phase or material amplitude arises from the differences in refractive index between different materials, leading to phaseshifts and constructive or destructive interference as light travels through these materials. The waveguiding phase and waveguiding amplitude are introduced by waveguiding effects, where the confinement of light within a structure can alter its phase and amplitude, opaque structures can occlude nearby structures, or some structures can alter the diffraction efficiency or reflectivity of nearby structures. By exploiting these phase, amplitude, and polarization mechanisms, either individually or in combination, the design method can achieve a wide range of spectral responses, providing precise control over the spatio-spectral profile of multiple output beams. One advantage of using these phase, amplitude, and polarization mechanisms is the ability to create complex spectral responses with a limited number of layers or structural features, reducing fabrication complexity and enhancing efficiency.

[0153] One example of using the geometric phase is the design of a diffractive optic with features of varying height, where the height of each feature determines the phase shift imparted on the reflected or transmitted light. By controlling the height profile across the optic’s surface, specific phase patterns can be created to achieve multi-focus or beam shaping capabilities. One example of using the material phase and material amplitude is the design of a multilayer optic, where the thickness and composition of each layer are chosen to create constructive or destructive interference for specific wavelengths. By controlling the layer stack, the optic can exhibit selective reflectivity or transmission for different wavelengths, providing spectral filtering or achromatic performance. One example of using the waveguiding phase and waveguiding amplitude is the design of a photonic crystal, a periodic structure that can guide and confine light within specific wavelength ranges. By adjusting the lattice parameters and material properties of the photonic crystal, its waveguiding properties can be tailored to create bandgaps or resonant modes, providing functionalities like spectral shaping or beam steering.

[0154] Designing a multi-beam spatio-spectral-controllable optic, also referred to as a multi-functional optic, can begin with defining the desired light distribution at a target location, such as a sample, a detector, or another optical element. This target field, denoted as Efocus(x, y, A), where x and y are the transverse spatial coordinates and A denotes the wavelength and polarization, specifies the desired intensity and phase at each point within the target region. The next stepinvolves determining the light distribution required at the optic to produce the desired field at the target location. This is achieved through numerical back-propagation, a mathematical technique that simulates the propagation of light backward from the target location to the optic’s surface, taking into account factors like diffraction and interference. The result of this back-propagation is a complex-valued field, denoted as Eesw(x, y, A), which describes the amplitude and phase of the light that can be present at the optic to generate the desired output.

[0155] If desired, designing the multi-beam spatio-spectral-controllable optic can include an estimation of the light field emanating from the source, denoted as Esource(x, y, A). This estimation accounts for the properties of the incident light, such as its spatial profile, divergence, and spectral content. If not estimated, this quantity can be approximated as 1 , numerically representing a plane wave.

[0156] The ideal optic, denoted as Eoptic(x, y, A), represents a theoretical optic that perfectly transforms the light from the source into the desired light at the target location. It is calculated as the ratio of the desired field at the optic (obtained through back-propagation) to the estimated field from the source: EoPtic(x, y, A) = EESW(X, y, A) I Esource(x, y, A). This ideal optic can include both amplitude and phase variations across its surface, encoding the necessary transformations to the incident light. It can be appreciated that the performance of an optic can be improved or limited depending on certain physical constraints. For instance, the magnitude of £optic(x,y,A) cannot exceed 1 in a physical system, so Esource(x,y, A) must have a greater magnitude at all (x,y) coordinates than Eesw(x,y, -f,A). If this is not satisfied, then the optic’s performance will not be as anticipated. For instance, the spot size at the focus might be smaller or larger than designed. A simple approach to ensuring that this does not happen is to improve the design of Eoptic(x,y,A') by using the method of Gerchberg and Saxton. In this method, one can perform the following steps: constrain Eoptic(x,y, A) to be physically realistic by modifying Esource(x,y,A) appropriately; then numerically propagate Esource(x,y,A) back to the focus, detector, etc. and constrain them to have the desired characteristics such as number of bright spots, ratio between the spots, 0AM content, shape, etc.; numerically propagate them back to the optic; repeat until a satisfactory, physical optic has been found.

[0157] Designing the multi-beam spatio-spectral-controllable optic can include converting the continuous, complex function of the ideal optic into a discrete, manufacturable form. This is achieved by grouping the pixels of the ideal optic into distinct regions or categories, each representing a specific range of phase values or amplitude changes. The choice of categories depends on the desired resolution and fabrication capabilities. One approach is to assign a category to each pixel based on its phase value, effectively segmenting the optic’s surface into regions with similar phase responses. Another approach is to employ a truth table, where each cell of the table corresponds to a specific combination of phase ranges or amplitude change ranges, providing more complex categorization schemes.

[0158] Once the optic has been segmented into categories, process includes selecting a physical structure for each category. This process involves considering the desired spectral response for each category and choosing appropriate materials, layer thicknesses, and structural features to achieve that response. The physical structures impart phase shifts and amplitude changes on the incident light based on various mechanisms, such as the geometric phase, material phase, material amplitude, waveguiding phase, and waveguiding amplitude. The geometric phase arises from the spatially varying topography of structures. The material phase and material amplitude arise from differences in refractive index between materials, and the waveguiding phase and waveguiding amplitude occur by confinement of light within structures, opaque structures occluding nearby structures, or some structures altering the diffraction efficiency of nearby structures. By exploiting these phase and amplitude altering mechanisms, the design method can create optics with tailored spectral responses, providing precise control over the spatio-spectral profiles of multiple output beams across a broad range of wavelengths, polarizations, and incidence angles.

[0159] It is contemplated that designing the multi-beam spatio-spectral- controllable optics can be divided into two sets of steps, steps A and steps B. The output of individual steps can be a digital format such as a bitmap.

[0160] According to steps A, the method for designing defines an ideal optic, with one design per spectral component. Here, the method includes defining the target field Ef0CUS(x,y,X) by selecting what the light beam looks like at a selected plane, e.g.,the sample, detector, and the like, whereinis a complex field and can be, e.g., a Gaussian beam profile, square shape, orbital angular momentum, and the like. The method includes defining the exit-surface wave fieldby determining what phase or amplitude a light beam would have at the optic(s) to accomplish that, whereinis a field of the exit surface wave, after the exit surface of the optic. The method includes optionally defining the impinging field by estimating the complex field representing the light emanating from the sourcethat is received by the optic. The method includes defining the ideal optic that transforms the light from the source into the light that produces the desired focus

[0161] According to the method, steps B provide designing a manufacturable optic. Here, the method includes defining the target optic by grouping the pixels into regions that represent the optic, definingas abitmap of the optic. The method includes defining a manufacturable optic by selecting physical structures that effect the phase shift or amplitude change for each group of pixels. The method includes fabricating the multi-beam spatio-spectral-controllable optic using the manufacturable optic as a template for fabrication.

[0162] As used herein, the terms “wavelength” and “spectral component” can be used interchangeably. Spectral component includes wavelength, polarization, incidence angle, and all other sources of mutual incoherence between two optical beams.

[0163] In an embodiment, the first step involves defining the spatially varying complex field (wherein x and y are transverse spatial coordinates and Ais the spectral composition, e.g., wavelength) at the sample or detector. The second step includes estimating the desired light at the optic by numerically back-propagating the light from the focus, detector, and the like. For precise results, the third step is performed, wherein the field is estimated that is generated from the sourceand impinges on the optic. Sometimes this can be approximated as a plane wave such thatThe effect of the optic is to transformintoIn the Born approximation, the optic’s effect can be modeled by multiplyingby a spatially-varying quantity thatdepends on the structure of the optic, and one can design an optic that satisfies the relation

[0164] The process for selecting a physical structure that impartscan involve design for a single spectral component, e.g., wavelength, polarization, incidence angle, and the like. Once multiple spectral components are introduced, three factors arise that affect design. Diffraction angles are wavelengthdependent so if one designs an optic that produces beams with substantially the same effect (e.g., the same focal length) for all wavelengths,varies substantially with wavelength and accomplishing that with physically realizable materials can be challenging. This problem can be referred to as chromatic aberration. Diffraction efficiencies can be important since SWL sources can generate few photons. If the diffractive optic is designed to alter a transmitted wave, diffraction can be caused by absorptive features and the maximum achievable efficiency is approximately 10%, which can occur even if the optic is designed for a single wavelength although the efficiency is the same for all wavelengths. If the diffractive optic is designed to alter a reflected wave, the efficiency can approach 90% at the design wavelength, but the efficiency of traditional zoneplates drops significantly (even going through zero) for wavelengths that deviate from the design wavelength. For phase-forming optics, the designed phase can be anywhere from 0 toat the design wavelength, but the imparted phase usually scales with wavelength causing the optic to be imperfect for wavelengths that deviate from the design. This problem can be referred to as chromatic efficiency. Consideration is made when designingso that the wavelength-dependence ofs physically achievable. This problem can be referred to as spectral control. The optic can be fabricated using standard additive or subtractive lithography approaches.

[0165] In an embodiment, with reference to FIG. 1 , a method for designing a multi-beam spatio-spectral-controllable optic is shown as a series of steps. The process begins by simulating the complex reflectance / transmittance of a plurality of physically realizable stackups (step 050). These stackups represent candidate structures for the optic, wherein each can include multiple layers of materials with varying optical properties. The complex reflectance / transmittance calculations capture how each stackup interacts with light, considering factors like reflection, transmission,absorption, and phase shifts or amplitude changes as a function of wavelength, polarization, and angle of incidence. Step 050 can involve numerical simulations using techniques like rigorous coupled-wave analysis (RCWA) or transfer matrix methods, generating a comprehensive dataset that describes the optical behavior of a vast library of potential stackup designs.

[0166] Step 051 involves defining fields at a focus, detector, and the like. Step 051 establishes target light distribution for the optic, specifying the desired intensity and phase pattern at the desired location. For example, if the optic is intended for focusing applications, the field at the focus could be defined as a tightly focused spot with a Gaussian intensity profile. Alternatively, if the optic is intended for beam shaping, the desired field could be a more complex pattern, such as a square or an array of spots with specific intensity ratios. The defined field is represented as a spatially varying complex electric field, capturing both the amplitude and phase of the light at each point in space.

[0167] Step 052 includes propagating fields defined in step 051 to the optic and can use a numerical propagator such as the spectrum of plane waves approach to calculate how the light field defined at the focus or detector evolves as it travels through space to the surface of the optic. The propagator accounts for diffraction and interference effects, ensuring an accurate representation of the light field transformation during propagation. The result of step 052 is a spatially varying complex electric field that describes the light distribution required at the optic’s surface to produce the desired field at the target location.

[0168] Optionally, the method estimates the field from the source (step 053). Step 053 can depend on the specific application and the level of precision required. If the incident light field is known or can be approximated, for instance as a plane wave from a collimated laser source, this information can be incorporated into the design process to further refine the optic’s performance. The estimated field from the source is represented as a spatially varying complex electric field, providing a detailed description of the light incident on the optic.

[0169] In step 054, the process defines the ideal optic that transforms light from the source into light that will produce the desired focus. The ideal optic representsa theoretical, often unrealizable, optic that perfectly provides the desired light manipulation. It can be calculated by dividing the complex field at the optic (obtained from back-propagation) by the complex field from the source (if estimated) or by a more complicated procedure, resulting in a spatially varying complex function that describes the ideal transformation the optic should perform. This function can include both amplitude and phase variations, capturing the required modifications to the incident light field to generate the desired output.

[0170] In step 055, the optic is segmented by grouping the pixels into regions that represent the optic. Step 055 converts the continuous, complex function of the ideal optic into a discrete representation suitable for fabrication. Segmentation involves dividing the optic’s surface into distinct regions, each with a relatively uniform phase or amplitude response. These regions represent areas of the optic that can be fabricated with specific structures to achieve the desired phase shifts or amplitude changes. Various segmentation algorithms can be employed, such as thresholding, clustering, or edge detection techniques, depending on the complexity of the ideal optic and the desired resolution.

[0171] The final steps involve selecting the stackup for each segment by comparing the physically realizable reflectances from the simulated stackups (step 050) to the segmented reflectances (step 055), selecting the stackup that minimizes the root mean squared (RMS) error (step 056), and then fabricating the optic (step 057). This selection process involves comparing the calculated complex reflectance of each simulated stackup to the desired complex reflectance for each segment of the ideal optic. The stackup with the lowest RMS error for each segment is chosen, ensuring the best possible match between the achievable optic and the ideal design. Fabrication involves using techniques like lithography, etching, and deposition to create the selected multilayer structures disposed on the substrate, physically realizing the designed optic.

[0172] The process shown in FIG. 1 can be adapted to various design goals and optical functionalities. For example, instead of focusing a single beam to a spot, the process could be used to create multiple focal spots, shape the intensity profile of a beam, or manipulate the polarization or orbital angular momentum of light. This flexibility, coupled with the ability to handle a broad range of spectral components,provides the creation of advanced, multifunctional optics with tailored properties for a wide array of applications.

[0173] The method for designing the optics can include a general numeric propagator. In some cases, a complex-valued matrix describing the field of the focus can be defined. Many numerical propagators exist to back-propagate this field to the optic. In an embodiment, the spectrum of plane waves approach is used as a transfer function:whereinis the propagated fieldis the field to be propagated, T’O is the Fourier transform, (x,y) are the transverse coordinates, z is the distance to be propagated, ands the z-component of the k-vector. In particular, where N is the number of pixels in eachdimension and dx is the transverse dimension of each pixel. Using this equation, the method calculates the amplitude and phase of the beam at any point in space. In some cases, the zoneplate optic is some distance away (denoted f) from the focus, e.g., from a millimeter to a few meters.

[0174] To perform step 052 of designing the zoneplate optic, compute the wave for the light to form upon leaving the optic asFor beam shaping, the phase can be more important than the amplitude, so the phase of(denotedis the phase for the light leaving the optic to possess and can be the primary consideration in designing the optic. If a plane wave (e.g., a collimated laser beam) impinges on the optic, the optic imparts a phaseIf the incident light has some other phase z.Esource(yc,y,A') (e.g., it can be slightly diverging), then the optic cancels that out and imparts a phase of . In total, then, it imparts a phase ofThis can be denoted straightforwardly as a field:To define multiple foci, each with a different position, amplitude, and the like, this generalizes asIt can be appreciated that the performance of an optic can be improved or limited depending on certain physical constraints. For instance, the magnitude ofcannot exceed 1 in a physical system, so must have a greater magnitude at all (x,y) coordinates thanIf this is not satisfied, then the optic’s performance will not be as anticipated. For instance, the spot size at the focus might be smaller or larger than designed. A simple approach to ensuring that this does not happen is to improve the design oby using the method of Gerchberg and Saxton. In this method, one can perform the following steps: constrainto be physically realistic by modifyingappropriately; then numerically propagateback to the focus, detector, etc. and constrain them to have the desired characteristics such as number of bright spots, ratio between the spots, 0AM content, shape, etc.; numerically propagate them back to the optic; repeat until a satisfactory, physical optic has been found.

[0175] One can define a different focal length for the two or more focal spots so that they focus to different distances. This can be useful, e.g., for beam diagnostics or for improving the alignment of an optic as in the alignment-assisting marks.

[0176] It can be appreciated that a general numeric propagator is a mathematical tool used to simulate the propagation of light through space, accounting for diffraction and interference effects. This simulation provides the calculation of the light field at any point along the beam’s path, given knowledge of the field at an earlier point. In the context of designing a multi-beam spatio-spectral-controllable optic, a numeric propagator plays a role in determining the light distribution required at the optic’s surface to produce the desired field at a target location, such as a sample or a detector.

[0177] As described above, one approach for implementing a numeric propagator is the spectrum of plane waves method that decomposes the light field into a superposition of plane waves, each with a specific direction and amplitude. The propagation of each plane wave is then calculated individually using a transfer function that accounts for the distance traveled and the wavelength of the light. After propagating all plane waves to the desired location, they are recombined to obtain thefinal light field. This approach can be represented mathematically as:This equation captures the essence of the spectrum of plane waves approach for how the initial field is decomposed into plane waves, propagated individually, and then recombined to obtain the field at the desired location. By applying this numeric propagator to the desired field at the focus or detector, the design process determines the required light distribution at the optic’s surface, providing the creation of diffractive structures that will generate the desired output upon illumination. The numeric propagator thus bridges the abstract design of the light field and the tangible realization of the optic, such that the fabricated device provides the targeted light manipulation.

[0178] In the method for designing the optics, regarding grouping the pixels into regions that represent the optic, in the simplest case, this step includes:and can be extended to multiple wavelengths in a number of ways, for instance by replacingThis approach can decrease efficiency of the optic. In the simplest case of designing a multi-beam spatio-spectral-controllable optic, the process focuses on a single wavelength of light, assuming a fully coherent light source. This simplification allows for a straightforward approach to defining the optic’s structure, where each pixel on the optic’s surface is assigned a phase value based on the desired phase shift at that location. This phase value, denoted as 0optic(x, y), can be chosen to be either 0 or IT, corresponding to regions of the optic that either transmit or block the incident light, respectively. This binary phase pattern creates a diffractive structure that manipulates the light wavefront to achieve the desired focusing or beam shaping.

[0179] The process for grouping pixels into regions representing the optic involves determining the phase value or amplitude value for each pixel based on the calculated field at the optic’s surface, obtained from the back-propagation step. An approach is to assign a phase value of IT to pixels where the calculated phase falls within a defined range, for example from -IT to 0, and a phase value of 0 to pixels where the calculated phase falls outside that range, for example from 0 to IT. Analternate approach, often applicable to transmission-mode optics, is to design the optic to alter amplitude instead of phase; this involves designing the optic to have a transmission amplitude of 0 where the phase from the back-propagation step falls within -IT to 0, and to be fully transmissive elsewhere. These methods effectively segment the optic’s surface into regions that will either impart a IT phase shift or no phase shift on the incident light, creating a binary diffractive pattern. This simplified approach, while effective for single-wavelength designs, becomes increasingly challenging when multiple wavelengths are introduced, as the wavelength dependence of diffraction and phase shifts complicates the design process.

[0180] In some embodiments, the design process provides optics for a fully coherent source, wherein the optics are designed for a single wavelength, polarization, incidence angle, and most other sources of mutual incoherence. Extending these designs to multiple spectral components is challenging and can involve maintaining the optic’s efficiency. The highest efficiency of a binary, transmission-mode optic can be ~10%, and the highest efficiency achievable using a binary, reflection-mode optic can be ~40% although blazed optics can have efficiencies around 90%. Some conventional design for zoneplates for multiple wavelengths negatively impact the efficiency by decreasing efficiency in proportion to the number of wavelengths involved in the design. The method for designing described herein is a new method for designing optics for a pair of wavelengths, polarizations, and the like that does not impact the efficiency and works for reflection-mode optics and for some transmissionmode optics.

[0181] In the design of a binary (i.e., two-level) zoneplate, the ideal phase of the zoneplate is determined, and a high phase range and a low phase range are defined (often [-pi,0) and [0, pi)). The optic design then proceeds by sorting each pixel into one of the two categories depending on its ideal phase. The process for designing a three- or four-level zoneplate to approximate a blazed optic proceeds in a similar manner with more phase ranges and is often used to improve the efficiency of reflection-mode zoneplate optics.

[0182] In cases where it is desirable to design an optic for two or more spectral components, an extension of this process can be made. It begins by repeating the above process for designing an optic, once for each spectral componentof interest. With multiple optics defined (as well as two or more phase ranges), the method sorts the pixels into categories depending on which spectral components were in which phase range. In the case of a binary optic defined for two wavelengths, the four categories can be represented graphically as shown in FIG. 2, wherein the four cells shaded in white are the four categories that can describe any given pixel. This approach can be applied to amplitude changes as well, by including amplitude ranges instead of or in addition to phase ranges in the truth table.

[0183] In an embodiment, with reference to FIG. 2, a truth table showing the truth table approach for designing a multi-beam spatio-spectral-controllable optic for two distinct wavelengths (A1 and A2) is shown. Each cell in the table represents a unique combination of phase ranges or amplitude ranges for the two wavelengths, wherein the four cells shaded in white are the four categories that can describe any given pixel. This categorization scheme allows for the design of an optic that can independently manipulate the phase or amplitude of two wavelengths, providing the creation of, e.g., achromatic lenses or wavelength-selective beamsplitters. The truth table can be extended to accommodate more wavelengths or multiple phase levels, providing the design of increasingly complex and versatile optics. For instance, a three-level optic designed for three wavelengths would require a three-dimensional truth table with 27 cells, representing all possible combinations of the three phase levels for each wavelength. This approach provides a systematic and efficient method for designing optics that can control the spatio-spectral profile of multiple beams across a range of spectral components.

[0184] In an embodiment, with reference to FIG. 3, the zoneplate design for one spectral component (A1 ) is shown in 255b and for a second spectral component (A2) is shown in 255a, and the allocation of each pixel into the four categories is shown below as 256a-d. FIG. 3 shows the truth table approach for designing a multi-beam spatio-spectral-controllable optic for two distinct wavelengths (A1 and A2). This approach starts by defining an ideal optic for each wavelength, shown as 255a and 255b, which represent the desired phase patterns for each wavelength independently. The pixels of these ideal optics are then sorted into categories based on the combination of phase values for both wavelengths, resulting in four distinct categories represented by the four squares 256a-256d in the truth table. Each category is thenassigned a different cross-section or physical structure to achieve the desired phase shifts for both wavelengths. The final target optic combines these structures according to the assigned categories of each pixel, as shown in the map defining the category representing each pixel. This method allows for the design of an optic that can independently control the phase of two wavelengths without sacrificing efficiency. Instead of designing a single optic that compromises between the desired phase shifts for both wavelengths, this approach creates a composite optic with distinct structures tailored to each wavelength’s requirements. This provides the creation of, for example, achromatic lenses that focus both wavelengths to the same point or wavelength- selective beam splitters that efficiently separate the two wavelengths.

[0185] The truth table approach can be extended to three-level, four-level, or higher-level zoneplates, as well as to three or more wavelengths. To design a three- level zoneplate for two wavelengths would involve constructing the chart in FIG. 4.

[0186] In an embodiment, with reference to FIG. 4, a truth table showing the design of a three-level multi-beam spatio-spectral-controllable optic for two wavelengths (A1 and A2) is shown. Each cell in the table represents a distinct category, defined by a unique combination of the desired phase shift for each wavelength. The phase shifts are quantized into three levels: 0, TT / 3, and 2TT / 3. This allows for more precise control over the spectral response of the optic compared to a two-level design. Each category in the table would correspond to a specific physical structure designed to impart the designated phase shifts for the two wavelengths. The final optic would be constructed by combining these structures according to the assigned categories of the pixels in the ideal optic. This approach can be extended to accommodate a larger number of phase levels, for example, four levels (0, TT / 2, IT, 3TT / 2), providing for an even more refined approximation of a continuous phase profile. Additionally, the truth table can be generalized to incorporate additional spectral components, such as polarization or incidence angle, providing the design of optics with multi-dimensional control over light.

[0187] That is, to design a two-level zoneplate for three wavelengths would involve extending the two-level zoneplate chart into the third dimension (sampling all combinations of high and low for the various wavelengths). The number of categories ultimately defined can be calculated as: (# Phase ranges)(# A). Continuing the exampleof a two-level (aka binary) zoneplate defined for two wavelengths: once the pixels have been sorted, four structures must be designed, one per category, that achieve the desired phase shift. If amplitude changes are included in the truth table, structures must be designed, one per category, that achieve the desired phase shift and amplitude changes. The method can differ if the optic is to be used on light that transmits through the optic or reflects from it. For transmission, achieving regions with high or low transmission for both wavelengths is the same as for normal zoneplates that can use free space for high transmission and opaque (e.g., gold) structures for low transmission. Structures that achieve high transmission for one wavelength and low for another rely on the pair of wavelengths straddling the absorption edge of a material. For instance, if designing for 13.7 nm and 10 nm, Si provides high transmission for 13.7 nm and low transmission for 10 nm, while Ru provides low transmission for 13.7 nm and high transmission for 10 nm. This is of import for semiconductor manufacturing. For scientific applications in the soft x-ray regime, there are many edges that can be used and, importantly, spectroscopic studies are specifically performed near absorption edges for similar reasons.

[0188] For reflection, achieving zero phase shift for both wavelengths is straightforward because these can be the regions consisting of only substrate. The other regions can be defined using the geometric phase, the material phase, the material amplitude, the waveguiding phase, or the waveguiding amplitude. For instance, if using the geometric phase, find a structure height that satisfies the following set of equations for each category of pixel with a system of equations:where is an arbitrary integer, h is the structure height, / is the index of the spectral component, is the desired phase shift for the ith spectral component, and the ith spectral component has wavelength and incidence angle

[0189] This procedure can be used to define zoneplates for multiple wavelengths, multiple polarizations, multiple incidence angles, or other effects resulting in mutual incoherence between the beams without loss of efficiency.

[0190] Further, the truth table approach provides a method for designing a multi-beam spatio-spectral-controllable optic for two or more spectral components, such as different wavelengths, polarizations, or incidence angles, without compromising efficiency. Conventional methods for designing optics for multiple wavelengths often result in a trade-off between efficiency and performance, as the optic must balance the desired phase shifts or amplitude changes for each wavelength. The truth table approach overcomes this limitation by creating a composite optic with distinct structures tailored to each spectral component’s requirements. In an embodiment, the process begins by designing an ideal optic for each spectral component of interest, as shown in FIG. 3 as 255a and 255b for two wavelengths,These ideal optics represent the desired phase patterns for each spectral component if it were the only component present. For each ideal optic, the pixels are grouped into regions based on their phase values or amplitude changes, can quantized into a discrete number of levels. For instance, in a binary optic, each pixel can be assigned either a 0 orphase shift. The next step involves constructing a truth table, where each cell corresponds to a unique combination of phase ranges or amplitude changes for the different spectral components. This table effectively maps out all possible combinations of phase values or amplitude changes that could be assigned to a given pixel, as shown in FIG. 3 for a two-level, two-wavelength design. Each cell in the truth table represents a distinct category, and each pixel in the ideal optics is assigned to a category based on its combination of phase values and amplitude changes. A different cross-section, or physical structure, is then defined for each category, as shown conceptually in FIG. 3 with different shading patterns for each cell. The selection of these structures depends on the specific spectral components being controlled and the desired phase shifts or amplitude changes. For example, if the optic operates in reflection, different structure heights can be used to impart different phase shifts based on the geometric phase, different material compositions, layer thicknesses, surface roughness or interface roughness can be employed to exploit the material phase or material amplitude, and different feature sizes and shapes can be used to control the waveguiding phase or waveguidingamplitude. The final target optic combines these different structures according to the assigned categories of the pixels in the ideal optics. This composite optic effectively provides the desired phase shifts and amplitude changes for each spectral component without sacrificing efficiency. This approach allows for a flexible and scalable design, providing the creation of optics that can handle a larger number of spectral components or a greater number of phase levels or amplitude levels. By extending the truth table to encompass more dimensions or more cells, increasingly complex and versatile optics can be designed. The truth table approach thus provides a powerful tool for controlling the spatio-spectral profiles of multiple beams across a range of spectral components, providing the development of advanced optical systems for diverse applications.

[0191] In a general case, for each spectral component there is a field the optic is desired to impart In this case, A can refer to the spectralcomponent: wavelength, polarization, or other forms of mutual incoherence. If many spectral components are present or many lithography steps are possible, the truth table approach becomes computationally difficult to achieve. Instead of defining multiple phase ranges or amplitude ranges, defining an optic for each spectral component, and then forming categories into which each pixel much be sorted, it is efficacious to instead form the categories from the start. Each category contains a phase-vs-A (or field-vs-A or amplitude-vs-A) that a physical stackup must be designed to achieve. This is equivalent to constructing a basis, and can be performed using standard linear or iterative operations, such as principal component analysis. Once the categories have been defined, each pixel can be sorted into the categories by finding which category represents it with the lowest RMS error over all spectral components.

[0192] When an optic is desired to control a large number of spectral components, the truth table approach can become computationally challenging due to the exponential increase in the number of categories as more spectral components, phase levels, or amplitude levels are considered. The general approach addresses this challenge by defining categories directly from the start, each category representing a specific phase-versus-wavelength (or, more generally, field-vs- wavelength) behavior that can be achieved with a physical multilayer structure. Theprocess begins by defining the desired field for each spectral component, denoted asrepresents the ithspectral component. These desired fields, which can be obtained through numerical back-propagation from the target location to the optic’s surface, specify the amplitude and phase distribution required for each spectral component at the optic. Instead of defining multiple phase ranges or amplitude ranges and then sorting pixels into categories based on those ranges, the general approach pre-defines categories based on a set of phase-versus-wavelength curves. In an embodiment, the phase-versus-wavelength curves include: a phase value for each design spectral component, an amplitude value for each design spectral component, or a combination comprising at least one of the foregoing values. This set of curves, which can be considered a basis set, is chosen to effectively capture the range of achievable spectral responses using physically realizable multilayer structures. Each pixel in the ideal optics is then assigned to a category based on its similarity to the defined phase-versus-wavelength curves. This can be achieved by calculating the root-mean-squared error between the pixel’s desired phase-versus-wavelength behavior and the behavior represented by each curve in the basis set. The category corresponding to the curve with the lowest root-mean-squared error is assigned to the pixel. This process effectively groups pixels with similar spectral responses into the same category, even if those pixels have slightly different phase values or amplitude changes at a given wavelength. Once all pixels have been assigned to categories, the design process proceeds to select a physical structure for each category. This involves considering the desired phase-versus-wavelength response for each category and choosing appropriate materials, layer thicknesses, and structural features to achieve that response. This selection process can use numerical simulations or optimization techniques to identify the multilayer structure that best approximates the desired phase-versus-wavelength behavior for each category. The final achievable optic is then defined by combining these physical structures according to the assigned categories of the pixels, resulting in an optic with tailored spectral responses for a large number of spectral components. This approach, by pre-defining categories based on achievable spectral responses, provides a more efficient and scalable design process compared to the truth table approach, particularly when dealing with a continuum of spectral components or a large number of phase levels or amplitude levels. It allows for the creation of complex, multifunctional optics with precisely controlled spatio-spectral properties, overcoming the limitations ofconventional design methods and expanding the possibilities for advanced optical applications.

[0193] In an embodiment, with reference to FIG. 5, the general approach for designing a multi-beam spatio-spectral-controllable optic for multiple spectral components across a range of photon energies (or wavelengths) is shown. This approach provides a desired phase response for each pixel of the optic across the entire spectral range. The process recalls the ideal optics for each spectral component, which represent the desired phase patterns for each component independently. Next, a basis set of phase-vs-photon energy curves is defined, each curve representing a distinct category. These curves capture a range of achievable spectral responses using physically realizable multilayer structures. The figure shows the “Phase of one spectral component of the ‘ideal optic’,” which represents the desired phase distribution for a single representative wavelength. The “Lineouts of the phases all spectral components of the ‘ideal optic’” depict the desired phase values for different wavelengths (or photon energies) along a specific line through the optic. This indicates the wavelength-dependent nature of the desired phase response. To categorize the pixels, the root-mean-squared (RMS) error between each category’s phase vs photon energy and the phase of each pixel in the ideal optics is calculated. This results in an RMS error value for each category, for each pixel. The category with the lowest RMS error is assigned to each pixel, effectively grouping pixels with similar spectral responses. The figure visually depicts the categorization process using a color-coded map, where each color corresponds to a different category. The blue region represents pixels assigned to “Category 1 ,” the red region represents pixels assigned to “Category 2,” and so on. The “Segment Phase” plot illustrates the phase- vs-photon energy curves for each category. Notably, the curves exhibit diverse shapes, capturing different spectral responses achievable with multilayer structures. For instance, “Category 4” (green) shows a relatively flat phase response across the photon energy range, while “Category 2” (red) exhibits a steeper, more wavelengthdependent phase change. Finally, the “Achieved Phase” section demonstrates the resulting phase distribution for one spectral component of the achievable optic. This shows how the assigned categories and their corresponding physical structures combine to create an optic with a spatially varying phase profile. The “SegmentingIndex” visualizes the spatial distribution of the assigned categories across the optic’s surface.

[0194] This general approach, by employing basis set decomposition and RMS error-based categorization, provides the design of optics with tailored spectral responses across a continuous range of wavelengths or photon energies. It allows for greater flexibility and efficiency compared to the truth table approach, particularly when dealing with a large number of spectral components or a fine quantization of phase levels or amplitude levels. This approach facilitates the creation of complex, multifunctional optics with precisely controlled spatio-spectral properties for diverse optical applications such as achromatic imaging, spectral shaping, and broadband beam manipulation.

[0195] If the optic is to be used in transmission, the phase is not generally something that can be altered significantly so design of these optics usually involves altering the amplitude in a binary manner, i.e. , using only regions that are fully opaque or fully transmissive, instead of altering the phase. This decreases the achievable efficiency to roughly 10% and involves selecting regions that are to be opaque or transmissive. In the simplest case, one selects regions to be opaque whereand transmissive otherwise (from). There are many intricacies that can enter the design of transmissive optics, such as designing support structures so that the opaque regions are freestanding and the transmissive features do not contain substrate.

[0196] The selection of regions to be opaque or transmissive can be based on the desired phase pattern for the optic, as determined by the previous steps of the design process, or can be based on the desired amplitude pattern for optics. An approach makes regions opaque where the desired phase shift is IT and transmissive where the desired phase shift is 0. This creates a binary amplitude mask that mimics the desired phase pattern, effectively manipulating the wavefront of the transmitted light. The opaque regions are often fabricated using a material that strongly absorbs the incident light, such as gold or another metal, while the transmissive regions consist of either free space or a material that is transparent to the incident light, such as silicon nitride or a thin membrane. The design of transmissive optics often requires careful consideration of the supporting structures to ensure mechanical stability and maintainthe integrity of the diffractive pattern. The opaque regions must be supported in a way that prevents sagging or collapse, while the transmissive regions can be free of any substrate material that could introduce unwanted phase shifts or absorption (i.e., amplitude changes). This can be achieved through fabrication techniques, such as creating freestanding structures or using a sacrificial layer that is removed after the optic is patterned.

[0197] If the optic is used as a reflective optic, the desired phase can be directly achieved with highly reflective structures on the optic, so the efficiency can be as high as roughly 90%. Desired amplitude changes can be directly achieved by using lower-reflectivity materials, but this is often undesirable because it negatively impacts the efficiency of the optic. A way to affect phase or, to a lesser degree, amplitude is to pattern a high-reflectivity material onto a high-reflectivity substrate. In some embodiments, the designer must select an incidence angle and material that have high reflectivity for the wavelength or spectral component of interest. Gold at or below 6- degrees from grazing is common. Structures with different heights produce a different phase shift and amplitude change on the impinging light.

[0198] In an embodiment, with reference to FIG. 6, a method for imparting a phase shift on light using the geometric phase is shown. This method involves patterning a high-reflectivity material onto a high-reflectivity substrate, creating structures with different heights that introduce a phase difference between light reflected from the structure and light reflected from the substrate. This phase difference, known as the geometric phase or topographic phase shift, is determined by the height of the structure, the wavelength of the incident light, and the angle of incidence. The figure depicts a cross-section of a simple structure on a substrate, with an incident beam of light striking the structure at an angleThe light reflected from the top surface of the structure travels a longer path compared to the light reflected from the substrate, introducing a phase difference proportional to the path length difference. This phase difference can be calculated using the equation: Geometric Phase where n is an integer representing the order of the phaseshift, A is the wavelength of the light, h is the height of the structure, andis the angle of incidence. By controlling the height of the structure, the geometric phase can be precisely tailored to achieve the desired phase shift for a specific wavelength andangle of incidence. This principle provides the creation of diffractive optics, such as zoneplates and gratings, with high efficiency and specific functionalities. For example, a zoneplate can be designed by creating concentric rings of varying heights, where the height of each ring is chosen to impart a phase shift that brings light from different rings to focus at a common point. Similarly, a grating can be created by patterning parallel lines with varying heights, where the height difference between adjacent lines determines the diffraction efficiency for a given wavelength.

[0199] The geometric phase method offers several advantages for designing reflective optics. It provides the creation of high-efficiency optics with minimal absorption losses, as the phase shift is introduced by a path length difference rather than propagation in an absorptive material. Furthermore, the geometric phase is independent of the material’s refractive index, providing for greater flexibility in material selection for the optic. However, the geometric phase is inherently wavelength-dependent, as the phase shift is proportional to the wavelength of the incident light. This wavelength dependence can reduce chromatic efficiency and lead to chromatic aberration, where different wavelengths are focused or diffracted at different angles, limiting the optic’s performance for broadband light sources.

[0200] To address the chromatic aberration and chromatic inefficiency inherent in the geometric phase, as well as to introduce the ability to alter the amplitude change precisely, various strategies can be employed. One approach is to combine the geometric phase with other phase and amplitude mechanisms, such as the material phase, material amplitude, waveguiding phase, or waveguiding amplitude, to create structures that compensate for the wavelength dependence and provide the ability to tune the amplitude change imparted by the structure. Another approach is to design optics for specific, discrete wavelengths, choosing structure heights that provide the desired phase shifts for those wavelengths. Additionally, the geometric phase can be used in conjunction with multilayer coatings, where the layer thicknesses and compositions are optimized to create constructive or destructive interference for different wavelengths, providing the design of achromatic or spectrally selective optics.

[0201] With reference to FIG. 6, there is a geometric phase shift (aka topographic phase shift) between the light reflected from the structure and from the substrate:where A is the wavelength of the light, h is the height of the structure, and 0 is the angle of incidence of the light on the optic. Therefore, the structure heights are designed using this equation in conjunction with the desired values of z.Eoptic(x,y,X'). Multiple heights can be used, either by using multiple lithography steps or by using grayscale lithography; since this provides a better match to Eoptic(x,y, A), the efficiency usually improves as the number of heights is increased. This has a limitation because the phase shift in the above equation is inversely proportional to the wavelength. So, a structure designed to impart a IT phase shift for a wavelength of A will impart 2TT=0 phase shift on a wavelength of A / 2. If the grating was a ruled grating, light with a wavelength of A would be diffracted with 40% efficiency into the first order, while light with a wavelength of A / 2 would remain unaffected. This is a problem of chromatic efficiency.

[0202] For a small number of discrete and dissimilar wavelengths, this can be partially solved by solving a system of equations to determine a height that provides the correct phase shift modulo 2TT for each wavelength. Achieving zero phase shift for both wavelengths is straightforward because these can be the regions consisting of only substrate. The following set of equations can be solved for h to determine the necessary height:where ntis an arbitrary integer, h is the structure height, / is the index of the spectral component, is the desired phase shift for the ithspectral component, and the ithspectral component has wavelengthand incidence angle

[0203] If the wavelengths are very close together or there are more than two wavelengths, the resulting height is usually quite tall relative to a single wavelength; inthis case, waveguiding effects come into play and complicate the scattering process, resulting in the need for numerical solvers to be used instead of the above set of equations.

[0204] It is contemplated that a solution to the problem of chromatic efficiency is to use multiple materials. Another approach for achieving a desired phase shift or amplitude change in reflective optics leverages the material phase, which arises from the interaction of light with the refractive index of materials. Unlike the geometric phase, which depends solely on the path length difference introduced by the structure height, the material phase arises from the multiple reflections and transmissions that occur within a multilayer structure. By selecting the materials and thicknesses of the layers, as well as the surface and interface roughness, the phase and amplitude of the reflected light can be controlled, even for structures with a constant height. To calculate the material phase shift, numerical methods like the Parratt formalism or rigorous coupled-wave analysis (RCWA) are often employed. These methods take into account the surface roughness, the refractive index, thickness, and interface roughness of each layer, as well as the angle of incidence and polarization of the incident light, to determine the complex reflectance of the multilayer structure. The phase and amplitude of this complex reflectance represents the overall phase shift and amplitude change imparted on the reflected light. For a given energy range, specific materials exhibit low absorption and a substantial material-dependent phase shift upon reflection. For example, aluminum is relatively transparent in the energy range of 30-65 eV, making it suitable for imparting a material phase shift on reflected light in that spectral region. By combining a material with a significant material phase shift with other materials, a multilayer structure can be designed to achieve a desired phase response and amplitude response for a given spectral component. The design process involves parameterizing candidate multilayer structures, varying layer thicknesses, compositions, interface roughness, and other structural parameters and calculating the phase shift or amplitude change imparted on each wavelength of interest. The root-mean-squared error between the calculated phase shift or amplitude change and the desired phase shift or amplitude change is then determined for each candidate structure, and the structure with the lowest error is selected. This approach allows for the creation of reflective optics with tailored phase responses and amplitude responses that can compensate for or enhance thegeometric phase, providing the design of optics with reduced chromatic aberration or specific spectral characteristics, as well as with tailored amplitude changes.

[0205] In an embodiment, with reference to FIG. 7, a cross-section of a multilayer structure designed to impart a desired phase shift or amplitude change on reflected light is shown. This structure consists of three layers of differing material composition, stacked atop a substrate. The top layer can be fabricated from a material like aluminum, which exhibits low absorption and a significant material phase shift in a specific energy range. The middle layer can include a material like gold that can be selected for its high reflectivity at the desired wavelength. The bottom layer can be fabricated from another material with a different refractive index, further contributing to the overall phase shift. The substrate provides mechanical support and acts as a base for the multilayer structure. Light incident on this multilayer structure undergoes multiple reflections and transmissions at each interface between the different layers. The phase of the reflected light is affected by the path length difference introduced by each layer, as well as by the material phase shift associated with each material and the multitude of reflections. By selecting the thicknesses and material compositions of the layers, the overall phase shift and amplitude change of the reflected light can be precisely controlled. The design of this multilayer structure involves considering the desired phase shift for a specific spectral component, such as a particular wavelength or polarization. Numerical simulations, employing techniques like Parratt method or the rigorous coupled-wave analysis (RCWA), are used to calculate the complex reflectance of the structure for a range of layer thicknesses and compositions. The phase of this complex reflectance represents the overall phase shift imparted on the reflected light. The structure parameters that minimize the difference between the calculated phase shift and the desired phase shift are then selected, ensuring the best possible match between the achievable structure and the design target.

[0206] This multilayer approach offers several advantages for designing reflective optics. It provides the creation of structures that impart precise phase shifts beyond those achievable solely with the geometric phase, expanding the range of achievable phase responses. Furthermore, it allows for the design of optics that provide a precisely-defined amplitude change by selecting materials and layer thicknesses that provide the desired amplitude change. Furthermore, it allows for thedesign of optics with reduced chromatic aberration by selecting materials and layer thicknesses that compensate for the wavelength dependence of the geometric phase. The material phase can also be used to create spectrally selective optics, where different wavelengths experience different phase shifts and amplitude changes, providing functionalities like spectral filtering or wavelength-dependent beam steering. This structure can be further enhanced by using a larger number of layers, providing more precise control over the phase response and amplitude response. Additionally, the thicknesses of the layers can be varied along the optic’s surface, creating a spatially varying phase profile and amplitude profile that provides functionalities like multi-focus or beam shaping. Moreover, the design can be tailored to specific polarization states by considering the polarization-dependent properties of the materials and their interfaces, as well as their structure that may cause polarizationdependent or polarization-altering waveguiding effects.

[0207] Again, with reference to FIG. 7, there is a phase shift and amplitude change between the light reflected from the structure and that from the substrate. The phase and amplitude depend on the many reflections that happen within the sample, and can be computed in several ways. One way is the method of Parratt, which involves applying the following equation iteratively to each layer of material (which is surrounded by a top interface and a bottom interface):where E7E is the ratio of the reflected beam (the beam reflected from the multi-layered structure) to the incoming beam, rtopand rbot are the reflectivities of the top and bottom interfaces as calculated by the Fresnel coefficients, n is the index of refraction of the layer, h is the thickness of the layer, / is the wavelength of the light, and 0 is the propagation angle (defined from grazing-incidence) within the layer calculated using Snell’s law. Surface roughness and interface roughness can be included as a series of layers with composition that varies from one layer to the other along the desired length scale. The deviation of this equation from the purely geometric phase shift above is what we refer to as the material phase shift. The deviation of this from the reflectivity of the substrate is what we refer to as the material amplitude. For certainmaterials and certain energy ranges (usually isolated elements, but sometimes compounds like B4C or SiC), the absorption of the material is low enough that a significant material-dependent phase is imparted while the light travels through the structure. For instance, aluminum is relatively transparent in the range of 30-65 eV, and performs well to impart a material phase shift on the reflected light.

[0208] If a structure is properly designed, this material phase shift can cancel or enhance the geometric phase shift, as well as provide a desired amplitude change. A suitable design to minimize chromatic inefficiency for 30-60 eV light can be arrived at by selecting the structure shown in FIG. 8 and computing the phase shift of that structure for each spectral component under consideration, at a range of each parameter (here, each height).

[0209] In an embodiment, with reference to FIG. 8, a cross-section of a multilayer structure designed to impart a desired phase shift or amplitude change on reflected light, specifically leveraging the material phase of aluminum (Al) in a certain energy range, is shown. The structure consists of a layer of aluminum (Al) with thickness hi , deposited on a gold (Au) sublayer with thickness h2. This bilayer is fabricated on a thick gold (Au) sublayer that provides a highly reflective base for the structure, and is deposited atop a silicon substrate that provides mechanical support. The choice of aluminum for the top layer stems from its low absorption and significant material phase shift in the energy range of 30-65 eV, providing efficient phase control without excessive loss of light due to absorption. The thick gold sublayer serves as a high-reflectivity layer, ensuring that most of the incident light is reflected back from the structure. The thickness of this sublayer, h2, also contributes to the overall phase shift through the multiple reflections that happen within the structure. The gold substrate provides a stable and highly reflective base for the structure, minimizing losses due to transmission through the substrate. The design process for this multilayer structure involves considering the desired phase shift or amplitude change for a spectral component within the 30-65 eV energy range. Numerical simulations, using techniques like the Parratt formalism or rigorous coupled-wave analysis (RCWA), are employed to calculate the complex reflectance of the structure for a range of thicknesses hi and h2. If desired, this calculation could be performed for a range of other structural parameters like surface roughness, or compositional parameters likedensity or doping. The phase of this complex reflectance represents the total phase shift imparted on the reflected light, encompassing both the geometric and material phase contributions. The amplitude of this complex reflectance represents the total amplitude change imparted on the reflected light. The thicknesses hi and h2 that minimize the difference between the calculated phase shift or amplitude change and the desired phase shift or amplitude change are then selected, ensuring a match between the achievable structure and the design target. This particular design, featuring aluminum and gold, is tailored to a specific energy range. Alternative material combinations can be employed to achieve desired phase shifts in other spectral regions. For instance, materials like silicon, molybdenum, or titanium can be used in the EUV range, while materials like nickel, palladium, or platinum could be suitable for soft x-rays. Furthermore, the composition of an individual layer can be altered by introducing additional elements to vary the absorption within that layer, for instance alloying aluminum with a small amount of gold to slightly increase the reflectivity. The choice of materials depends on their optical properties, such as their refractive index and absorption coefficient, within the desired wavelength range, as well as their compatibility with fabrication processes and their stability under the operating conditions. The thicknesses of the Al, hi , and Au sublayer, h2, can be adjusted to finetune the phase response. Additionally, the number of layers in the structure can be increased to provide more precise tailoring of the phase or amplitude response. This can involve incorporating additional materials with different refractive indices or using multiple layers of the same material with varying thicknesses or interface quality. Furthermore, altering the surface roughness, density of a layer, or interface roughness between layers can affect the phase shift or amplitude change even more precisely, which can be useful for even shorter wavelengths of light.

[0210] This multilayer approach, by combining the geometric and material phase effects as well as the material amplitude, provides the design of reflective optics with tailored spectral responses, providing for the creation of optics with reduced chromatic aberration or specific functionalities like spectral filtering or wavelengthdependent beam steering. This approach offers a powerful tool for manipulating light across a broad range of wavelengths, expanding the possibilities for advanced optical applications in areas such as microscopy, spectroscopy, and lithography.

[0211] It can be appreciated that parameters that can be varied include layer thicknesses, compositions (elements, compounds, ratio of elements, densities, dopants, impurities), surface or interface roughness, line-edge roughness. To select the best stackup, we compute the phase shift or amplitude change imparted on each spectral component for the candidate structuresand determine the RMS error between that phase or amplitude and the desired phase or amplitude. For instance, if the structure should impart IT phase shift on all spectral components, compute the RMS error between the computed phases and IT. If we are performing this calculation for the two layer thicknesses shown in FIG. 8, the resulting 2D error map as shown in FIG. 9, where lower values are better.

[0212] In an embodiment, with reference to FIG. 9, a multilayer approach for selecting physical structures that impart desired phase shifts on reflected light is shown. This approach involves parameterizing candidate multilayer solutions, computing their merit by comparing achieved and desired reflectivities, and selecting the best solution. FIG. 9 shows a map that depicts the root-mean-squared (RMS) error between the achieved and desired reflectivities for a range of multilayer structures. The horizontal axis represents the thickness of the bottom layer, composed of gold (Au), while the vertical axis represents the thickness of the top layer, composed of aluminum (Al). Each point on the map corresponds to a specific bilayer structure with defined thicknesses for the gold and aluminum layers. The grayscale intensity at each point represents the RMS error, with lighter shades indicating higher error and darker shades indicating lower error. The map reveals a complex pattern of RMS error values, providing a relationship between layer thicknesses and the resulting reflectivity. Regions with lower RMS error, indicated by darker shades, represent structures that more closely match the desired reflectivity. The red ‘x’ marks the optimal solution, representing the bilayer structure with the lowest RMS error and, therefore, the best match to the target reflectivity. This multilayer approach leverages the combined effects of the geometric phase and the material phase to achieve precise control over the phase of the reflected light. By tuning these thicknesses, the desired phase response for a given spectral component can be achieved.

[0213] Computation of the RMS error can be performed using a variety of methods. Electromagnetic analysis, such as RCWA, can provide accurate calculationsof the reflectivity for complex multilayer structures. Alternatively, simpler approaches based on transfer matrix methods or approximate analytical expressions can be employed, offering a trade-off between computational speed and accuracy. The choice of method depends on the complexity of the structure, the desired accuracy, and the available computational resources.

[0214] This map represents the selection process for a single category of pixels with a specific desired phase shift. For optics with multiple categories, each category will have its own RMS error map, and the optimal structure for each category will be selected based on its corresponding map. The final achievable optic is then defined by combining these optimized multilayer structures according to the assigned categories of the pixels in the ideal optic.

[0215] This multilayer approach offers several advantages for designing reflective optics. It provides a broader range of achievable phase shifts and amplitude changes compared to using only the geometric phase, providing greater flexibility in tailoring the spectral response of the optic. Furthermore, it allows for the design of optics with reduced chromatic aberration by selecting materials and layer thicknesses that compensate for the wavelength dependence of the geometric phase. The multilayer approach can also be used to create spectrally selective optics, where different wavelengths experience different phase shifts or amplitude changes, providing functionalities like spectral filtering or wavelength-dependent beam steering.

[0216] Alternative material combinations can be explored to achieve desired phase shifts and amplitude changes in different spectral regions. For instance, in the EUV range, materials like silicon, molybdenum, or titanium could be used instead of aluminum for the top layer. The choice of materials depends on their optical properties, fabrication compatibility, and stability under the operating conditions. Furthermore, the number of layers in the structure can be increased beyond two, providing even finer control over the phase response and providing the creation of more complex spectral profiles. By optimizing the multilayer design, high-performance optics with tailored phase responses and reduced chromatic aberration can be achieved, expanding the possibilities for advanced optical applications.

[0217] The optimum solution from FIG. 9 is indicated with a red ‘x’, and has the phase-vs-photon-energy plot shown in FIG. 10.

[0218] In an embodiment, with reference to FIG. 10, a graph for the phase shift imparted on reflected light as a function of photon energy for a multilayer structure, as compared to the phase shift achievable using only the geometric phase, is shown. The horizontal axis represents the photon energy of the incident light, ranging from 50 eV to 63 eV, while the vertical axis represents the phase shift imparted on the reflected light, expressed in radians. The solid horizontal line represents the ideal phase shift (IT radians), which would be desirable for a wide range of applications, such as broadband spectroscopy or beam shaping. The dotted line represents the phase shift achievable using only the geometric phase, which is inversely proportional to the wavelength (or, equivalently, proportional to the photon energy). This line exhibits a steep slope, indicating a strong wavelength dependence of the phase shift. Such a strong wavelength dependence can lead to significant chromatic inefficiency, limiting the optic’s performance for broadband light sources. The dashed line represents the phase shift achieved with a multilayer optic designed to minimize chromatic inefficiency over the 30-60 eV energy range. This curve is not constrained to be a straight line, as is the case with the geometric phase. Instead, it exhibits a more complex shape, with a flatter region in the middle of the energy range, indicating a reduced wavelength dependence in that region. Notably, the dashed curve intersects the ideal phase shift line in two places, achieving the desired IT phase shift at those specific photon energies.

[0219] FIG. 10 indicates the advantage of using a multilayer approach for controlling the phase of reflected light. By selecting the materials and thicknesses of the layers in the multilayer structure, the phase response can be tailored to achieve a desired spectral behavior, even for structures with a constant height. The ability to shape the phase-vs-photon energy curve allows for the design of optics with reduced chromatic aberration and chromatic inefficiency compared to optics relying solely on the geometric phase. This specific example demonstrates the design of a multilayer optic for minimizing chromatic inefficiency in the 30-60 eV energy range. Alternative multilayer designs can be tailored to different spectral regions or achieve other desired phase responses. For instance, a multilayer optic could be designed to impart aspecific phase shift that varies linearly with photon energy, providing functionalities like spectral dispersion, achromatic focusing, or wavelength-dependent beam steering. Furthermore, the multilayer design can be optimized to maximize reflectivity at specific wavelengths, providing the creation of highly reflective mirrors for narrowband applications. The number of layers in the multilayer structure can also be varied to achieve different levels of phase control. A larger number of layers generally allows for more precise tailoring of the phase response, providing more complex spectral profiles and improved compensation for chromatic aberration. However, increasing the number of layers also increases fabrication complexity and potential for defects, leading to a trade-off between performance and manufacturability. The choice of materials for the multilayer structure is a parameter for achieving the desired spectral response. Materials with different refractive indices and absorption coefficients will exhibit different phase shifts and reflectivity characteristics. The design process involves selecting materials that are suitable for the desired energy range, considering factors like absorption, reflectivity, stability, and compatibility with fabrication processes. This multilayer approach, by providing precise control over the phase of reflected light as a function of photon energy, opens new possibilities for designing advanced optics with tailored spectral responses and enhanced performance.

[0220] Again, the ideal phase shift (pi) is shown as a solid horizontal line in FIG. 10. The achieved phase shift with a multi-layered optic is shown as a dashed line, and intersects the ideal in two places. For reference, the best phase shift achievable using just a geometric phase shift is shown as a dotted line in FIG. 10. This captures the power of one aspect of this invention since this curve is no longer confined to be a diagonal line, but can be shaped or flattened.

[0221] A correction can be made to the reflectivity calculation, which can be advantageous because it gives an enhanced ability to tune the optic’s performance differently for different polarizations and incidence angles.

[0222] In previous cases, edge effects were not used in calculating the reflectivity of structures. More generally, we have assumed that the reflectivity of a structure could be calculated (e.g., using Parratt’s formalism) regardless of the size of the structure (transverse or height) and the proximity of neighboring structures. Thisis approximately correct if the structures are topographically mostly flat relative to a wavelength (that is, their cross section is not very high) or the features are very wide relative to a wavelength, and the edges of the structures are all straight or as designed (that is, relatively little line-edge roughness, LER). When this approximation breaks down, the deviation of the phase from the geometric and material phase is termed the “waveguiding phase” (and similarly the “waveguiding amplitude”, together “waveguiding effect”). The waveguiding effect includes effects like the induced phase when each photon interacts multiple times with the optic, but also other effects such as shadowing, wherein tall, opaque structures might obstruct the view of smaller features at their bases. The waveguiding effect is difficult to calculate, so the computation is often best done using pre-built packages for calculating electromagnetic scattering.

[0223] Conveniently, the waveguiding effect has greater dependence on polarization and incidence angle than the material phase and geometric phase; therefore, one can design structures that use it and thereby exhibit unusual behavior relative to these items. For instance, if a grating with the cross section shown in FIG. 11 is made of an opaque material, it will have a reduced dependence on incidence angle due to its very tall, narrow features.

[0224] In an embodiment, with reference to FIG. 11 , a cross-section of a grating structure designed to exploit the waveguiding effect for controlling the diffraction efficiency of light is shown. This grating structure consists of tall, narrow features fabricated from an opaque material deposited on a substrate. The tall, narrow geometry of the features leads to a reduced dependence of the diffraction efficiency on the angle of incidence compared to structures with wider or shorter features. This reduced angular dependence arises from the waveguiding effect, where the confinement of light within the narrow features alters its interaction with the structure boundaries. When light is incident on this grating structure, a significant portion of the light is reflected from the top surfaces of the tall features. The tall, narrow geometry of the features exhibits the shadowing effect, where incident light is blocked from reaching the base of the features at larger angles of incidence. This ensures that a substantial portion of the incident light reflects from the topmost surface of the structure, and most of the remaining light is absorbed in the many reflections betweenthe tall structures. This behavior is exhibited even at oblique angles, contributing to a more consistent diffraction efficiency over a broader angular range.

[0225] The design of this grating structure involves considering the desired reflectivity for a specific spectral component and angle of incidence range. Numerical simulations, employing rigorous electromagnetic solvers like finite-difference timedomain (FDTD) or finite element methods (FEM), are used to calculate the reflectivity for a range of feature widths and heights. The dimensions that best match the desired reflectivity over the target angle of incidence range are then selected. This specific example features tall, narrow features made from an opaque material to achieve a reduced angular dependence of reflectivity. Alternative designs can be implemented to achieve other desired optical properties. For instance, the features could be fabricated from a transparent material, providing for the transmission of light through the grating while still exploiting the waveguiding effect to modulate the phase, polarization or amplitude of the transmitted light.

[0226] The shape of the features can also be varied. Instead of rectangular features, triangular, trapezoidal, or curved profiles could be employed, leading to different waveguiding effects and spectral responses. Furthermore, the line-edge roughness and spacing between the features can be adjusted to control the diffraction properties of the grating. The design can be enhanced by incorporating multiple layers of materials with different refractive indices. This can create a photonic crystal structure that exhibits bandgaps or resonant modes at specific wavelengths, providing functionalities like spectral filtering or wavelength-selective beam steering. By engineering the geometry, material composition, and periodicity of the structure, a wide range of optical properties can be achieved, providing the creation of advanced and versatile reflective optics for diverse applications.

[0227] There are sometimes multiple structures that will achieve the same phase shift or amplitude change. Selection of a proper structure can mitigate other issues, such as overlay during fabrication. Consider, for instance, that the two structures shown in FIG. 12A and FIG. 12B might represent the same grating in theory, but the one in FIG. 12B is more robust to overlay errors.

[0228] In an embodiment, with reference to FIG. 12A, different structures that can be used to impart a desired phase shift and amplitude change on reflected light are shown. The figure shows a cross-section of five different structures, each representing a unique combination of geometric phase, material phase, material amplitude, waveguiding phase, and waveguiding amplitude contributions. The structures are shown as a series of layers stacked atop a substrate, represented by the region at the bottom. The middle regions represent layers of a high-reflectivity material, such as gold, while the top regions represent layers of materials with varying refractive indices and thicknesses, chosen to impart specific phase shifts or amplitude changes through their material properties. These five structures represent a small subset of the vast range of possibilities achievable with multilayer designs. Alternative materials can be employed to tailor the spectral response to different wavelength ranges or to exploit specific material properties. For instance, materials with high refractive indices can introduce large phase shifts, while materials with low absorption can minimize losses due to absorption.

[0229] The number of layers can be further increased, providing even finer control over the phase and amplitude response and providing the creation of more complex spectral profiles. The layer thicknesses can be varied along the optic’s surface, generating a spatially varying phase profile that can be used for multi-focus or beam shaping applications. The flexibility of multilayer designs, coupled with the ability to control multiple phase and amplitude mechanisms, provides the creation of advanced reflective optics with tailored spectral responses and enhanced performance. This approach opens up exciting possibilities for manipulating light and creating novel optical devices for diverse applications in imaging, spectroscopy, sensing, and communication.

[0230] In an embodiment, with reference to FIG. 12B and FIG 14, different structures that can be used to impart a desired phase shift or amplitude change on reflected light, including structures for fabrication using multi-step lithography, are shown. The figure shows a cross-section of different structures, each representing a unique combination of geometric phase, material phase, material amplitude, waveguiding phase and waveguiding amplitude contributions. The structures are shown as a series of layers stacked atop a substrate, represented by the region at thebottom. These structures represent a subset of the diverse range of possibilities achievable with multi-step lithography. The number of layers and the number of steps in each layer can be varied to create structures with a higher number of levels, providing a more precise approximation of continuous phase profiles. Alternative materials can be employed to achieve desired phase shifts in different spectral regions or to exploit specific material properties. For example, materials with high refractive indices can introduce substantial phase shifts, while materials with low absorption can minimize losses due to absorption. The choice of materials depends on their optical properties, fabrication compatibility, and stability under the operating conditions. The width of the features in each layer can also be adjusted to control the waveguiding phase, further enhancing the design flexibility. For instance, narrow features can enhance the waveguiding effect, while wider features can reduce it. This approach, by combining multi-step lithography with multiple materials, offers a powerful method for creating reflective optics with tailored spectral responses and enhanced performance. The ability to precisely control the phase of reflected light using these structures opens new avenues for designing advanced optical devices for a wide range of applications.

[0231] Another way to modify the structure is to use grayscale lithography. Using grayscale lithography to form the bottom layer, the structure above can provide a closer match to Eopticand be made more efficient; such an optic might have the cross section shown in FIG. 13.

[0232] In an embodiment, with reference to FIG. 13, different structures for fabrication using grayscale lithography are shown. The figure shows a cross-section of five(?) different structures, each with a continuously varying height profile, designed to impart a desired phase shift on reflected light. The structures are shown as a series of layers with varying shades of gray, stacked atop a substrate, represented by the region at the bottom. Layers can be fabricated from a high-reflectivity, opaque material, such as a thick layer of gold, designed to completely block the transmission of light. Some regions can include layers of a high-reflectivity material with continuously varying thicknesses. These layers contribute to the overall phase shift through the geometric phase, which is determined by the path length difference between light reflected from the top surface of the structure and light reflected from the substrate, as well as the material phase and waveguiding phase. The grayscalegradient within each layer represents the continuous variation in thickness, providing a smooth and precise control over the geometric phase shift. This continuous height profile contrasts with the discrete steps achievable with multi-step lithography, as shown in FIG. 12B, providing for a closer approximation of a continuous phase profile and potentially enhancing diffraction efficiency. Grayscale lithography offers several advantages for fabricating diffractive optics. It provides the creation of structures with smooth, continuous height profiles, providing a more accurate representation of the desired phase and amplitude patterns and potentially reducing scattering losses. Furthermore, it allows for the fabrication of complex shapes and profiles, expanding the design space for diffractive optics and providing the realization of novel functionalities. Alternative grayscale profiles can be designed to achieve different optical properties. For instance, a sinusoidal profile could be used to create a sinusoidal grating, while a more intricate profile could be employed to generate a diffractive optic with multiple focal points or a specific beam shape. The choice of materials for the multilayer structure can also be varied to tailor the spectral response to different wavelength ranges or to exploit specific material properties. The number of layers in the structure can be increased, providing even finer control over the phase response and providing the creation of more complex spectral profiles.

[0233] Many types of structures might serve to enhance the grating in various ways such as shown in FIG. 14 that shows some examples of the type of structures that can be used to impart geometric phase, material phase, material amplitude, and waveguiding effects. The different shades of grey represent different materials or elements.

[0234] In an embodiment, with reference to FIG. 14, a plurality of different structures that can impart a desired phase shift or amplitude change on reflected or transmitted light is shown. These structures provide flexibility in designing multi-beam spatio-spectral-controllable optics, providing the tailoring of optical properties by combining various phase and amplitude mechanisms, materials, and structural configurations. The figure shows a cross-section of different structures, each representing a unique combination of geometric phase, material phase, material amplitude, and waveguiding effect contributions. The structures are shown as a series of layers stacked atop a substrate at the bottom. The different shades of gray representdifferent materials or elements, providing for the creation of multilayer structures with varying refractive indices and optical properties. Alternative materials, layer thicknesses, feature sizes, and shapes can be explored to tailor the spectral response to different wavelength ranges, polarization states, and incidence angles. This flexibility allows for the creation of advanced reflective optics with tailored properties and enhanced performance.

[0235] In the design of multi-beam spatio-spectral-controllable optics, there are often multiple physical structures that can achieve the same desired phase shift for a given spectral component. While these structures can be theoretically equivalent in terms of their optical performance, they can differ significantly in their practical implementation and fabrication feasibility. Selecting an appropriate structure involves considering factors such as fabrication complexity, robustness to errors, and potential for integration with other optical elements. For example, two structures might theoretically represent the same grating, but one might be more robust to overlay errors during fabrication. Overlay errors occur when multiple layers or patterns are not perfectly aligned during the fabrication process, leading to deviations from the intended structure. A structure with larger features or more gradual transitions between features is generally less sensitive to overlay errors, ensuring a more accurate and reproducible fabrication. Another approach for improving structure selection is to use grayscale lithography. Grayscale lithography provides the creation of structures with continuous height profiles, as opposed to the discrete height levels achievable with conventional binary lithography. This allows for a closer match to the desired phase profile and can enhance the efficiency of the optic by reducing unwanted diffraction into undesired orders. However, grayscale lithography can be more challenging to implement than binary lithography, requiring specialized equipment and more intricate fabrication processes. The choice of structure can also be influenced by the need to integrate the optic with other optical elements. For instance, if the optic is to be combined with a focusing lens, the structure can be designed to minimize any distortions or aberrations introduced by the lens. Similarly, if the optic is intended for use in a high-power laser system, the structure can be robust to damage from intense light.

[0236] The fabrication of multi-beam spatio-spectral-controllable optics can include a combination of lithography, deposition, and etching techniques, providing the creation of intricate multilayer structures with precise control over the thickness and composition of each layer and the lateral distribution of these layers. These structures are designed to impart specific phase shifts on light, providing the manipulation of multiple beams with tailored spatio-spectral properties. The fabrication process can begin with the preparation of a suitable substrate, such as gold, silicon, or sapphire, chosen for its mechanical stability, compatibility with subsequent processing steps, and optical properties. If the substrate material itself is not suitable for reflecting light at the desired wavelength, a high-reflectivity material, either a single material or a multilayer coating, is deposited onto the substrate.

[0237] A photosensitive or electron-sensitive resist layer can be deposited onto the substrate or the high-reflectivity layer. This resist layer, which changes its chemical properties upon exposure to light or electron beams, serves as a template for transferring a pattern onto the underlying material. The desired pattern is then transferred to the resist layer using lithography techniques. Photolithography uses a mask with the desired pattern, which is illuminated with ultraviolet light to expose the resist in the desired areas. Electron beam lithography, on the other hand, uses a focused beam of electrons to directly write the pattern onto the resist. The choice between these techniques depends on the desired resolution, feature size, and complexity of the pattern. For an additive process, after the resist layer has been patterned, a material for the next layer of the optic is deposited using techniques such as sputtering, evaporation, or chemical vapor deposition. This material covers both the resist and the exposed substrate areas. A solvent is typically used to remove the resist and the material deposited on top of it, leaving behind the patterned layer on the substrate and is typically called a “lift-off” process. This process for resist deposition, patterning, material deposition, and lift-off is repeated for each additional layer, creating the desired multilayer structure.

[0238] The specific materials used for each layer, their thicknesses, and the pattern defined by each lithography step are determined by the design process. Numerical simulations, incorporating the desired optical functionality and the target spectral components, can be used to calculate the ideal phase profile for the optic.This phase profile is then translated into a discrete height profile by assigning specific heights to different regions of the optic based on the desired phase shifts. The fabrication process accurately creates the structure with these specified heights, physically realizing the designed optic.

[0239] FIG. 16 and FIG. 17 show atomic force micrographs (AFM) of fabricated multi-beam spatio-spectral-controllable optics, having distinct height levels achievable with this fabrication process. The uniformity and sharp transitions between layers indicate precise control over layer thicknesses and accurate pattern transfer.

[0240] Alternative fabrication techniques, such as subtractive etching methods, can also be employed to create the multilayer structures. In a subtractive process, layers are deposited sequentially, and then the desired pattern is etched into each layer using techniques like reactive ion etching or focused ion beam milling. The choice between additive and subtractive processes, or a combination of both, depends on factors like the desired materials, layer thicknesses, feature sizes, and the overall complexity of the structure. This fabrication process, by leveraging the precision and versatility of lithography, deposition, and etching techniques, provides the creation of complex multilayer structures that can manipulate light across a broad range of wavelengths and polarizations. This capability allows for the making multi-beam spatio-spectral-controllable optics with tailored spectral responses, enhancing performance and providing novel functionalities for a wide array of optical applications.

[0241] A process for making a multifunctional optic can be additive or subtractive or combination thereof. FIG 15 presents an example of an additive fabrication process. A substrate A01 , e.g., silicon, oxidized silicon, sapphire, is provided. If the substrate itself is not used as one of the desired materials to reflect the light, then material A02 is deposited on top of the substrate that contains the desired optical properties, which hereafter A02 is an optional layer based on this requirement. Layer A02 can be a single material or consist of multiple materials and layers, e.g., inclusion of adhesion, seed layers. A photosensitive or electron sensitive resist layer A03 is deposited on the sample, e.g., via a spin-on process. In step A13, the desired pattern is transferred to the resist layer via photolithography or electron beam lithography. The desired material, e.g., metal, dielectric, for the second layer of the optic is deposited which coats the top of the resist A04 and regions in-between theresist A05 which is directly in contact with A02 / A01 as shown in Step A14. Material A04 and A05 can be similar or dissimilar materials to those in A01 and A02. Layers A03 and A04 are removed leaving behind the patterned layer A05 as shown in Step A15. Steps A12 through A15 are then repeated to form the third layer of the optics which is seen by depositing resist layer A06 and patterning that layer via photolithography or electron beam lithography. The third material, which can be similar or dissimilar to the previously deposited materials, is then deposited on top of A07 and in between A08 the resist. Layers A06 and A07 are removed leaving behind the patterned layer A08 on the optic as shown in Step A18. To form additional layers in the stack up, steps A12 through A15 (or equivalently, A16 through A18) are then repeated until the desired number of layers in the stack up are achieved.

[0242] In an embodiment, with reference to FIG. 15, a process for fabricating a multifunctional optic using a combination of additive and subtractive techniques is shown. The process begins with a substrate A01 . This substrate provides a base for the optic and can be composed of materials like silicon, oxidized silicon, or sapphire, chosen for their compatibility with subsequent fabrication processes and their optical properties. If the substrate material is not suitable for reflecting light at the desired wavelength, an optional layer, labeled A02, is deposited on top of the substrate. This layer can consist of a single material or multiple layers designed to enhance reflectivity or provide other desired optical properties. A photosensitive or electron-sensitive resist layer, labeled A03, is then deposited onto the substrate. This resist layer is sensitive to either light or electron beams, providing the transfer of a pattern onto the substrate using lithography techniques. The desired pattern is transferred to the resist layer in step A13, using either photolithography or electron beam lithography. Photolithography uses a mask with the desired pattern, which is illuminated with ultraviolet light to expose the resist in the desired areas. Electron beam lithography uses a focused beam of electrons to directly write the pattern onto the resist. The choice between these techniques depends on the desired resolution, feature size, and complexity of the pattern. After the resist layer is patterned, a material for the second layer of the optic is deposited, creating layers labeled A04 and A05. This deposition can be performed using techniques like sputtering, evaporation, or chemical vapor deposition. Layer A04 represents the material deposited on top of the resist, while layer A05 represents the material deposited directly onto the substrate in the regionswhere the resist has been removed. The materials used for A04 and A05 can be similar or dissimilar, providing for the creation of multilayer structures with varying refractive indices and optical properties. In step A15, the resist layer A03 and the material deposited on top of it, A04, are removed, leaving behind the patterned layer A05 on the substrate. This removal process can involve a chemical etch or a lift-off process, where the resist and the overlying material are dissolved or peeled away. The resulting structure now has a single patterned layer, A05, on the substrate. To create additional layers, the process is repeated. A new resist layer, labeled A06, is deposited and patterned, followed by the deposition of a third material, creating layers A07 and A08. Layers A06 and A07 are then removed, leaving behind the patterned layer A08 on top of the existing structure. This process can be repeated as many times as necessary to achieve the desired number of layers in the stackup.

[0243] Alternative fabrication processes can be employed to create multilayer structures. For instance, instead of an additive process using resist and liftoff, a subtractive process involving etching can be used. In this approach, layers are deposited sequentially, and then the desired pattern is etched into each layer using techniques like reactive ion etching or focused ion beam milling. The choice between additive and subtractive processes, or a combination of both, depends on factors like the desired materials, layer thicknesses, feature sizes, and the complexity of the structure. This fabrication process, using a combination of lithography, deposition, and etching techniques, provides the creation of complex multilayer structures with precise control over the thickness and composition of each layer.

[0244] An example of a fabricated optic that was produced by this method with 3 levels of lithography is shown in Fig 16. Here a 36 pm x 36 pm topographical image taken on one section of the optic shows the 4 geometric levels.

[0245] In an embodiment, with reference to FIG. 16, an atomic force micrograph (AFM) image of a fabricated dual-focus optic made according to the process for FIG. 15 is shown. The top portion of the figure presents a 36 pm x 36 pm topographical image of a section of the optic, revealing the surface structure with four distinct height levels, represented by the varying color intensities. The darkest regions correspond to the lowest points on the surface, while the lightest regions represent the highest points, with a color scale indicating the height range from -173.4 nm to 21.5nm. The bottom portion of the figure provides a cross-sectional profile of the optic along the white line indicated in the top image. This profile clearly shows the four distinct layers, each with a relatively uniform height, confirming the successful fabrication of a multilayer structure using the described additive lithography process. The bottom layer, representing the substrate, forms the base of the structure. The next three layers, fabricated using sequential lithography and deposition steps, create the desired height profile for the dual-focus optic. The fabrication process uses a combination of lithography, deposition, and etching techniques to create these four layers. A photosensitive or electron-sensitive resist is spun onto the substrate, and a pattern is transferred onto the resist using either photolithography or electron beam lithography. A material, such as gold or a multilayer coating, is then deposited, covering both the resist and exposed substrate areas. The resist and the material deposited on top of it are then removed, leaving behind the patterned layer on the substrate. This process is repeated for each additional layer, creating the desired multilayer structure.

[0246] The specific height profile of the fabricated optic is determined by the design process described in previous sections. Numerical simulations, incorporating the desired focal lengths and intensity ratios for the two focal spots, are used to calculate the ideal phase profile for the optic. This phase profile is then translated into a discrete height profile by assigning specific heights to different regions of the optic based on the desired phase shifts. The fabrication process then creates the structure with these specified heights, realizing the design.

[0247] The atomic force micrograph (AFM) image in FIG. 16 demonstrates the precise control over layer thicknesses achievable with the fabrication process. The relatively uniform height of each layer and the sharp transitions between layers indicate accurate pattern transfer and precise material deposition. This precision is crucial for achieving the desired optical performance, ensuring that the fabricated optic closely matches the designed phase profile and exhibits the desired multi-focus functionality. Alternative fabrication methods, such as subtractive etching techniques, could also be employed to create this multilayer structure. The choice between additive and subtractive methods depends on factors such as the desired materials, layer thicknesses, feature sizes, and the overall complexity of the structure.Additionally, the number of layers and the height of each layer can be adjusted to create optics with different functionalities or for operation in different spectral ranges.

[0248] In an embodiment, with reference to FIG. 17, an atomic force micrograph (AFM) image of another section of the same dual-focus optic shown in FIG. 16 is presented, further showing the fabrication of a four-level multilayer structure using the additive lithography process. This image, encompassing a 36 pm x 36 pm area of the optic’s surface, provides a topographical map with varying color intensities representing different heights. The darkest regions correspond to the lowest points on the surface, while the lightest regions represent the highest points, with a color scale indicating the height range from -930.3 nm to -743.9 nm. The image reveals a distinct pattern of parallel stripes, each stripe exhibiting a relatively uniform height. These stripes correspond to the four different layers of the multilayer structure, confirming the successful fabrication of the desired height profile. The pixelation reflects the discrete nature of the fabrication process. The pixel size defines the smallest designed feature size on the optic’s surface. This image indicates the uniformity and reproducibility of the fabrication process across the entire optic’s surface. The consistency in layer heights and the clear delineation between layers indicate accurate pattern transfer and precise material deposition. This level of precision provides the desired optical performance, ensuring that the fabricated optic closely matches the designed phase profile and exhibits the intended multi-focus functionality.

[0249] The fabrication process employs a combination of lithography, deposition, and etching techniques to create these four layers. A photosensitive or electron-sensitive resist is spun onto the substrate, and a pattern is transferred onto the resist using either photolithography or electron beam lithography. A material, such as gold or a multilayer coating, is then deposited, covering both the resist and exposed substrate areas. The resist and the material deposited on top of it are then removed, leaving behind the patterned layer on the substrate. This process is repeated for each additional layer, creating the desired multilayer structure. The specific height profile of the fabricated optic is determined by the design process described in previous sections. Numerical simulations, incorporating the desired focal lengths and intensity ratios for the two focal spots, are used to calculate the ideal phase profile for the optic. This phase profile is then translated into a discrete height profile by assigning specificheights to different regions of the optic based on the desired phase shifts. The fabrication process then creates the structure with these specified heights, physically realizing the design.

[0250] The methods described above provide the design and fabrication of a wide array of novel and useful optics, including diagnostic optics, multilayer gratings, dual-grating beamsplitters, and multi-focus optics. These optics offer enhanced performance and unique capabilities compared to conventional optics, providing advancements in various fields, such as microscopy, spectroscopy, lithography, and optical communications.

[0251] A diagnostic optic is designed to provide information about the properties of a light beam, such as its intensity profile, spatial distribution, and spectral content. It can be implemented in both transmission and reflection modes, depending on the wavelength range and the desired functionality. An example of a diagnostic optic is shown in FIG. 18, embodied as a combination of a zoneplate and a grating fabricated on a reflective substrate. The zoneplate focuses a portion of the incident beam to produce an image of the beam at or near its focus, while the grating diffracts another portion of the beam, potentially dispersing it spectrally to reveal its wavelength composition. By adjusting the duty cycle of the grating and the phase shift or amplitude change introduced by the diffractive structures, the intensity of the unaltered beam and the focused beams can be controlled.

[0252] A multilayer grating is a diffraction grating that uses multiple layers of materials with different optical properties to achieve a desired phase or amplitude response as a function of wavelength. This multilayer structure provides the design of high-efficiency gratings with a wider bandwidth than achievable with conventional gratings fabricated from a single material. The varying thicknesses of the layers in the multilayer stackup create a spatially varying phase or amplitude profile along the grating structure, providing for precise control over the diffraction angles and efficiencies for different wavelengths. This capability provides the creation of, for example, achromatic gratings that diffract multiple wavelengths at the same angle or spectrally selective gratings that enhance or suppress diffraction for specific wavelength ranges.

[0253] A dual-grating beamsplitter efficiently splits an incident beam of light into two or more components with minimal loss and spectral distortion. It can include a beam-splitting grating and a spectral collimation grating, fabricated on individual substrates and affixed to a common fixture. The beam-splitting grating divides the incident beam into multiple orders, e.g. a zeroth order and a first order, with a controllable intensity ratio determined by the grating’s phase or amplitude profile. The spectral collimation grating then diffracts one of the diffracted orders, compensating for its spectral dispersion and creating a spectrally collimated output beam. This arrangement ensures that the reference beam and the primary beam exhibit minimal relative instability in terms of intensity, position, and spectral content, for applications requiring stable and reliable beam splitting.

[0254] A multi-focus optic is designed to generate multiple focal spots from a single incident beam, providing parallel processing or simultaneous illumination of multiple points. It can be implemented in various forms, including simple multi-focus optics, beam shaping multi-focus optics, 0AM multi-focus optics, and spectral control multi-focus optics. Simple multi-focus optics can use multiple zoneplates or other diffractive structures to create multiple focal spots with controlled spacing and intensity ratios. Beam shaping multi-focus optics can create focal spots with different beam profiles, such as circular, square, or those with hard or soft edges, providing tailored illumination patterns for applications like lithography or optical trapping. 0AM multifocus optics generate focal spots with different orbital angular momentum (0AM) content, providing advanced light manipulation techniques in areas like optical tweezers or high-resolution microscopy. Spectral control multi-focus optics use multilayer structures to focus different spectral components of the incident beam to different locations, providing functionalities like multi-wavelength microscopy or polarization-sensitive imaging.

[0255] In an embodiment, the multi-beam spatio-spectral-controllable optic is a diagnostic optic configured to produce a plurality of images of an incident beam of light and comprises a substrate, a first diffractive structure on the substrate, the first diffractive structure configured to produce a focused image of at least one spectral component of the incident beam of light, and a second diffractive structure on the substrate, the second diffractive structure configured to diffract a portion of the incidentbeam of light. In an embodiment, the first diffractive structure is a zoneplate. In an embodiment, the second diffractive structure is a grating. In an embodiment, the second diffractive structure is configured to spectrally disperse the diffracted portion of the incident beam of light. In an embodiment, the plurality of images comprises an image of an unaltered portion of the incident beam of light. In an embodiment, the first diffractive structure and second diffractive structure are configured to leave a portion of the incident beam of light unaltered. In an embodiment, the first diffractive structure is configured to produce an in-focus image of the at least one spectral component of the incident beam of light. In an embodiment, the first diffractive structure is further configured to produce at least one out-of-focus image of the at least one spectral component of the incident beam of light. In an embodiment, the substrate is transparent to at least a portion of the incident beam of light.

[0256] Conventional diagnostic tools for characterizing light beams often require multiple separate optics, each performing a specific function, such as focusing, spectral dispersion, or beam splitting. This approach leads to increased complexity, alignment challenges, and potential for instability in the measurements. Furthermore, conventional diagnostic optics often lack the versatility to simultaneously image multiple aspects of the beam, limiting their effectiveness for applications requiring comprehensive beam characterization. The diagnostic optic described herein overcomes these limitations by integrating multiple functionalities within a single compact device, providing efficient and versatile beam diagnostics. It can be appreciated that, without a mirror, this single optical component fabricated with a single lithography step can produce spatially separated images of multiple features of the beam, that are all detectable by a single camera.

[0257] In an embodiment, a diagnostic optic comprises a substrate 214 that serves as the base for the optic and provides mechanical support for the diffractive structures. This substrate can be made from various materials, such as metal, silicon, glass, or a multilayer coating, chosen for their compatibility with fabrication processes and their optical properties at the desired wavelength. The substrate’s surface can be smooth and flat to ensure accurate fabrication and minimize scattering losses. A diagnostic optic comprises a first diffractive structure 216 on the substrate, and the first diffractive structure is configured to produce a focused image of at least onespectral component of the incident beam of light. This diffractive structure can be implemented as a zoneplate, a grating, or a combination of both, depending on the desired functionality. Zoneplates are particularly well-suited for focusing light to a single point or creating multiple focal points. Gratings, on the other hand, diffract light into multiple orders at specific angles, providing spectral dispersion. The first diffractive structure in a diagnostic optic can be designed to focus specific wavelengths or polarization states, providing detailed analysis of the beam’s spectral content. The diagnostic optic can include a second diffractive structure 218 on the substrate, and the second diffractive structure is configured to diffract a portion of the incident beam of light. This second diffractive structure can be implemented as a grating, a Fresnel zone plate, another diffractive element capable of splitting the incident beam, or a combination of these. The duty cycle, phase shift (aka visibility), and orientation of the first and second diffractive structures can be tailored to control the intensity ratio and direction of the diffracted orders. The first diffracted order and second diffracted order can be tailored to diffract a pre-specified amount of the incoming beam. This arrangement provides simultaneous imaging of both the unaltered beam and the diffracted portion, providing a reference measurement that can improve the accuracy and stability of the diagnostic measurements. The diagnostic optic described herein offers several technical advantages. The use of a substrate provides mechanical stability and a base for the precise fabrication of diffractive structures, providing accurate control over the optic’s properties. The first diffractive structure provides focused imaging of specific spectral components, providing for detailed analysis of the beam’s composition. The second diffractive structure provides diffraction of a portion of the incident beam, facilitating simultaneous imaging of both altered and unaltered portions of the beam, providing a reference measurement that enhances diagnostic accuracy and stability.

[0258] A diagnostic optic can include a first diffractive structure that comprises a zoneplate. A zoneplate is a diffractive lens usually consisting of concentric rings or segments of rings with alternating opaque and transparent regions. The spacing of the rings is designed such that light diffracted from different zones interferes constructively at a focal point, providing efficient focusing of light. Zoneplates are advantageous for use with short wavelengths, such as EUV or other SWL where traditional refractive lenses are ineffective due to strong absorption. A diagnostic opticcan include a second diffractive structure that comprises a grating. A grating is a diffractive element consisting of a periodic array of structures, e.g., lines or grooves. When light is incident on a grating, it is diffracted into multiple orders at specific angles, determined by the grating equation. This spectral dispersion property of gratings allows for the separation of different wavelengths within a beam of light. A second diffractive structure can be configured to spectrally disperse the diffracted portion of the incident beam of light. This spectral dispersion provides information about the wavelength composition of the beam, which can be valuable for characterizing light sources or analyzing the spectral response of optical elements.

[0259] The plurality of images produced by a diagnostic optic can include an image of an unaltered portion of the incident beam of light. This unaltered portion serves as a reference, providing for direct comparison between the original beam and the portion that has been diffracted or focused by the optic. A second diffractive structure can be configured to diffract the unaltered portion of the incident beam of light. This allows for the creation of an image of the unaltered beam at a location different from the original beam path, facilitating simultaneous imaging of multiple beam characteristics without overlapping features.

[0260] A diagnostic optic can include a mirror 220 configured to reflect the diffracted portion of the incident beam of light. This mirror provides redirection of the diffracted beam to a different location on the detector, facilitating spatial separation of the different images produced by the optic and providing for more flexible experimental setups. The angle of the mirror can be adjusted to control the position of the reflected beam.

[0261] A first diffractive structure can be configured to produce an in-focus image of at least one spectral component of the incident beam of light. This in-focus image allows for detailed analysis of the spatial profile of the selected spectral component, providing information about the beam’s shape, size, and intensity distribution at the focal point. A first diffractive structure can be further configured to produce at least one out-of-focus image of the at least one spectral component of the incident beam of light. This out-of-focus image, which can be an image of the unaltered beam, can be close enough to the focal point to be detected with the same camera,and provides additional information about the beam’s divergence and wavefront characteristics.

[0262] A diagnostic optic can use a substrate 214 that is transparent to at least a portion of the incident beam of light. This allows for the transmission of a portion of the beam through the optic without being diffracted or reflected, providing the creation of an additional unaltered image of the beam. This is often useful for conducting experiments.

[0263] This diagnostic optic provides a number of technical advantages: A zoneplate for the first diffractive structure provides efficient focusing of light, especially for short wavelengths; a grating for the second diffractive structure provides spectral dispersion, providing information about the wavelength composition of the beam; proper design of the diffractive structures results in spatial separation of the different images without the need for an additional mirror; optionally, a mirror provides additional redirection of the diffracted beam, facilitating additional spatial separation of different images; the ability to produce in-focus, out-of-focus, and unaltered images provides a comprehensive characterization of the beam’s spatial and wavefront properties; and a transparent substrate allows for the transmission of an additional unaltered portion of the beam, which can be used for further measurements. These features combined create a versatile and efficient diagnostic tool for characterizing light beams, providing the simultaneous visualization of multiple beam characteristics and facilitating the optimization of optical systems and the development of advanced optical techniques.

[0264] It can be appreciated that a diagnostic optic is an optical device designed to provide multiple images of an incident beam of light, providing simultaneous visualization and characterization of the beam’s spatial and spectral properties. This capability is particularly valuable for applications requiring precise knowledge of the beam characteristics, such as optimizing beamline performance, diagnosing light sources, and developing advanced optical techniques. The diagnostic optic can be implemented in both transmission and reflection modes, depending on the wavelength range and the desired functionalities. A common approach for designing a diagnostic optic is to combine a zoneplate and a grating on a common substrate, as shown in FIG. 18. The zoneplate, a diffractive lens including concentricrings with alternating opaque and transparent zones, focuses a portion of the incident beam to produce an image of the beam at or near its focus. The grating, a diffractive element with a periodic array of lines or grooves, diffracts another portion of the beam, potentially dispersing it spectrally to reveal its wavelength composition.

[0265] The relative intensities of the focused, spectrally non-dispersed beam and the focused, spectrally dispersed beam can be controlled by adjusting the duty cycle of the grating, which determines the ratio of opaque to transparent regions within the grating structure. A duty cycle of 50% will cause the beam to be completely spectrally dispersed, so the spectrally non-dispersed beam will not appear. A duty cycle higher or lower than 50% will cause the spectrally non-dispersed beam to appear. The relative intensities of the unaltered beam and the focused beams can be controlled by adjusting the diffraction efficiency of the physical structure performing the diffraction, by imparting less than a full 180deg phase shift. A 180deg phase shift will cause the full intensity to be in the focused beams (the unaltered beam will have essentially no brightness). This flexibility allows for tailoring the diagnostic optic to specific measurement requirements, emphasizing either the spatial or spectral characteristics of the beam.

[0266] The XOR operation is commonly used to combine the zoneplate and grating patterns within the diagnostic optic. This logical operation ensures that only one phase shift (either 0 or IT) is imparted on the incident light at each point on the optic, preserving the high diffraction efficiency of the zoneplate while incorporating the spectral dispersion capability of the grating.

[0267] Experimental results obtained using a fabricated diagnostic optic with a grating duty cycle that is not 50% are shown in FIG. 20. The image reveals three distinct features: a focused, spectrally dispersed beam; an unaltered portion of the incident beam; a focused, spectrally non-dispersed beam that is displaced from the unaltered beam due to the structure and alignment of the optic. This demonstrates the versatility of the diagnostic optic in characterizing light beams, providing simultaneous visualization of multiple beam characteristics, including spectral content, spatial profile, and wavefront properties.

[0268] Experimental results obtained using a fabricated diagnostic optic with a 50% grating duty cycle are shown in FIG. 21. The image shows the absence of a focused, spectrally non-dispersed beam as well as a different ratio of amplitudes between the unaltered beam and focused, spectrally dispersed beam; these indicate the tunability of the optic to different experimental requirements, as well as the optic’s ability to provide both spatial and spectral information about the incident beam.

[0269] Alternative designs for diagnostic optics can incorporate multiple gratings with different orientations, duty cycles or periods, providing spectral dispersion in multiple directions or with varying resolution. Additionally, the optic could be fabricated using multilayer or waveguiding structures to handle multiple wavelengths or polarization states, providing a more comprehensive and detailed analysis of the incident beam. The diagnostic optic, by integrating multiple functionalities within a single compact device, offers a powerful tool for characterizing light beams. Its ability to produce multiple images with distinct properties provides the simultaneous visualization of spatial and spectral information, facilitating the optimization of optical systems, the diagnosis of light sources, and the development of advanced optical techniques.

[0270] The diagnostic optic could be designed to operate either in reflectionmode or transmission-mode such that the optic is configured to have this effect on a beam that is reflected from the optic or transmitted through it. This can be designed as described below, designed for two or more discrete spectral components using the truth table approach, or designed using the general approach to be effective for a wider range of spectral content.

[0271] The diagnostic optic produces an image of an unaltered beam as well as one or more images of the beam at or through the focus, and might also spectrally disperse one or more of the focused / focusing beams.

[0272] The design procedure for the simplest form of such an optic, shown in FIG. 18, results from interfering a zoneplate optic with a grating. If it is desired to produce the optic in one lithographic step, this interference can be computed as an XOR operation between the zoneplate and the grating. The visibility of the optic (what phase shift the structures give relative to the substrate) sets the power of the unalteredbeam. A IT phase (100% visibility) sets the unaltered beam to have zero power. A 0 phase sets the unaltered beam to have full power. The duty cycle of the grating sets the power of the focused, spectrally undispersed beam (shown dimly in the center of the fourth column focal image) relative to the focused, spectrally dispersed beam. If the optic has IT phase, then a duty cycle of 50% gives this beam no brightness while duty cycles of 0% or 100% give this beam full brightness.

[0273] FIG. 18 shows how to design such an optic, wherein the different columns represent different designs of the diffractive optic. The top row shows the optic designs and the bottom row shows what the focus would look like for each. Note that only one wavelength is present in this simulation. If multiple wavelengths were present, then the spots at the far left and right of most of the focus images will be located at different positions for the different wavelengths, forming spectra.

[0274] In an embodiment, with reference to FIG. 18, the design process for a diagnostic optic is shown, showing the optic’s pattern, functionality, and resulting focal image. The figure presents a series of five columns, each representing a different design variation of the diagnostic optic. The first two columns show components of the diagnostic optic, but do not by themselves exhibit as much functionality as a diagnostic optic. The top row depicts the optic’s design pattern, while the bottom row shows the corresponding simulated focal image. The first column shows a zoneplate, a diffractive optic that focuses light to a single point. The corresponding focal image shows a single bright spot, representing the focused light. The second column illustrates a grating with a 50% duty cycle and near-pi phase shift, a structure that diffracts light into multiple orders. The accompanying image depicts the result of shining a beam from this grating, showing a very dim central, spectrally undispersed spot flanked by two spectrally dispersed spots. Since the beam is not focusing prior to the grating and there is no focusing structure on the optic, the beams are all large. The remaining three columns show the diagnostic optic design, created by combining the zoneplate and grating patterns using an XOR operation. The third column depicts a diagnostic optic with a 50% visibility, where white regions represent areas that impart a IT phase shift and black regions represent areas with 0 phase shift. The corresponding focal image shows two bright spots, each representing a focused, spectrally dispersed beam. Since the white regions are configured to impart a IT phase shift relative to theblack regions, the unaltered beam has no intensity. Since the duty cycle of the grating is 50%, the focused, spectrally undispersed, focused beam has no intensity. The fourth column illustrates a diagnostic optic with a 40% grating duty cycle (i.e., the width of some lines is greater than others), resulting in a different intensity distribution between the spectrally dispersed and spectrally undispersed, focused spots in the corresponding focal image. The spectrally un-dispersed spot appears fainter compared to the spectrally dispersed spots due to the 40% duty cycle of the grating. If the grating had a 10% duty cycle, the spectrally undispersed spot would appear brighter relative to the spectrally dispersed spots. The fifth column shows a diagnostic optic with a 10% grating visibility (i.e., pi / 10 phase shift of the white structures relative to the dark structures) and 40% duty cycle. In this design, the grating pattern is barely visible, resulting in fainter focused spots in the corresponding focal image. As a result, the unaltered beam has approximately the same brightness as the focused beams. This design process for the diagnostic optic indicates the flexibility in tailoring its functionality by adjusting the visibility or duty cycle of the grating. A higher grating visibility leads to a stronger diffracted beam, enhancing the intensity of the focused spots, while a lower visibility favors the unaltered beam. A 50% duty cycle enhances the intensity of the focused, spectrally dispersed beams relative to the focused, spectrally non-dispersed beam. The choice of visibility and duty cycle depends on the desired balance between these three components in the diagnostic image.

[0275] Alternative designs can be implemented by varying the orientation and periodicity of the grating. For instance, a grating oriented perpendicular to the zoneplate rings would disperse the light in a different direction. The grating period can be adjusted to control the angular separation between the diffracted orders, providing customization of the diagnostic image for different spectral ranges. The XOR operation used to combine the zoneplate and grating patterns ensures that only one phase shift (either 0 or IT) is imparted on the incident light at each point on the optic. This approach preserves the high diffraction efficiency of the zoneplate while incorporating the spectral dispersion capability of the grating, providing the creation of a compact and efficient diagnostic optic. Furthermore, the design can be extended to handle wider bandwidths by incorporating multilayer structures. By selecting the materials and thicknesses of the layers, the optic can be designed to focus and disperse different wavelengths independently, providing more comprehensive spectral information.

[0276] In an embodiment, with reference to FIG. 20, experimental results obtained using a fabricated diagnostic optic with a grating duty cycle that is not 50% are presented, demonstrating the optic’s ability to produce multiple images of an incident beam with distinct functionalities. The figure shows a color-coded image of the beam pattern at the detector plane, where different colors represent varying intensities of light. The blue background represents low intensity, while colors ranging green to yellow to red, indicate increasing intensity. The image reveals four distinct features, each corresponding to a specific function of the diagnostic optic. Features 224.4c, located at the bottom of the image and enclosed in dashed ovals, represent a pair of focused, spectrally dispersed beams. There are two dashed ovals, one each for the first and second diffracted orders of the grating. The second diffracted order (the bottom oval) exhibits stronger spectral separation. This feature appears as a series of vertically aligned spots, each spot corresponding to a different wavelength within the incident beam. The vertical alignment indicates spectral dispersion in the vertical direction, where different wavelengths are deflected at different angles by the grating structure of the diagnostic optic. Feature 224.4. b, located in the middle of the image and indicated by a solid black arrow and a dashed circle, represents focused, spectrally non-dispersed beam. This feature appears as a bright, spectrally nondispersed spot, indicating that the duty cycle of the grating is not exactly 50%. Feature 224.4. a, located to the right of 224.4. b, represents an unaltered beam. This feature appears as a bright, non-dispersed spot indicating that a portion of the incident light reflects from the optic without being diffracted or focused. This feature is in a different location than 224.4. b due to the design and alignment of the diagnostic optic. An advantage of the diagnostic optic is that these beams are all present and in different locations, even without the need for an additional mirror.

[0277] This diagnostic optic, by incorporating both a zoneplate and a grating, provides simultaneous imaging of multiple aspects of the incident beam. The zoneplate focuses the light to create focused images, while the grating diffracts a portion of the light, introducing spectral dispersion. The relative intensity of the dispersed and non-dispersed beams can be adjusted by controlling the duty cycle of the grating. A duty cycle of 50% would result in equal intensities for the dispersed and non-dispersed beams, while a duty cycle different from 50% creates an imbalance, as demonstrated in this figure. A visibility of 100% (i.e., diffractive structures imparting api phase shift relative to the substrate) would result in all of the intensity being in the focused beams, while a visibility of less than 100% would result in an image of the unaltered beam also. Alternative designs could employ multiple gratings with different orientations or periods, providing spectral dispersion in multiple directions or with varying resolution. Additionally, the optic could be fabricated using multilayer structures to handle multiple wavelengths or polarization states, providing a more comprehensive analysis of the incident beam.

[0278] FIG. 20 indicates the versatility and functionality of a diagnostic optic in characterizing light beams, providing the simultaneous visualization of spatial and spectral information. This capability can be valuable for optimizing beamline performance, diagnosing light sources, and developing advanced optical techniques requiring precise knowledge of the beam’s properties.

[0279] In an embodiment, with reference to FIG. 21 , experimental results obtained using a fabricated diagnostic optic with a grating duty cycle of 50% and a low visibility are presented, showing the optic’s ability to produce multiple images of an incident beam with distinct functionalities. The figure displays a color-coded image of the beam pattern at the detector plane, where different colors represent varying intensities of light. The dark blue background represents low intensity, while the brighter colors, transitioning from green to yellow to red, indicate increasing intensity. FIG. 21 reveals distinct features, each corresponding to a specific function of the diagnostic optic. The central feature, labeled as “Unfocused beam,” represents an unaltered portion of the incident beam. This feature appears as a large, bright circular spot, indicating that a significant portion of the incident light reflects from the optic without being diffracted or focused. The large, circular shape confirm that this portion of the beam retains its original spatial profile. The feature on the left side of the image, labeled as “Spectrally dispersed focused beam,” represents a portion of the incident beam that has been both focused and spectrally dispersed (the +1 order of the grating). This feature appears as a series of horizontally aligned spots, each spot corresponding to a different wavelength within the incident beam. The horizontal alignment indicates spectral dispersion in the horizontal direction, where different wavelengths are deflected at different angles by the grating structure of the diagnostic optic. The relatively small size of each spot indicates focusing, where the zoneplatestructure of the diagnostic optic concentrates light of each wavelength to a distinct focal point. The feature on the right side of the image, labeled as “Spectrally dispersed focused beam,” represents another portion of the incident beam that has been both focused and spectrally dispersed (the -1 order of the grating). This feature exhibits a similar horizontal alignment of spots as the feature on the left, indicating spectral dispersion. However, this feature is positioned at a different location on the detector, reflecting a different diffraction angle introduced by the grating. The relative positions of the two spectrally dispersed focused beams can be adjusted by changing the orientation or period of the grating structure within the diagnostic optic.

[0280] This diagnostic optic, by incorporating both a zoneplate and a grating with a 50% duty cycle, provides the simultaneous visualization of both the unaltered beam and the focused, spectrally dispersed beam. The 50% duty cycle ensures that the focused, spectrally non-dispersed beam is not present and will not interfere with the unaltered beam. The balance between the two spectrally dispersed, focused beams and the unaltered beam allows for a comprehensive characterization of the incident beam, providing information about both its spatial profile and its spectral composition. Alternative designs could incorporate multiple gratings with different orientations or periods, providing spectral dispersion in multiple directions or with varying resolution. Furthermore, the optic could be fabricated using multilayer structures to handle multiple wavelengths or polarization states, providing a more comprehensive analysis of the incident beam. FIG. 21 demonstrates the effectiveness of a diagnostic optic in characterizing light beams, showing its ability to generate multiple images with distinct functionalities. This capability is useful for optimizing beamline performance, diagnosing light sources, and developing advanced optical techniques that involve precise knowledge of the beam’s spatial and spectral properties.

[0281] In an embodiment, the multi-beam spatio-spectral-controllable optic is a multi-layer grating that is configured to diffract an incident beam of light and comprises a substrate and a plurality of grating structures on the substrate, each grating structure comprising a stackup of at least two layers of differing material composition, wherein a thickness of at least one layer of the stackup varies along a length of the grating structure. In an embodiment, the grating structure is configuredto impart a pre-determined phase shift and amplitude change that is the same for a spectral range. In an embodiment, the grating structure is configured to impart a predetermined phase shift or amplitude change that varies with at least one spectral component of the incident beam of light. In an embodiment, the pre-determined phase shift or amplitude change is configured to maximize diffraction efficiency for a spectral range. In an embodiment, the pre-determined phase shift or amplitude change is configured to make the diffraction efficiency for a spectral range largely the same, with a particular diffraction efficiency. In an embodiment, the pre-determined phase shift or amplitude change is configured to optimize the diffraction angles such that two separate spectral ranges can be viewed on a more compact detector. In an embodiment, the plurality of grating structures is configured to diffract light having a bandwidth wider than achievable with a single material. In an embodiment, the predetermined phase shift increases from 0 to 2TT along a single period of the grating structure. In an embodiment, the pre-determined phase shift or amplitude change are configured to provide a ratio of v between a first and zeroth order of the diffracted beam of light, with minimal light in other diffracted orders. In an embodiment, a thickness of at least one layer of the stackup is configured to reduce diffraction efficiency for at least one spectral range. In an embodiment, the grating structures are further configured to diffract each wavelength of the incident beam in a pre-specified direction. In an embodiment, the at least one spectral component comprises at least one of: wavelength, polarization, or angle of incidence. In an embodiment, the grating diffracts in multiple directions (e.g., a 2D grating on a rectangular or hexagonal grid). In an embodiment, the layers of the stackup are formed from a material including: metals, dielectrics, and semiconductors.

[0282] Conventional diffraction gratings, which can be fabricated from a single material, often suffer from limited bandwidths that exhibit high diffraction efficiency, particularly for SWL. The diffraction efficiency of most gratings is inherently wavelength-dependent, leading to reduced performance for broadband light sources. Furthermore, conventional gratings offer limited flexibility in tailoring their spectral response, restricting their applicability for specialized functions like spectral filtering. The multi-layer grating described herein overcomes these limitations by employing a multilayer structure that provides precise control over the phase and amplitude ofdiffracted light as a function of wavelength, offering enhanced efficiency, broader bandwidth, and greater design flexibility.

[0283] In an embodiment, a multi-layer grating comprises a substrate 224 that provides mechanical support for the grating structures. This substrate can be made from various materials, such as metal, silicon, glass, or a multilayer coating, chosen for their compatibility with fabrication processes and their optical properties at the desired wavelength. The substrate’s surface can be smooth and flat to ensure accurate fabrication of the grating structures and minimize scattering losses.

[0284] In an embodiment, a multi-layer grating comprises a plurality of grating structures 226 on the substrate, each grating structure comprising a stackup of at least two layers 228, 229 of differing material composition. These grating structures, consisting of structures with a periodic spacing, are responsible for diffracting the incident light. The multilayer stackup within each grating structure provides the creation of a complex phase or amplitude profile along a length of the grating by exploiting the interaction of light with the different layers. By selecting the materials and thicknesses of the layers, the grating can be designed to exhibit specific diffraction properties for different wavelengths.

[0285] A thickness or composition of at least one layer of the stackup varies along a length of the grating structure, and the grating structure is configured to impart a pre-determined phase shift or amplitude change that can vary with at least one spectral component of the incident beam of light. This varying thickness or composition, achieved through precise fabrication techniques like grayscale lithography or multi-step lithography, creates a spatially varying phase or amplitude profile along the grating structure. This allows for tailored control over the diffraction angles and efficiencies for different wavelengths, providing the design of gratings with specific functionalities.

[0286] The multi-layer grating offers several technical advantages. The use of a substrate provides mechanical stability and a base for the accurate fabrication of the grating structures. The multilayer stackup within each grating structure allows for the creation of a complex phase or amplitude profile, providing precise control over the diffraction properties for different wavelengths. The varying thickness orcomposition of at least one layer further enhances this control, providing the design of gratings with tailored spectral responses, such as enhanced diffraction efficiency over a wider bandwidth or optimized diffraction angles for two separate spectral ranges. These features combined create a versatile and efficient diffractive optic capable of manipulating light across a broad range of wavelengths with high precision.

[0287] A multi-layer grating can be configured such that the plurality of grating structures 226 are designed to diffract light having a bandwidth wider than achievable with a single material. This broader bandwidth for high diffraction efficiency stems from the ability of the multilayer structure to control the phase response for different wavelengths independently. Conventional gratings, made from a single material, can exhibit high efficiency only over a narrow range of wavelengths, limiting their applicability for broadband light sources. The multilayer grating, by tailoring the phase or amplitude profile through the varying thicknesses and compositions of its layers, can achieve high diffraction efficiency over a much broader range of wavelengths, providing more efficient and versatile light manipulation.

[0288] A multi-layer grating can be configured such that the pre-determined phase shift increases from 0 to 2TT along a single period of the grating structure 226. This linear phase profile creates a blazed grating, where most of the incident light is diffracted into a single order, maximizing diffraction efficiency for the chosen wavelength. This type of grating can be used in applications involving high throughput, such as monochromators or spectrometers.

[0289] A multi-layer grating can be configured such that the pre-determined phase shift is designed to provide a specific ratio of v between a first and zeroth order of the diffracted beam of light, and minimize the amount of light in unwanted diffracted orders. This can require configuring the phase profile and amplitude profile of the multilayer grating. This capability allows for the creation of beamsplitters with controlled intensity ratios between the different diffracted orders. By adjusting the phase or amplitude profile of the grating structure, the designer can determine the fraction of light diffracted into each order, providing the creation of beamsplitters with various splitting ratios, such as 50 / 50, 25 / 75, or any other desired ratio.

[0290] A multi-layer grating can be configured with a thickness of at least one layer of the stackup 228, 229 specifically designed to reduce diffraction efficiency for at least one spectral range. This functionality provides the creation of spectral filters that selectively block or attenuate certain wavelengths while transmitting others. By choosing the materials and thicknesses of the layers, the designer can create a filter that exhibits high transmission for desired wavelengths while exhibiting low transmission for unwanted wavelengths. This can be valuable for applications like fluorescence microscopy, where excitation light needs to be filtered out to enhance the signal from the emitted fluorescence.

[0291] A multi-layer grating can be configured such that the grating structures 226 are designed to diffract each wavelength of the incident beam in a prespecified direction. This capability provides the creation of gratings that can separate and direct different wavelengths to different locations, potentially enhancing the efficiency and versatility of spectroscopic measurements or optical communication systems. Specifically, this can provide an even spacing between wavelengths, as opposed to the uneven spacing between wavelengths that is usually the case when diffracted by a simple grating.

[0292] A multi-layer grating can be designed to control at least one spectral component, which can encompass wavelength, polarization, or angle of incidence. This versatility stems from the ability of the multilayer structure to manipulate light based on various parameters. The thickness and composition of the layers can be tailored to achieve desired phase shifts or amplitude changes for specific wavelengths, polarizations, or angles of incidence, providing the creation of optics with diverse functionalities.

[0293] A multi-layer grating can employ a stackup of layers formed from various materials, including metals, alloys, dielectrics, and semiconductors. The choice of materials depends on the desired spectral range and the desired optical properties. For visible wavelengths, metals can be used for high reflectivity, while dielectrics offer low absorption and can be used for anti-reflection coatings or to create interference effects. Semiconductors can be used for their unique optical properties, such as their ability to change their refractive index with applied voltage or light intensity. Alloying materials allows for tailoring of the optical properties for a specificapplication. For shorter wavelengths like EUV and SXR, reflectivity is usually determined by the wavelength’s proximity to atomic absorption edges of the constituent elements within the material rather than whether that material is a metal, dielectric, etc.

[0294] The multilayer grating provides the technical advantages of broader bandwidth for high diffraction efficiency providing versatile light manipulation, blazed grating profile for maximum efficiency in a single order, specific splitting ratios for beamsplitter applications, spectral filtering capabilities for selective wavelength control, and directional diffraction for spatial separation of wavelengths. These features, combined with the flexibility in material selection, offer a powerful tool for creating high-performance gratings with tailored spectral responses, exceeding the capabilities of conventional single-material gratings and expanding the possibilities for advanced optical applications.

[0295] Further, a multi-layer grating can be a specialized diffraction grating that uses multiple layers of materials with varying optical properties to achieve a controllable phase-versus-wavelength response, providing enhanced functionality and performance compared to conventional single-material gratings. This multilayer structure, which can be fabricated using techniques like those described in the “Fabrication” section, provides precise tailoring of the grating’s diffraction properties, providing the creation of optics with specific spectral characteristics. The multilayer grating can include a substrate 224 that provides mechanical support for the grating structures. This substrate can be fabricated from various materials, such as silicon, glass, or a multilayer coating, chosen for their compatibility with fabrication processes and their optical properties at the desired wavelength. The substrate’s surface can be smooth and flat to ensure accurate fabrication of the grating structures and minimize scattering losses.

[0296] For the plurality of grating structures 226 disposed on the substrate, each grating structure, consisting of a periodic array of structures, e.g., lines, shapes or grooves, diffracts light into multiple orders at specific angles, determined by the grating equation. However, unlike conventional gratings, each grating structure in a multilayer grating can include a stackup of at least two layers 228, 229 of differingmaterial composition. This multilayer stackup provides precise control over the phase shift or amplitude change imparted on the diffracted light as a function of wavelength.

[0297] The thickness of at least one layer within the stackup varies along the length of the grating structure. This variation in layer thickness, achieved through precise fabrication techniques like grayscale lithography or multi-step lithography, creates a spatially varying phase profile along the grating structure, providing for tailored control over the diffraction angles and efficiencies for different wavelengths. This capability provides the design of gratings with unique functionalities, such as enhanced diffraction efficiency over a wider bandwidth.

[0298] The pre-determined phase shift or amplitude change imparted by the grating structure can be configured to achieve specific functionalities. For instance, by designing the phase shift to increase linearly from 0 to 2TT along a single period of the grating structure, a blazed grating can be created, maximizing diffraction efficiency into a single order. Alternatively, the phase shift or amplitude change can be tailored to provide a specific ratio between the intensities of different diffracted orders, providing the creation of beamsplitters with controlled splitting ratios.

[0299] Furthermore, the thickness of at least one layer within the stackup can be adjusted to reduce diffraction efficiency for specific spectral ranges, providing the creation of spectral filters that selectively block or attenuate unwanted wavelengths. The grating structures can also be configured to diffract each wavelength of the incident beam in a pre-specified direction, providing for spatial separation and manipulation of different wavelengths.

[0300] The multilayer grating offers a versatile and powerful tool for manipulating light across a broad range of wavelengths, exceeding the capabilities of conventional single-material gratings. Its ability to control the phase and amplitude response for different wavelengths independently provides the creation of optics with tailored spectral characteristics and enhanced performance, opening up new possibilities for applications in microscopy, spectroscopy, lithography, and optical communications.

[0301] The multilayer grating can operate in a reflection-mode geometry, though there might be certain wavelengths for which a transmission-mode geometrymight be efficacious. The multilayer grating can be designed as described below, designed for two or more discrete spectral components using the truth table approach, or designed using the general approach to be effective for a wider range of spectral content.

[0302] Multi-layer stackups can provide controllable phase-versus- wavelength, phase-vs-photon energy, or controllable phase-vs-spectral-component. An immediate consequence of this is the design of high-efficiency gratings with a wider bandwidth than is conventionally achievable in the SWL regime. By designing stacks to provide phase-versus-wavelength curves at a series of values between 0 and 2*TT, the cross section shown in FIG. 23 can be arrived at.

[0303] In an embodiment, with reference to FIG. 23, a cross-sectional view of a multilayer grating structure designed to provide a controllable phase-versus- wavelength response is shown. The grating structure includes a repeating pattern of ridges, each ridge composed of a stackup of two layers with varying thicknesses. The bottom layer, represented by the darker gray region, can be composed of a material like gold, chosen for its high reflectivity at the desired wavelength range. The top layer, represented by the lighter gray region, might be fabricated from a material such as aluminum, which has low absorption and a significant material phase shift in a specific energy range. The thickness of both the top and bottom layers increases progressively from left to right across the figure, corresponding to a gradual increase in the desired phase shift imparted on the reflected light. This structure exemplifies a blazed grating, where the phase shift introduced by the structure increases linearly from 0 to 2rm along a single period of the grating. This linear phase profile maximizes the diffraction efficiency into a single order, which can be the first order for n=1 , concentrating most of the reflected light into a specific direction. The varying thicknesses of the top and bottom layers contribute to the overall phase shift through both the geometric and material phases.

[0304] This design is tailored to achieve high diffraction efficiency for a specific wavelength range, but alternative designs can be implemented to achieve different spectral responses. For example, the thickness variation could be designed to create a non-linear phase profile, providing the diffraction into multiple orders; alternatively, the amplitude can be tailored to create spectral filters that selectivelyblock or attenuate certain wavelengths. Additionally, the number of layers in the stackup can be increased beyond two, providing even finer control over the phase or amplitude response and providing the creation of more complex spectral profiles.

[0305] The choice of materials for the top and bottom layers can be varied based on the desired wavelength range and the optical properties of the materials. For instance, in the EUV range, materials like silicon, molybdenum, or titanium could be used instead of aluminum for the top layer. Similarly, materials like platinum, palladium, or nickel could be used for the bottom layer, depending on their reflectivity and compatibility with the top layer material.

[0306] The fabrication of this multilayer grating involves precise deposition and patterning techniques. The layers can be deposited using methods like sputtering, evaporation, or chemical vapor deposition, ensuring uniform thickness and smooth interfaces. The desired thickness variations can be achieved using techniques like grayscale lithography or multi-step lithography, where the exposure dose or the number of lithography steps is controlled to create a gradient in the layer thickness.

[0307] This multilayer grating structure, by exploiting the interplay between geometric, material phases, material amplitudes, and waveguiding effects, provides the creation of high-efficiency diffraction gratings with tailored spectral responses. This capability extends beyond the limitations of conventional single-material gratings, opening new possibilities for manipulating light and creating novel optical devices for a wide range of applications.

[0308] In an embodiment, with reference to FIG. 24, a cross-sectional view of a multilayer grating designed to provide controllable phase-versus-wavelength response is shown, indicating the ability to tailor the spectral characteristics of diffracted light using a multilayer structure. The grating consists of a repeating pattern of ridges, each ridge composed of a stackup of layers with varying thicknesses and compositions. The darker gray region at the bottom represents the substrate, which provides mechanical support for the grating structure. The dark regions represent layers of a high-reflectivity material, such as gold. The lighter regions represent layers of a high-reflectivity material with varying thicknesses, potentially composed of the same material as the black regions or a different material, contributing to the overallphase shift through the geometric phase. These regions can be layers of a different material, chosen to impart specific phase shifts or amplitude changes through their material properties, exploiting the material phase.

[0309] The specific design of the multilayer grating depends on the desired spectral response. For instance, to create a high-efficiency grating with a wide bandwidth, the thicknesses and compositions of the layers can be optimized to achieve a relatively flat phase-versus-wavelength response across the desired spectral range. This minimizes the variation in diffraction efficiency for different wavelengths, enhancing efficiency over a broader bandwidth. To create a spectral filter that selectively blocks or attenuates certain wavelengths, the layer thicknesses can be tailored to create destructive interference for those wavelengths. Conversely, to enhance diffraction efficiency for specific wavelengths, the layer thicknesses can be designed to create constructive interference.

[0310] In an embodiment, with reference to FIG. 25, a cross-sectional view of a multilayer grating designed to provide controllable phase-versus-wavelength response is shown, indicating tailoring of the spectral characteristics of diffracted light by using multiple materials and varying layer thicknesses. The grating includes a repeating pattern of ridges, each ridge composed of a stackup of layers with varying thicknesses and compositions. The darker region at the bottom represents the substrate, which provides mechanical support for the grating structure. The dark sloping regions represent layers of a high-reflectivity, opaque material, such as a thick layer of gold, designed to provide a more continuous phase shift. The lightest regions represent layers of a high-reflectivity material that contributes to the overall phase shift or amplitude change. Together, they provide a phase shift that closely resembles the linear 0-to-2pi phase ramp exhibited by an idealized blazed grating, but for a wide bandwidth of spectral components; together with the amplitude change that they also provide, a high efficiency into the desired diffracted order can be designed for wide bandwidths, with little loss into other orders.

[0311] The specific design of the multilayer grating depends on the desired spectral response. To create a high-efficiency grating with a wide bandwidth, the thicknesses and compositions of the layers are optimized to achieve a relatively flat phase-versus-wavelength response across the desired spectral range. This minimizesthe variation in diffraction angle for different wavelengths, enhancing efficiency over a wider bandwidth. To create a spectral filter that selectively blocks or attenuates certain wavelengths, the layer thicknesses can be tailored to create destructive interference for those wavelengths. Conversely, to enhance diffraction efficiency for specific wavelengths, the layer thicknesses can be designed to create constructive interference.

[0312] Furthermore, the spectral content of each order of this grating can be configured. For instance, if it is desired for the grating to have all power go into the first order, then something like a blazed grating can be defined, with the phase for all spectral components increasing linearly from 0 to 2TT over a single period of the grating. If it is desired for the grating to have a first and zeroth order with an intensity ratio v between the first and zeroth order, then the reflectivity for all spectral components can be defined as follows over a period, T:

[0313] In certain instances, it is useful to alter the beam’s spectral content - for instance, a reduced diffraction efficiency at one or more wavelength ranges. Such a feature can be useful to help to calibrate a spectrometer. Spectral selectivity can be achieved by altering the phase or amplitude as described in this document. Using the general approach, one can also design a grating that exhibits different periods for the different spectral components, and therefore diffracts each spectral component in a pre-specified direction.

[0314] In an embodiment, the multi-beam spatio-spectral-controllable optic is a dual-grating beamsplitter that is configured to split an incident beam of light into a primary beam and a reference beam and comprises a first grating configured to diffract the incident beam of light into at least two orders, for instance a zeroth order and a first order; a second grating configured to diffract at least one order of the diffracted beam of light from the first grating; and a fixture, wherein the first grating is on the fixture, and wherein the second grating is on the fixture. In an embodiment, the fixture comprises a single, monolithic piece. In an embodiment, the substrate comprises at least two separate pieces. In an embodiment, the first grating is configured to provide a ratio of v between intensity of the first order and intensity of the zeroth order. In anembodiment, the second grating is configured to diffract a first order of the diffracted beam of light from the first grating. In an embodiment, the dual-grating beamsplitter further comprises a mirror configured to reflect at least one order of the diffracted beam of light from the second grating. In an embodiment, the dual-grating beamsplitter further comprises a mirror configured to reflect at least one order of the beam of light from the first grating. In an embodiment, the zeroth order of the diffracted beam of light from the first grating is the primary beam. In an embodiment, the first order of the diffracted beam of light from the second grating is the reference beam. In an embodiment, the first grating and the second grating are multilayer gratings. In an embodiment, the first grating and the second grating are configured to substantially eliminate spectral dispersion of the reference beam. In an embodiment, the first grating or the second grating is configured also to focus the beam.

[0315] Conventional beamsplitters can have operational limitations such as low efficiency, spectral dispersion of the split beams, and sensitivity to source instability, especially in the SWL spectral region. These drawbacks hinder their use in applications requiring high photon throughput, applications with broadband or unstable beams, or applications requiring precise intensity measurements. The dual-grating beamsplitter described herein addresses these limitations by employing two diffraction gratings in a configuration that provides efficient, spectrally controlled beam splitting with minimal sensitivity to source fluctuations.

[0316] In an embodiment, the dual-grating beamsplitter can include a first grating 234, which can be a primary beam-splitting element. This grating diffracts the incident beam of light into multiple orders. In an embodiment, those two orders include at least a zeroth order and a first order. The zeroth order corresponds to a specularly deflected portion of the beam, while the first order is diffracted at a specific angle determined by the grating equation. The first grating can be implemented as a multilayer grating, a blazed grating, or a conventional grating with a specific phase or amplitude profile, depending on the desired splitting ratio and spectral characteristics. By tailoring the grating’s properties, the intensity ratio between the zeroth and first orders can be controlled, providing the creation of beamsplitters with various splitting ratios.

[0317] In an embodiment, the dual-grating beamsplitter includes a second grating 236, which acts on the light diffracted by the first grating. This second grating can be positioned to intercept one of the diffracted orders from the first grating, and it is configured to diffract this order further. The second grating can also be implemented as a multilayer grating, a blazed grating, or a conventional grating, depending on the desired functionality. By choosing the grating’s properties, such as its period, groove shape, and material composition, the designer can control the direction and spectral content of the output beam.

[0318] The first grating 234 and the second grating 236 can be fabricated on a substrate 238, which provides mechanical support, and attached to a fixture 239 that provides a platform for their precise alignment. The substrate material can be chosen based on its compatibility with the desired wavelength range and the fabrication processes used. The substrate’s surface can be smooth and flat to ensure accurate fabrication and minimize scattering losses. The fixture material can be chosen based on its rigidity, machinability, and vacuum-compatibility. The fixture can be machined precisely to affix the two gratings in a precisely aligned configuration.

[0319] The dual-grating beamsplitter offers several technical advantages. The first grating efficiently splits the incident beam into multiple orders with a controllable intensity ratio. The second grating further diffracts one of the orders, providing precise control over the direction, shape, and spectral content of the output beams. The substrate and fixture provide mechanical stability and facilitate precise alignment of the two gratings, ensuring stable and reproducible beam splitting. These elements combined create a highly efficient and versatile beamsplitter capable of generating spectrally controlled beams with minimal sensitivity to source fluctuations, enhancing the performance and capabilities of various optical systems and experiments.

[0320] In an embodiment, the dual-grating beamsplitter can include a fixture 239 that comprises a single, monolithic piece. This monolithic fixture, along with the substrates on which the gratings are first fabricated, provides a rigid and stable platform for the two gratings, ensuring their precise relative positioning and minimizing any potential for misalignment due to mechanical stresses or thermal expansion. Alternatively, the fixture can comprise at least two separate pieces. This approachallows for greater flexibility in fabrication and assembly, potentially providing the use of different materials or specialized coatings for each grating. The separate pieces can be bonded together or mounted on a common support structure, ensuring accurate alignment and stability.

[0321] In an embodiment, the dual-grating beamsplitter includes a first grating 234 that is configured to provide a specific ratio of v between the intensities of the multiple orders. This ratio, determined by the grating’s phase and amplitude profile, controls the relative power distribution between the primary beam and the reference beam. By adjusting the grating’s design, the splitting ratio can be tailored to specific application requirements. For instance, a 50 / 50 beamsplitter would have v = 1 , while a beamsplitter with a 25 / 75 splitting ratio would have v = 1 / 3.

[0322] In an embodiment, the dual-grating beamsplitter includes a second grating 236 that is configured to diffract a non-zeroth order of the diffracted beam of light from the first grating. This arrangement allows for the spectral collimation of the reference beam, compensating for the wavelength-dependent diffraction angle introduced by the first grating. The second grating can be designed to have all its power diffracted into a single order, ensuring efficient redirection of the reference beam.

[0323] In an embodiment, the dual-grating beamsplitter includes a mirror 240 configured to reflect at least one order of the diffracted beam of light from the second grating. This mirror provides flexible redirection of the output beams, providing for customized beam paths and facilitating integration into existing optical systems. The angle of the mirror can be adjusted to control the direction of the reflected beam, providing precise control over the beam path and the relative positions of the primary and reference beams.

[0324] In an embodiment, the dual-grating beamsplitter includes a mirror 240 configured to reflect at least one order of the diffracted beam of light from the first grating. This mirror provides flexible redirection of the output beams, providing for customized beam paths and facilitating integration into existing optical systems. The angle of the mirror can be adjusted to control the direction of the reflected beam,providing precise control over the beam path and the relative positions of the primary and reference beams.

[0325] In an embodiment, the dual-grating beamsplitter includes the zeroth order of the diffracted beam of light from the first grating 234 as the primary beam. The zeroth order, corresponding to the undeflected portion of the incident beam, can carry the majority of the power and is not spectrally dispersed; in other words, it is spectrally collimated. This makes it suitable for use as the primary beam in applications requiring a high-intensity, spectrally stable beam.

[0326] In an embodiment, the dual-grating beamsplitter uses a non-zeroth order of the diffracted beam of light from the second grating 236 as the reference beam. In an embodiment, this order is the first order. This non-zeroth order, diffracted by both the first and second gratings, is spectrally collimated by the second grating, ensuring minimal spectral dispersion. This makes it suitable for use as a reference beam for monitoring source intensity or for other applications requiring a spectrally stable beam. In an embodiment, the second grating also is a zoneplate that focuses the light, forming a resolved spectrum. In an embodiment, the second grating is configured to diffract the wavelengths at particular angles to overlap at a predetermined point. In an embodiment, the second grating also is a zoneplate that focuses the light, forming a series of beams, one per wavelength, that are focusing and overlap at a point. In an embodiment, the In an embodiment, the first grating is also a zoneplate that focuses the light (for instance onto a sample).

[0327] In an embodiment, the dual-grating beamsplitter uses a non-zeroth order of the diffracted beam of light from the second grating 236 as the reference beam. In an embodiment, this order is the first order. This non-zeroth order, diffracted by both the first and second gratings, is designed to have a particular spectral divergence. This makes it suitable for use as a reference beam for monitoring source intensity or for other applications requiring a spectrally stable beam. In an embodiment, the second grating also is a zoneplate that focuses the light, forming a resolved spectrum. In an embodiment, the first grating is also a zoneplate that focuses the light (for instance onto a sample).

[0328] In an embodiment, the dual-grating beamsplitter includes multilayer gratings for both the first and second gratings. Multilayer gratings, as described previously, offer advantages in terms of bandwidth, efficiency, and spectral control compared to conventional single-material gratings. This arrangement provides the creation of a highly efficient and versatile beamsplitter with precise control over the spectral characteristics of both the primary and reference beams.

[0329] In an embodiment, the dual-grating beamsplitter includes the first grating 234 and the second grating 236 that are configured to substantially eliminate spectral dispersion of the reference beam. This is achieved by selecting the grating parameters, such as the period, groove shape, and incidence angles, to minimize the wavelength-dependent diffraction angle of the reference beam. This spectral collimation ensures that the reference beam maintains a consistent spectral profile, even for broadband light sources, providing accurate intensity monitoring and improving the stability of optical measurements.

[0330] The dual-grating beamsplitter provides several technical advantages. The monolithic fixture minimizes misalignment, while a multi-piece fixture offers flexibility in fabrication and material selection. The first grating provides a controllable intensity ratio between the primary and reference beams, providing tailored splitting ratios. The second grating spectrally collimates the reference beam, ensuring minimal spectral dispersion. The mirror provides flexible redirection of the output beams for customized beam paths. The use of the zeroth order as the primary beam ensures high intensity and spectral stability. The use of the first order as the reference beam, combined with spectral collimation by the second grating, minimizes spectral dispersion for a stable reference measurement. Using multilayer gratings for both the first and second gratings enhances bandwidth, efficiency, and spectral control. These features, combined, create a highly efficient and versatile beamsplitter capable of generating spectrally stable beams, improving the performance and capabilities of various optical systems and experiments.

[0331] It is contemplated that, to be maximally useful within some preexisting experiments or apparatuses, the dual-grating beamsplitter is designed to minimize spectral dispersion of the reference beam. This is accomplished by selecting the grating parameters, including their periods, groove shapes, and incidence angles,to compensate for the wavelength-dependent diffraction introduced by the first grating. Spectral collimation ensures a spectrally stable reference beam, even for broadband light sources, providing accurate intensity monitoring and improving the stability of optical measurements. The dual-grating beamsplitter, by combining two diffraction gratings in a designed configuration, provides a robust and versatile tool for splitting light beams. Its ability to control both the intensity ratio and spectral content of the output beams makes it suitable for a wide range of applications, including spectroscopy, ref lectom etry, interferometry, and optical metrology, where precise and stable beam splitting is essential.

[0332] The dual-grating beamsplitter can be operated in transmission-mode or in a reflection-mode geometry. There are many applications in which it is useful to split a light beam into multiple components. For instance, producing a second beam (reference beam) to monitor the intensity of a source while using the primary beam to measure a sample is a common technique that dramatically improves the signal to noise ratio of many optical measurements. Here, the reference beam and the primary beam exhibit no relative instability. Splitting an SWL beam in a manner that is efficient, versatile, and insensitive to the instability of the source has no known conventional solution. The instability of these sources might manifest as small fluctuations in beam position, beam pointing, intensity, shape, or spectrum. For instance, narrowband EUV sources that nominally produce a sharp 13 nm wavelength spectral emission might produce 13 nm for a few milliseconds, and then produce a 13.1 nm spectral emission, which can impact the relative intensity of the primary and reference beams produced by conventional beamsplitters. Some practitioners use a single grating for this application, using the first order as the reference beam and the zeroth as the primary beam. This does not work well in all geometries because the reference beam is spectrally dispersing. Advantageously, the dual-grating beamsplitter does not exhibit relative instability between the primary beam and the reference beam and can be configured to minimize spectral dispersion of each beam.

[0333] In an embodiment, the dual-grating beamsplitter produces two beams (reference beam and primary beam) with pre-specified power and propagation angle. Other useful configurations can produce more beams or provide control of otheroptical characteristics such as altering the wavelength, polarization, focusing, or 0AM content of the beams.

[0334] In an embodiment, with reference to FIG. 26, various configurations of a dual-grating beamsplitter designed to split an incident beam of light into a primary beam and a reference beam are shown. Each configuration employs two gratings arranged, and the purple lines represent the path of the incident beam and the resulting split beams. The gray lines represent the orientation of the grating substrates. The top left configuration shows a design where both the primary beam and the reference beam are parallel to the input beam. This is achieved by using a mirror, represented by the orange line, to reflect the primary beam after it is diffracted by the second grating. This arrangement can be advantageous for applications requiring parallel beam paths, simplifying the experimental setup and facilitating integration into existing optical systems. However, mirrors can introduce losses due to reflection, potentially reducing the overall efficiency of the beamsplitter. The bottom left and bottom right configurations depict designs where the primary beam and the reference beam are not parallel to the input beam. These configurations omit the mirror, maximizing photon efficiency by using direct diffraction from the gratings to create the output beams. The angles between the input beam, primary beam, and reference beam can be adjusted by varying the periods and orientations of the two gratings, offering flexibility in tailoring the beam paths to specific experimental requirements. For instance, the configuration shown in the bottom right could be configured to make the reference beam parallel to the input beam. The top right configuration of the dualgrating beamsplitter creates multiple output beams. By adjusting the design of the gratings, more than two beams can be generated, providing functionalities like multichannel spectroscopy or parallel processing of multiple wavelengths.

[0335] The first grating in the dual-grating beamsplitter, referred to as the beam-splitting grating, is designed to diffract the incident beam into at least two orders, for instance a zeroth order and a first order, with a controllable intensity ratio between the two orders. This intensity ratio, denoted as v, can be adjusted by tailoring the phase or amplitude profile of the grating. The phase and amplitude profile are determined by the shape and depth of the grating grooves and lines, as well as the material properties of the grating grooves and lines. The second grating, referred to as the spectralcollimation grating, diffracts one of the orders from the first grating, can be the first order, and is usually designed to minimize spectral dispersion. Spectral dispersion, which is the wavelength-dependent propagation angle, can lead to a spread in the reference beam’s spectral content, making it unsuitable for certain applications. The second grating can compensate for this dispersion by diffracting different wavelengths at slightly different angles, such that they emerge from the grating parallel to each other, creating a spectrally collimated reference beam. The second grating can also over-com pensate for this dispersion, such that the different wavelengths emerge from the grating not spectrally collimated, but in non-parallel directions that will overlap at a pre-specified distance from the grating.

[0336] The choice of grating design and configuration depends on the specific application requirements. For instance, applications requiring high photon throughput might prefer configurations that omit the mirror to maximize efficiency. Applications demanding precise control over the splitting ratio might necessitate careful design of the first grating’s phase or amplitude profile. Applications sensitive to spectral dispersion would benefit from configurations that employ spectral collimation to ensure a spectrally stable reference beam. The dual-grating beamsplitter, by combining two diffraction gratings in a designed configuration, offers a versatile and efficient tool for splitting light beams. Its ability to control both the intensity ratio and spectral content of the output beams makes it suitable for a wide range of applications, including spectroscopy, interferometry, ref lectom etry, and optical metrology, where precise and stable beam splitting is essential.

[0337] In the highest-efficiency implementation, the first grating is designed with a controllable power between the zeroth order and one other order (for instance, the first order). The grating is designed such that no other orders contain substantial power. The zeroth order from the first grating is not spectrally dispersed, and can serve as a primary beam. The first order from that grating is spectrally dispersed, but is “re-spectrally-collimated” by the second grating. The second grating is designed to diffract all of the power into a single diffraction order (for instance, the first order). Parameters for design include the periodicity of each grating, the incidence angle on each grating, and the stackup of each grating to put the desired amount of power into each diffracted order. The period and incidence angle are coupled parameters. In thesimplest case, the gratings can have the same periodicity, the same incidence angle, and the input beam is therefore parallel to the reference beam. A general approach to design the period and incidence angles is to use the grating equation to calculate the diffraction angles of each wavelength after it reflects from the first and second grating. One can do this calculation for all candidate incidence angles and grating periods. One can define a spectral collimation parameter (that is, the negated RMS deviation of final propagation angle of all wavelengths) and select the candidate with the highest spectral collimation.

[0338] If the incidence angle on the first grating is desired to be 8 degrees, and the incidence angle on the second grating is desired to be 10 degrees (from grazing), and we are considering wavelengths from 10 nm to 70 nm, then the map shown in FIG. 27 can be generated. In an embodiment, with reference to FIG. 27, a graph indicating the spectral collimation achieved by a dual-grating beamsplitter for different grating periods is shown that signifies the relationship between the grating parameters and the spectral dispersion of the reference beam. The graph displays spectral collimation, a measure of the beam’s spectral quality, as a function of the grating periods for the two gratings in the beamsplitter. The horizontal axis represents the period of the second grating, ranging from 0 pm to 70 pm, while the vertical axis represents the period of the first grating, ranging from 0 pm to 70 pm. The grayscale intensity at each point on the graph represents the degree of spectral collimation, with lighter shades indicating better collimation and darker shades indicating poorer collimation. The graph has a diagonal band of high spectral collimation, indicated by the bright, almost white region stretching from the bottom left to the top right of the plot. This band corresponds to combinations of grating periods that result in minimal spectral dispersion of the reference beam. In this example calculation, the angle of incidence (AOI) on the first grating is 8 degrees from grazing, and the AOI on the second grating is 10 degrees from grazing. These incidence angles, combined with the specific grating periods within the bright band, ensure that different wavelengths within the reference beam are diffracted at angles that compensate for their initial spectral dispersion, resulting in a spectrally collimated output beam. The darker regions surrounding the bright band represent combinations of grating periods that result in significant spectral dispersion of the reference beam. In these regions, the diffraction angles for different wavelengths are not adequately compensated by thesecond grating, leading to a spread in the reference beam’s spectral content. This spectral dispersion can be detrimental for applications requiring a spectrally nondiverging reference beam, such as when incorporating such an optic into a pre-existing instrument. The graph indicates the effect of selecting the grating periods for a dualgrating beamsplitter to achieve optimal spectral collimation. The specific combination of periods required for collimation depends on the desired wavelength range and the angles of incidence on the two gratings.

[0339] The design process for the dual-grating beamsplitter involves calculating the spectral collimation for a range of grating periods, using numerical simulations or analytical expressions based on the grating equation. The grating periods that maximize spectral collimation within the desired wavelength range are then chosen. The graph in FIG. 27 provides a visual representation of this optimization process, guiding the selection of grating periods to achieve a spectrally pure reference beam.

[0340] Alternative designs could explore different angles of incidence or incorporate additional gratings to further enhance spectral collimation or achieve more complex beam splitting functionalities. For instance, by using a third grating, the spectral dispersion introduced by the first two gratings could be further compensated, extending the collimation bandwidth, providing the separation of multiple wavelengths with high spectral purity, or providing spectral collimation as well as ensuring that the wavelengths are located in the same position. FIG. 27 demonstrates the relationship between grating periods and spectral collimation in a dual-grating beamsplitter, showing the importance of careful design to achieve a spectrally pure reference beam. The ability to control and minimize spectral dispersion is crucial for enhancing the performance and accuracy of optical systems and experiments that rely on precise beam splitting and spectral analysis. Furthermore, the sensitivity of the splitting ratio to various sources of instability can be included directly in the optimization scheme, to further improve the performance of the dual-grating beamsplitter.

[0341] Again, the region where this plot is bright indicates designed grating periodicities that will produce reference beams that are not spectrally dispersed. The relative intensity of the two beams is set by the relative diffraction efficiencies into the two orders. Diffraction efficiencies can be estimated, and calculation can involverigorous solvers. A grating that has a reflectivity of (1 + V?ei 2 n x T') over one period T will have a ratio of roughly v between the first and zeroth diffracted orders. If the second grating has an efficiency E into the relevant diffracted order, then the ratio between the reference beam and the primary beam will be v*E.

[0342] In an embodiment, the multi-beam spatio-spectral-controllable optic is a multi-focus optic designed to produce multiple focal spots from a single incident beam of light, providing parallel processing, multi-point illumination, and the creation of complex optical fields. This capability offers advantages for a wide range of applications, including microscopy, spectroscopy, ref lectom etry, lithography, optical trapping, and beam shaping. The design of multi-focus optics can be achieved through several approaches, depending on the desired functionalities and the target spectral components. A method involves combining multiple diffractive structures, such as zoneplates, on a common substrate. Each diffractive structure focuses a portion of the incident beam to a different location, creating multiple focal spots with controlled spacing and intensity ratios.

[0343] One example of a simple multi-focus optic is shown in FIG. 29, where two zoneplates are interfered to create a dual-focus zoneplate optic. This interference pattern results in a diffractive structure that splits the incident beam and focuses each portion to a different location, creating two distinct focal spots. The relative intensities of the two focal spots can be controlled by adjusting the relative strengths of the two zoneplates during the interference process. Similarly, the relative phases of the two focal spots can be controlled by adjusting the relative phases of the two zoneplates. This allows for the creation of multi-focus optics with tailored intensity and phase relationships between the focal spots.

[0344] Beyond simple multi-focus optics, this concept can be extended to create optics with more complex functionalities, including beam shaping, optical angular momentum (0AM) control, and spectral control. Beam shaping multi-focus optics can generate focal spots with different beam profiles, such as circular, square, or those with hard or soft edges, providing tailored illumination patterns for applications like lithography or optical trapping. 0AM multi-focus optics create focal spots with different 0AM values, a property of light associated with its helical wavefront. Beams with different 0AM values can be used for applications like optical trapping, high-resolution microscopy, and quantum information processing. Spectral control multifocus optics use multilayer structures to focus different spectral components, such as wavelengths or polarization states, to different locations. This provides functionalities like multi-wavelength microscopy, where different wavelengths are used to excite different fluorescent probes, or polarization-sensitive imaging, where the polarization state of light provides information about the sample’s properties.

[0345] The design of multi-focus optics can involve the truth table approach or the general approach, as described previously. By selecting the structures and materials for each category of pixels in the ideal optics, the desired multi-focus functionality can be achieved. The flexibility of these design methods, coupled with advances in fabrication techniques like grayscale lithography and multi-step lithography, provides the creation of highly versatile and efficient multi-focus optics with tailored properties for a wide range of optical applications.

[0346] The multi-focus optics can be designed to operate either in reflectionmode or transmission-mode (that is, be configured to have this effect on a beam that is reflected from the optic or transmitted through it). The multi-focus optics can be designed as described below, designed for two or more discrete spectral components using the truth table approach, or designed using the general approach to be effective for a wider range of spectral content.

[0347] In an embodiment, the multi-focus optics is structured to produce a plurality of spots at or near the focus of the beam. The multi-focus optic can perform one or more of the following operations: focus or defocus the incident beam; have a controllable power ratio between the beamlets; have a controllable phase between the two beamlets; alter or select the polarization of one or more of the beamlets; alter or select the shape (geometric shape of the amplitude, geometric shape of the phase, spectral shape, and the like) of one or more of the beamlets; alter or select the orbital angular momentum (0AM) content of one or more of the beamlets; correct the spatial aberration of another optic; correct the chromatic aberration of another optic; or disperse one or more of the beamlets spectrally.

[0348] In an embodiment, the multi-beam spatio-spectral-controllable optic is a simple multi-focus optic designed to create multiple focal spots from a singleincident beam, providing parallel processing or multi-point illumination in a straightforward manner. This functionality can be achieved by combining multiple diffractive structures, e.g., zoneplates, on a common substrate. Each zoneplate focuses a portion of the incident beam to a distinct location, generating multiple focal spots with controllable spacing and intensity ratios.

[0349] In an embodiment, a method for creating a dual-focus optic involves interfering two zoneplate optics, as shown in FIG. 29, where the interference pattern results in a composite diffractive structure that splits the incident beam and focuses each portion to a different location. The relative intensities of the two focal spots can be controlled by adjusting the relative strengths of the two zoneplates during the interference process. This control over intensity ratios provides the creation of optics with balanced or unbalanced power distribution between the focal spots, tailored to the specific requirements of an application. The relative phases of the two focal spots can also be controlled by adjusting the relative phases of the two zoneplates during the interference process. This phase control allows for the creation of multi-focus optics with specific phase relationships between the focal spots, which can be advantageous for applications like interferometry or structured illumination microscopy.

[0350] Interfering zoneplate patterns can be extended to create optics with more than two focal spots. By interfering three zoneplate optics, a triple-focus optic can be generated, and by increasing the number of interfering zoneplates, optics with even more focal spots can be designed. This flexibility provides the creation of multifocus optics with a wide range of functionalities, tailored to specific applications.

[0351] In an embodiment, a multi-focus optic is configured to produce a plurality of focal spots from an incident beam of light and comprises a substrate and a plurality of diffractive structures on the substrate, wherein each diffractive structure is configured to focus a portion of the incident beam of light to a different location. In an embodiment, each diffractive structure comprises a zoneplate. In an embodiment, at least two of the diffractive structures are configured to focus a portion of the incident beam of light to substantially the same location. In an embodiment, the plurality of diffractive structures are configured to produce at least two focal spots having acontrollable intensity ratio. In an embodiment, the plurality of diffractive structures is configured to produce at least two focal spots having a controllable phase relationship.

[0352] Conventional optics for focusing light can create a single focal spot, limiting their applicability for techniques requiring simultaneous illumination or processing of multiple points. The multi-focus optic described herein overcomes this limitation by generating a plurality of focal spots from a single incident beam, providing parallel processing, multi-point illumination, and the creation of complex optical fields. In an embodiment, a multi-focus optic 242 comprises a substrate 244 that provides mechanical support for the diffractive structures and acts as a base for the optic. This substrate can be made from a variety of materials, such as silicon, glass, or a multilayer coating, chosen for their compatibility with fabrication processes and their optical properties at the desired wavelength. The substrate’s surface can be smooth and flat to ensure accurate fabrication of the diffractive structures and minimize scattering losses, thereby enhancing the optic’s performance. In an embodiment, the multi-focus optic comprises a plurality of diffractive structures 246 on the substrate. These diffractive structures, which can be implemented as zoneplates, gratings, or other diffractive elements, are responsible for focusing portions of the incident beam to different locations. The specific design and arrangement of the diffractive structures determine the number, spacing, and intensity distribution of the focal spots. By tailoring these parameters, a multi-focus optic can be designed to achieve a specific illumination pattern for a given application. In an embodiment, each diffractive structure within the multi-focus optic is configured to focus a portion of the incident beam of light to a different location. This spatial separation of the focal spots provides parallel processing or multi-point illumination, expanding the capabilities of optical techniques. For instance, in microscopy, this could provide simultaneous imaging of multiple regions of a sample, potentially increasing throughput and reducing measurement time.

[0353] The multi-focus optic provides several technical advantages. The substrate provides mechanical stability, ensuring accurate fabrication and minimizing scattering losses. The plurality of diffractive structures provides the creation of multiple focal spots with controlled spacing and intensity distribution. Each diffractive structure focuses a portion of the incident beam to a different location, providing parallelprocessing or multi-point illumination. These features create a versatile optic capable of generating tailored illumination patterns for a variety of applications, enhancing the capabilities of optical techniques and expanding the possibilities for advanced light manipulation.

[0354] In a multi-focus optic, each diffractive structure 246 can comprise a zoneplate. Zoneplates, as previously described, are diffractive structures of concentric rings or segments of rings with alternating zones designed to focus light through diffraction. The use of zoneplates as diffractive structures in a multi-focus optic offers advantages in terms of efficiency and flexibility. Zoneplates can achieve high diffraction efficiency, particularly for short wavelengths, and they can be designed to create focal spots with varying sizes and shapes by adjusting the ring patterns and zone widths.

[0355] In an embodiment, the multi-focus optic can be configured such that at least two of the diffractive structures 246 are configured to focus a portion of the incident beam of light to substantially the same location. This arrangement provides the creation of multiple focal spots that overlap, potentially enhancing the intensity or creating interference effects at the common focal point. This can be advantageous for applications like optical trapping, where multiple beams can be used to create complex trapping potentials, or for increasing the overall intensity at a specific location.

[0356] In an embodiment, the multi-focus optic can be configured such that the plurality of diffractive structures 246 are designed to produce at least two focal spots having a controllable intensity ratio. The intensity ratio between the focal spots can be adjusted by varying the relative strengths of the diffractive structures. This provides the creation of optics with balanced or unbalanced power distribution between the focal spots, tailored to specific application requirements. For instance, in microscopy, a multi-focus optic with a controllable intensity ratio could be used to illuminate different regions of a sample with different intensities, providing simultaneous imaging of both bright and dim features.

[0357] In an embodiment, the multi-focus optic can be configured such that the plurality of diffractive structures 246 are designed to produce at least two focal spots having a controllable phase relationship. This phase control provides thecreation of optics that can generate structured light patterns with specific phase distributions. The relative phases of the focal spots can be adjusted by introducing phase delays into the diffractive structures, either during fabrication or by using external phase-shifting elements. This capability is valuable for applications like interferometry, holography, or structured illumination microscopy, where precise control over the phase of light is essential.

[0358] In an embodiment, with reference to FIG. 29, the process for creating a dual-focus zoneplate optic by interfering two zoneplate optics is shown. The figure consists of three rows, each row depicting a different aspect of the design process. The left and middle columns show the individual zoneplate optics and their corresponding focal spots, while the right column displays the combined dual-focus optic and its resulting focal pattern. The top row depicts the “Spherical Wave Phase” for each beam. The left image represents the phase pattern required to focus beam 1 to a specific location, while the middle image shows the phase pattern for focusing beam 2 to a different location. These phase patterns are characterized by concentric rings of increasing radius, where the spacing between the rings determines the focal length of the zoneplate. The right image in the top row illustrates the superposition of the two spherical wave phases, demonstrating the combined phase pattern that would result from interfering the two zoneplates. This superposition creates a more complex phase distribution, with regions of constructive and destructive interference, leading to the formation of two distinct focal spots. The middle row depicts the “Zoneplate” patterns for each beam, which are binary representations of the corresponding spherical wave phases and reflect the actual design of a two-level zoneplate optic. The black regions represent zones that introduce a IT phase shift on the incident light, while the white regions represent zones with 0 phase shift. The left image shows the zoneplate for beam 1 , and the middle image displays the zoneplate for beam 2. The right image in the middle row illustrates the combined zoneplate pattern for the dualfocus optic, created by superimposing, or interfering, the individual zoneplate patterns. This superposition results in a more intricate pattern with smaller features, reflecting the combined phase distribution from the interference of the two zoneplates. The bottom row depicts the “Focus” for each beam, showing the intensity distribution of the focused light at the detector plane. The left and middle images show single bright spots, representing the focused beams 1 and 2, respectively. The right image in thebottom row illustrates the focal pattern of the dual-focus optic, exhibiting two distinct bright spots corresponding to the two focal points. The separation between the focal spots is determined by the relative positions of the initial focal points for beams 1 and 2.

[0359] FIG. 29 demonstrates the principle of creating a multi-focus optic by interfering the phase patterns of individual zoneplates. The superposition of the phase patterns leads to a composite diffractive structure that can focus light to multiple locations, providing parallel processing or multi-point illumination. The intensity and phase relationship between the focal spots can be controlled by adjusting the relative strengths and phases of the individual zoneplates during the interference process. Alternative multi-focus optic designs could be implemented by using different types of diffractive structures, such as gratings or Fresnel zone plates, or by combining multiple diffractive structures in different arrangements. The number of focal spots can be increased beyond two by interfering more zoneplates or other diffractive structures. Additionally, the focal lengths of the individual zoneplates can be varied to create focal spots at different distances from the optic, providing functionalities like depth-resolved imaging or multi-plane microscopy. FIG. 29 indicates the flexibility and versatility of diffractive optics in manipulating light and creating tailored illumination patterns. The ability to generate multiple focal spots with controlled properties opens up new possibilities for advanced optical applications in various fields, such as microscopy, lithography, optical trapping, and beam shaping.

[0360] In an embodiment, with reference to FIG. 30, the creation of a triplefocus zoneplate optic by interfering three zoneplate optics is demonstrated. The figure includes three rows, each representing a different aspect of the design process. The left, middle, and right columns show the individual zoneplate optics and their corresponding focal spots, while the right column displays the combined triple-focus zoneplate optic and its resulting focal pattern. The top row depicts the “Spherical Wave Phase” for each beam. The left image represents the phase pattern required to focus beam 1 to a specific location, the middle image shows the phase pattern for focusing beam 2 to a different location, and the right image depicts the phase pattern for focusing beam 3 to a third location. These phase patterns are characterized by concentric rings of increasing radius, where the spacing between the rings determinesthe focal length of the zoneplate. The superposition of these three spherical wave phases creates a more complex phase distribution, with regions of constructive and destructive interference, leading to the formation of three distinct focal spots in the combined optic. The middle row depicts the “Zoneplate” patterns for each beam, which are binary representations of the corresponding spherical wave phases. The black regions represent zones that introduce a IT phase shift on the incident light, while the white regions represent zones with 0 phase shift. The left image shows the zoneplate for beam 1 , the middle image displays the zoneplate for beam 2, and the right image depicts the zoneplate for beam 3. The combined zoneplate pattern for the triple-focus optic is created by superimposing the individual zoneplate patterns, resulting in a more intricate pattern with smaller features, reflecting the combined phase distribution from the interference of the three zoneplates. The bottom row depicts the “Focus” for each beam, showing the intensity distribution of the focused light at the detector plane. The left, middle, and right images show bright spots, representing the focused beams 1 , 2, and 3, respectively. The rightmost image illustrates the focal pattern of the triple-focus optic, exhibiting three distinct bright spots corresponding to the three focal points. The separation between the focal spots is determined by the relative positions of the initial focal points for beams 1 , 2, and 3. This figure demonstrates the principle of creating a multi-focus optic with three focal spots by interfering the phase patterns of three individual zoneplates. The superposition of the phase patterns leads to a composite diffractive structure that can focus light to multiple locations, providing parallel processing or multi-point illumination. The intensity and phase relationship between the focal spots can be controlled by adjusting the relative strengths and phases of the individual zoneplates during the interference process.

[0361] This concept can be further extended to create multi-focus optics with more than three focal spots by interfering additional zoneplate optics. The number of focal spots, their spacing, and their relative intensities can be tailored to specific application requirements by adjusting the design parameters of the individual zoneplates and their relative phases during interference. Alternative multi-focus optic designs could be implemented by using different types of diffractive structures, such as gratings or Fresnel zone plates, or by combining multiple diffractive structures in different arrangements. The focal lengths of the individual zoneplates can be varied to create focal spots at different distances from the optic, providing functionalities likedepth-resolved imaging or multi-plane microscopy. FIG. 30 indicates the flexibility and versatility of diffractive optics in manipulating light and creating tailored illumination patterns. The ability to generate multiple focal spots with controlled properties opens up new possibilities for advanced optical applications in various fields, such as microscopy, lithography, optical trapping, and beam shaping.

[0362] In an embodiment, with reference to FIG. 31 , the process for controlling the relative intensities of two focal spots in a dual-focus zoneplate optic by adjusting the strength of each optic during interference is shown. The figure includes three rows, each representing a different aspect of the design process. The left and middle columns show the individual zoneplate optics and their corresponding focal spots, while the right column displays the combined dual-focus optic and its resulting focal pattern. The relative strengths of the two zoneplate optics are varied across the columns, demonstrating the control over the intensity ratio between the two focal spots. The top row depicts the “Spherical Wave Phase” for each beam. The phase patterns for beams 1 and 2, shown in the left and middle images, respectively, are identical to those in FIG. 29, characterized by concentric rings of increasing radius with spacing determined by the focal length. The right image illustrates the superposition of the two spherical wave phases, where the relative strength of beam 2 is increased compared to beam 1. This results in a modified phase distribution, where the phase contribution from beam 2 dominates in certain regions, leading to a brighter focal spot for beam 2 in the combined optic. The middle row depicts the “Zoneplate” patterns for each beam, which are binary representations of the corresponding spherical wave phases. As before, the black regions represent zones that introduce a IT phase shift, while the white regions represent zones with 0 phase shift. The zoneplate patterns for beams 1 and 2 are identical to those in FIG. 29. The right image displays the combined zoneplate pattern for the dual-focus optic, created by superimposing the individual zoneplate patterns, taking into account the adjusted relative strengths. The resulting pattern exhibits a modified distribution of black and white zones, reflecting the altered phase relationship due to the increased strength of beam 2. The bottom row depicts the “Focus” for each beam and the combined dualfocus optic. The left and middle images show single bright spots, representing the focused beams 1 and 2, respectively. The right image illustrates the focal pattern of the dual-focus optic, exhibiting two distinct bright spots corresponding to the two focalpoints. However, in contrast to FIG. 29, the focal spot corresponding to beam 2 is significantly brighter than the focal spot for beam 1 , reflecting the adjusted intensity ratio due to the increased strength of beam 2 during interference. This figure demonstrates the ability to control the relative intensities of the focal spots in a multifocus optic by adjusting the relative strengths of the individual zoneplates during the interference process. By enhancing the strength of one zoneplate relative to the other, the corresponding focal spot becomes brighter, providing the creation of optics with tailored intensity ratios between the focal points.

[0363] This control over intensity ratios is advantageous for applications requiring specific power distribution between multiple focal spots. For instance, in laser processing, a dual-focus optic with a controlled intensity ratio could be used to ablate two different materials with different laser powers simultaneously, providing more efficient and precise material processing. Similarly, in optical trapping, a multi-focus optic with adjustable intensity ratios could create a stronger trapping potential at one location while maintaining a weaker trap at another, providing the manipulation of multiple particles with different sizes or optical properties. Alternative designs can further enhance this intensity control by incorporating additional parameters, such as the relative phases of the zoneplates, the number of interfering zoneplates, and the shape and size of the focal spots. This flexibility in design allows for the creation of multi-focus optics with a wide range of functionalities, tailored to the specific requirements of various optical applications.

[0364] In an embodiment, with reference to FIG. 32, the process for controlling the relative phases of two focal spots in a dual-focus zoneplate optic by adjusting the phase of each optic during interference is shown. The figure consists of three rows, each representing a different aspect of the design process. The left and middle columns show the individual zoneplate optics and their corresponding focal spots, while the right column displays the combined dual-focus optic and its resulting focal pattern. The relative phases of the two zoneplate optics are varied across the columns, demonstrating the control over the phase relationship between the two focal spots. The top row depicts the “Spherical Wave Phase” for each beam. The phase patterns for beams 1 and 2, shown in the left and middle images, respectively, are identical to those in FIG. 29, characterized by concentric rings of increasing radiuswith spacing determined by the focal length. The right image illustrates the superposition of the two spherical wave phases, where the phase of beam 2 is shifted relative to beam 1. This phase shift introduces a displacement in the interference pattern, leading to a modified phase distribution in the combined optic. The middle row depicts the “Zoneplate” patterns for each beam, which are binary representations of the corresponding spherical wave phases. The black regions represent zones that introduce a IT phase shift, while the white regions represent zones with 0 phase shift. The zoneplate patterns for beams 1 and 2 are identical to those in FIG. 29. The right image displays the combined zoneplate pattern for the dual-focus optic, created by superimposing the individual zoneplate patterns, taking into account the adjusted relative phases. The resulting pattern exhibits a shift in the alignment of the black and white zones, reflecting the altered phase relationship due to the phase difference between beams 1 and 2. The bottom row depicts the “Focus” for each beam and the combined dual-focus optic. The left and middle images show single bright spots, representing the focused beams 1 and 2, respectively. The right image illustrates the focal pattern of the dual-focus optic, exhibiting two distinct bright spots corresponding to the two focal points. The positions of the focal spots are identical to those in FIG. 29, but the interference pattern between the two spots is modified due to the phase shift introduced during the interference process. This altered interference pattern can lead to constructive or destructive interference between the two beams at specific locations, providing the creation of structured light patterns with tailored intensity and phase distributions.

[0365] FIG. 32 demonstrates the ability to control the relative phases of the focal spots in a multi-focus optic by adjusting the phases of the individual zoneplates during interference. This phase control is advantageous for applications requiring specific phase relationships between multiple focal spots, such as interferometry, holography, and structured illumination microscopy. By manipulating the phase difference between the interfering beams, the resulting interference pattern can be tailored to create complex optical fields with specific intensity and phase distributions. Alternative designs can further enhance this phase control by incorporating additional parameters, such as the relative strengths of the zoneplates, the number of interfering zoneplates, and the shape and size of the focal spots. This flexibility in design allowsfor the creation of multi-focus optics with a wide range of functionalities, specifically tailored to the requirements of various optical applications.

[0366] It can be appreciated that the ability to alter both the relative phase and the relative intensity ratio between the focal spots can be achieved by altering the design of the transverse structure of the multi-focus optic, for instance those shown in FIG. 31 and FIG. 32. The physical structures that are fabricated to match that design can operate by imparting a phase shift or an amplitude change on the incident beam of light. Perhaps counterintuitively, then, a multi-focus optic that is composed of only phase-shifting features can create an amplitude difference between the focal spots or a phase shift between them, while a multi-focus optic that is composed of amplitudechanging features can also create an amplitude or phase difference between the two focal spots. As such, the multi-focus optics shown here can be designs either for reflection-mode optics or for transmission-mode optics, and can be achieved using a variety of physical structures.

[0367] Empirical results of a dual focusing optic that operated in the 72 eV to 50 eV range of photon energies are shown in FIG. 33. The top image shows the two focused spot sizes where one spot (left) was engineered to be 50 % intensity relative to the other (right). The lower panel in the image is the same optic with a grating spectrometer inserted between the optic and the camera to spectrally disperse the beam. This demonstrates the spectral uniformity of the two foci. This optic was designed using the truth table approach, and you can see that the beams on the far right and the far left exhibit the cleanest focus shape. The optic was designed using the truth table approach, a method that provides the efficient design of optics for multiple wavelengths without sacrificing efficiency. This approach involves categorizing pixels of the ideal optics based on their desired phase shifts or amplitude changes for different wavelengths and assigning specific structures to each category. The cleaner focus shape observed for the beams on the far right and left of the bottom image is attributed to the truth table approach, which optimizes the structure for each design wavelength (in this case, two design wavelengths), minimizing chromatic aberration and enhancing focusing efficiency. Alternative measurement setups could further characterize the performance of the dual-focus optic. For instance, a knife- edge scan could be used to measure the size and shape of the focal spots with higherprecision. Interferometric techniques could be employed to analyze the wavefront quality of the focused beams, providing information about aberrations or distortions introduced by the optic.

[0368] This experimental realization of a dual-focus optic shows the successful implementation of the design and fabrication techniques described in previous sections. The ability to create multiple focal spots with controlled intensity ratios and uniform spectral responses, coupled with the flexibility in design offered by the Truth Table Approach, provides the creation of versatile and efficient multi-focus optics for a wide range of applications, including microscopy, lithography, optical trapping, and beam shaping.

[0369] In an embodiment, with reference to FIG. 34, an atomic force micrograph (AFM) image of the dual-focus optic used to acquire the experimental data presented in FIG. 33 is shown. This image provides a detailed visualization of the optic’s surface topography, revealing the four distinct layers fabricated using the additive lithography process described in previous sections. The left side of the figure displays a two-dimensional topographical map of the optic’s surface, with a color scale representing different heights. The darkest regions correspond to the lowest points on the surface, while the lightest regions represent the highest points, with a height range spanning from -930.3 nm to -743.9 nm. The image reveals a clear pattern of alternating stripes, each stripe corresponding to a specific layer in the multilayer structure. The distinct boundaries and uniform height within each stripe demonstrate the precise control over layer thicknesses achieved with the fabrication process. The right side of the figure presents a three-dimensional rendering of the same topographical data, providing a more intuitive visualization of the optic’s surface structure. The ridges and valleys of the surface are clearly visible, with the different layers appearing as distinct steps in the height profile. This three-dimensional representation emphasizes the stairstep pattern of the multilayer structure, where each layer creates a discrete jump in height.

[0370] The fabrication of this dual-focus optic involves a multi-step process using lithography, deposition, and etching techniques. A photosensitive or electronsensitive resist is spun onto the substrate, and a pattern is transferred onto the resist using either photolithography or electron beam lithography. A high-reflectivity material,such as gold, is then deposited, covering both the resist and exposed substrate areas. The resist and the material deposited on top of it are then removed, leaving behind the patterned layer on the substrate. This process is repeated for each additional layer, creating the desired multilayer structure with four distinct height levels.

[0371] The specific height profile of the optic is determined by the design process described in previous sections. Numerical simulations, incorporating the desired focal lengths and intensity ratios for the two focal spots, are used to calculate the ideal phase or amplitude profile for the optic. This profile is then translated into a discrete height profile by assigning specific heights to different regions of the optic based on the desired phase shifts or amplitude changes. The fabrication process aims to accurately create the structure with these specified heights, physically realizing the designed optic.

[0372] The AFM image in FIG. 34 provides visual confirmation of the successful fabrication of the dual-focus optic, showing the precise control over layer thicknesses and the ability to create complex multilayer structures using the described additive lithography process. The uniformity and sharp transitions between layers, evident in both the two-dimensional and three-dimensional representations, indicate accurate pattern transfer and precise material deposition. This level of precision is crucial for achieving the desired optical performance, ensuring that the fabricated optic closely matches the designed phase or amplitude profile and exhibits the intended multi-focus functionality. Alternative fabrication methods, such as subtractive etching techniques, could also be employed to create this multilayer structure, depending on the desired materials, layer thicknesses, feature sizes, and overall complexity of the structure. Additionally, the number of layers and the height of each layer can be adjusted to create optics with different functionalities or for operation in different spectral ranges. This flexibility in design and fabrication provides the creation of a wide range of multi-beam spatio-spectral-controllable optics with tailored spectral responses, expanding the possibilities for diverse optical applications.

[0373] In an embodiment, with reference to FIG. 35, an atomic force micrograph (AFM) image and a corresponding height profile of the dual-focus optic used to acquire the experimental data presented in FIG. 33 are shown, providing detailed visualization of the optic’s surface topography and demonstrating the precisefabrication of the designed multilayer structure. The top portion of the figure displays a two-dimensional topographical map of a 36 pm x 36 pm section of the optic’s surface, where varying color intensities represent different heights. The darkest regions correspond to the lowest points on the surface, while the lightest regions represent the highest points, with a height range spanning from -173.4 nm to 21.5 nm. The image reveals a clear pattern of alternating stripes, each stripe corresponding to a specific layer in the multilayer structure. The distinct boundaries and uniform height within each stripe demonstrate the precise control over layer thicknesses achieved with the fabrication process. The pixelation, evident as a grid-like pattern within each stripe, reflects the discrete nature of the fabrication pr...

Claims

What is claimed is:

1. A computer-implemented method for designing a multi-beam spatio- spectral-controllable optic, comprising: defining, with a processor, a first spatially varying complex electric field at a first location 202; numerically back-propagating with the processor the first spatially varying complex electric field to a second location 201 , thereby defining a second spatially varying complex electric field at the second location; defining, with the processor, a basis set of phase-versus-wavelength curves 361-364, each phase-versus-wavelength curve corresponding to a category 361 -364; determining, with the processor, a root-mean-squared error value for each pixel of the second spatially varying complex electric field relative to each curve of the basis set, thereby generating a plurality of root-mean-squared error values for each pixel; assigning, with the processor, a category to each pixel based on which curve of the basis set corresponds to the lowest root-mean-squared error value of the pixel; and defining, with the processor, an achievable optic by selecting a physical structure for each category based on the assigned categories of the pixels.

2. The computer-implemented method of claim 1 , wherein the first spatially varying complex electric field is a focal spot on a sample.

3. The computer-implemented method of claim 1 , wherein the second location is a surface of the optic.

4. The computer-implemented method of claim 1 , wherein the basis set of phase-versus-wavelength curves is defined using principal component analysis.

5. The computer-implemented method of claim 1 , wherein the achievable optic operates in reflection.

6. The computer-implemented method of claim 1 , wherein the achievable optic operates in transmission.

7. The computer-implemented method of claim 1 , wherein selecting a physical structure comprises using the geometric phase, wherein structures having different heights impart different phase shifts.

8. The computer-implemented method of claim 1 , wherein selecting a physical structure comprises using the material phase, wherein structures having different layer structure or material compositions impart different phase shifts.

9. The computer-implemented method of claim 1 , wherein selecting a physical structure comprises using the material amplitude, wherein structures having different layer structure or material compositions impart different amplitude changes.

10. The computer-implemented method of claim 1 , wherein selecting a physical structure comprises using waveguiding effects, wherein structures having different sizes and shapes impart different phase shifts or amplitude changes.11 . The computer-implemented method of claim 1 , wherein selecting a physical structure comprises using a combination of the geometric phase, the material phase, the material amplitude, the waveguiding phase, and the waveguiding amplitude.

12. A computer-readable, non-transitory medium having stored thereon computer-executable instructions for causing a processor to design a multi-beam spatio-spectral-controllable optic, the instructions comprising: defining a first spatially varying complex electric field at a first location; numerically back-propagating the first spatially varying complex electric field to a second location, thereby defining a second spatially varying complex electric field at the second location; defining an ideal optic for each spectral component by applying a transform to the second spatially varying complex electric field; grouping pixels of the ideal optics into categories based on a combination of the ideal optics, the categories corresponding to a physical structure; and defining an achievable optic by applying the physical structures to the ideal optics according to the categories.

13. The computer-readable, non-transitory medium of claim 12, wherein the first spatially varying complex electric field is a focal spot on a sample.

14. The computer-readable, non-transitory medium of claim 12, wherein the second location is a surface of the optic.

15. The computer-readable, non-transitory medium of claim 12, wherein defining an ideal optic comprises dividing the second spatially varying complex electric field into a plurality of regions, wherein each region is associated with a phase value.

16. The computer-readable, non-transitory medium of claim 12, wherein defining an ideal optic comprises assigning a phase value to each pixel of the second spatially varying complex electric field, based on the pixel’s phase.

17. The computer-readable, non-transitory medium of claim 12, wherein grouping pixels comprises creating a truth table, wherein each cell of the truth table corresponds to a combination of phase ranges.

18. The computer-readable, non-transitory medium of claim 12, wherein the achievable optic operates in reflection.

19. The computer-readable, non-transitory medium of claim 12, wherein the achievable optic operates in transmission.

20. The computer-readable, non-transitory medium of claim 12, wherein the physical structures impart a phase shift or amplitude change based on a combination of geometric phase, material phase, material amplitude, waveguiding phase, and waveguiding amplitude.

21. The computer-readable, non-transitory medium of claim 12, wherein the achievable optic comprises at least one of: a diagnostic optic, a multi-layer grating, a dual-grating beamsplitter, a multi-focus optic, a discrete-wavelength optic, an achromatic optic, a pre-sample dispersive optic, or an alignment-assisted optic.

22. A diagnostic optic 212 that produces a plurality of images of an incident beam of light, the diagnostic optic comprising: a substrate 214; a first diffractive structure 216 on the substrate, the first diffractive structure configured to produce a focused image of at least one spectral component of the incident beam of light; and a second diffractive structure 218 on the substrate, the second diffractive structure configured to diffract a portion of the incident beam of light, such that the first diffractive structure 216 and the second diffractive structure 218 are interposed on the substrate and interact simultaneously with the incident beam of light.

23. The diagnostic optic of claim 22, wherein the first diffractive structure is a zoneplate.

24. The diagnostic optic of claim 22, wherein the second diffractive structure is a grating.

25. The diagnostic optic of claim 24, wherein the second diffractive structure is configured to spectrally disperse a portion of the focused image.

26. The diagnostic optic of claim 22, wherein the plurality of images comprises an image of an unaltered portion of the incident beam of light.

27. The diagnostic optic of claim 26, wherein the second diffractive structure is configured to diffract the unaltered portion of the incident beam of light.

28. The diagnostic optic of claim 22, further comprising a mirror 220 that reflects the diffracted portion of the incident beam of light.

29. The diagnostic optic of claim 22, wherein the first diffractive structure produces an in-focus image of the at least one spectral component of the incident beam of light.

30. The diagnostic optic of claim 29, wherein the first diffractive structure produces at least one out-of-focus image of the at least one spectral component of the incident beam of light.31 . The diagnostic optic of claim 22, wherein the substrate is transparent to at least a portion of the incident beam of light.

32. A multi-layer grating 222 that diffracts an incident beam of light, the multilayer grating comprising: a substrate 224; and a plurality of grating structures 226 disposed on the substrate, each grating structure comprising a stackup of at least two layers 228, 229 of differing material composition, wherein a thickness of at least one layer of the stackup varies along a length of the grating structure, and wherein the grating structure imparts a predetermined phase shift or a pre-determined amplitude change that is specified for a spectral range.

33. The multi-layer grating of claim 32, wherein the plurality of grating structures diffract light having a bandwidth wider than achievable with a single material.

34. The multi-layer grating of claim 32, wherein the pre-determined phase shift increases from 0 to 2TT along a single period of the grating structure.

35. The multi-layer grating of claim 32, wherein the pre-determined phase shift or the pre-determined amplitude change provides a ratio of v between a first and zeroth order of the diffracted beam of light.

36. The multi-layer grating of claim 32, wherein a thickness of at least one layer of the stackup reduces diffraction efficiency for at least one spectral range.

37. The multi-layer grating of claim 32, wherein the grating structures diffract each wavelength of the incident beam in a pre-specified direction.

38. The multi-layer grating of claim 32, wherein the at least one spectral component comprises at least one of: wavelength, polarization, or angle of incidence.

39. A dual-grating beamsplitter 232 that splits an incident beam of light into a primary beam and a reference beam, the dual-grating beamsplitter comprising: a first grating 234 that diffracts the incident beam of light into at least two orders;a second grating 236 that diffracts at least one order of the diffracted beam of light from the first grating; and a fixture 238, such that the first grating is disposed on the fixture, and the second grating is disposed on the fixture.

40. The dual-grating beamsplitter of claim 39, wherein the fixture comprises a single, monolithic piece.41 . The dual-grating beamsplitter of claim 39, wherein the fixture comprises at least two separate pieces.

42. The dual-grating beamsplitter of claim 39, wherein the first grating provides a ratio of v between intensity of the two orders.

43. The dual-grating beamsplitter of claim 39, wherein the second grating diffracts a first order of the diffracted beam of light from the first grating.

44. The dual-grating beamsplitter of claim 39, further comprising a mirror 240 that reflects at least one order of the diffracted beam of light from the second grating.

45. The dual-grating beamsplitter of claim 39, wherein the zeroth order of the diffracted beam of light from the first grating is the primary beam.

46. The dual-grating beamsplitter of claim 45, wherein the first order of the diffracted beam of light from the second grating is the reference beam.

47. The dual-grating beamsplitter of claim 39, wherein the first grating and the second grating are multilayer gratings.

48. The dual-grating beamsplitter of claim 39, wherein the first grating and the second grating substantially eliminate spectral dispersion of the reference beam.

49. A multi-focus optic 242 that produces a plurality of focal spots from an incident beam of light, the multi-focus optic comprising: a substrate 244; and a plurality of diffractive structures 246 disposed on the substrate, such that each diffractive structure focuses a portion of the incident beam of light to a different location.

50. The multi-focus optic of claim 49, wherein each diffractive structure comprises a zoneplate.51 . The multi-focus optic of claim 49, wherein at least two of the diffractive structures focus a portion of the incident beam of light to substantially the same location.

52. The multi-focus optic of claim 49, wherein the plurality of diffractive structures produces at least two focal spots having a controllable intensity ratio.

53. The multi-focus optic of claim 49, wherein the plurality of diffractive structures produces at least two focal spots having a controllable phase relationship.

54. A multi-focus optic 242 that produces a plurality of focal spots with different beam profiles, the multi-focus optic comprising: a substrate 244; and a plurality of diffractive structures 246 disposed on the substrate, such that each diffractive structure focuses a portion of the incident beam of light to a different location with a different beam profile.

55. The multi-focus optic of claim 54, wherein at least one diffractive structure produces a focal spot with a hard edge.

56. The multi-focus optic of claim 54, wherein at least one diffractive structure produces a focal spot with a soft edge.

57. The multi-focus optic of claim 54, wherein at least one diffractive structure produces a focal spot with a non-circular shape.

58. A multi-focus optic 242 that produces a plurality of focal spots with a selected orbital angular momentum (OAM) content, the multi-focus optic comprising: a substrate 244; and a plurality of diffractive structures 246 disposed on the substrate, such that each diffractive structure focuses a portion of the incident beam of light to a different location with a different OAM value.

59. The multi-focus optic of claim 58, wherein at least one diffractive structure produces a focal spot with an integer-valued azimuthal OAM quantum number.

60. The multi-focus optic of claim 58, wherein at least one diffractive structure produces a focal spot with a non-integer-valued azimuthal OAM quantum number.61 . The multi-focus optic of claim 58, wherein at least two diffractive structures produce focal spots with a non-zero radial OAM quantum number.

62. A multi-focus optic 242 that produces a plurality of focal spots with different spectral components, the multi-focus optic comprising: a substrate 244; and a plurality of diffractive structures 246 disposed on the substrate, such that each diffractive structure comprises a stackup of at least two layers 248, 250 of differing material composition, and each diffractive structure focuses a portion of the incident beam of light having a selected spectral component to a different location.

63. The multi-focus optic of claim 62, wherein the selected spectral component comprises a first wavelength, and wherein at least one other diffractive structure focuses a portion of the incident beam of light having a second wavelength, different from the first wavelength, to a different location.

64. The multi-focus optic of claim 62, wherein the selected spectral component comprises a first polarization, and wherein at least one other diffractive structurefocuses a portion of the incident beam of light having a second polarization, different from the first polarization, to a different location.

65. The multi-focus optic of claim 62, wherein the stackup of at least two layers of each diffractive structure provides a pre-determined phase shift that varies with at least one spectral component of the incident beam of light.

66. The multi-focus optic of claim 65, wherein the pre-determined phase shift reduces chromatic aberration of the focused portion of the incident beam of light.

67. The multi-focus optic of claim 62, wherein each diffractive structure comprises a zoneplate.

68. The multi-focus optic of claim 62, wherein the multi-focus optic operates in reflection.

69. A discrete-wavelength optic 252 that focuses a plurality of discrete spectral components of an incident beam of light to different locations, the discrete-wavelength optic comprising: a substrate 254; and a plurality of diffractive structures 257 disposed on the substrate, such that each diffractive structure comprises a stackup of at least two layers 258, 260 of differing material composition, such that each diffractive structure focuses a portion of the incident beam of light having a selected spectral component to a different location.

70. The discrete-wavelength optic of claim 69, wherein each diffractive structure comprises a zoneplate.

71. The discrete-wavelength optic of claim 69, wherein the plurality of diffractive structures focus at least two of the plurality of discrete spectral components to substantially the same location.

72. The discrete-wavelength optic of claim 69, wherein the stackup of at least two layers of each diffractive structure provides a pre-determined phase shift that varies with at least one spectral component of the incident beam of light.

73. The discrete-wavelength optic of claim 72, wherein the pre-determined phase shift reduces chromatic aberration of the focused portion of the incident beam of light.

74. The discrete-wavelength optic of claim 69, wherein the selected spectral component comprises a first wavelength, and wherein at least one other diffractive structure focuses a portion of the incident beam of light having a second wavelength, different from the first wavelength, to a different location.

75. The discrete-wavelength optic of claim 69, wherein the plurality of discrete spectral components comprise at least two wavelengths.

76. The discrete-wavelength optic of claim 69, wherein the plurality of discrete spectral components comprise at least two polarizations.

77. The discrete-wavelength optic of claim 69, wherein the discrete-wavelength optic operates in reflection.

78. A discrete-wavelength grating 262 that diffracts a plurality of discrete spectral components of an incident beam of light at different angles, the discretewavelength grating comprising: a substrate 264; and a plurality of grating structures 266 on the substrate, such that each grating structure comprises a stackup of at least two layers 268, 270 of differing material composition, such that each grating structure diffracts a portion of the incident beam of light having a selected spectral component at a pre-determined angle.

79. The discrete-wavelength grating of claim 78, wherein the discretewavelength grating is a beam combiner, and wherein plurality of discrete spectral components comprises at least two incidence angles.

80. An achromatic optic 272 that focuses an incident beam of light comprising a plurality of spectral components to substantially the same location, the achromatic optic comprising: a substrate 274; and a diffractive structure 276 disposed on the substrate, such that the diffractive structure comprises a stackup of at least two layers 278, 280 of differing material composition, such that the diffractive structure imparts a phase shift that varies with at least one spectral component of the incident beam of light.

81. The achromatic optic of claim 80, wherein the diffractive structure comprises a zoneplate.

82. The achromatic optic of claim 80, further comprising at least one alignment mark 282 that diffracts or reflects visible or infrared light.

83. The achromatic optic of claim 80, wherein the achromatic optic operates in reflection.

84. An achromatic orbital angular momentum (0AM) phase plate 360 that imparts substantially the same 0AM to an incident beam of light comprising a plurality of spectral components, the achromatic 0AM phase plate comprising: a substrate 362; and a diffractive structure 364 disposed on the substrate, such that the diffractive structure comprises a stackup of at least two layers 366, 368 of differing material composition, and the diffractive structure imparts an azimuthally increasing phase shift that is substantially independent of spectral component of the incident beam of light.

85. The achromatic 0AM phase plate of claim 84, further comprising at least one alignment mark 370 that diffracts or reflects visible or infrared light.

86. The achromatic 0AM phase plate of claim 84, wherein the achromatic 0AM phase plate operates in reflection.

87. An achromatic aberration-correcting optic 372 that corrects spatial aberrations of a secondary optic 374, the achromatic aberration-correcting optic comprising:a substrate 376; and a diffractive structure 378 disposed on the substrate, such that the diffractive structure imparts a phase shift that cancels spatial aberrations of the secondary optic.

88. The achromatic aberration-correcting optic of claim 87, further comprising a diverging optic that increases a beam size incident on the secondary optic.

89. The achromatic aberration-correcting optic of claim 87, wherein the secondary optic is selected from a group consisting of: a toroid, an ellipsoid, and a spherical mirror.

90. A pre-sample dispersive optic 200 that focuses multiple spectral components of an incident beam of light onto a sample 202 and spectrally disperses the beam of light after the sample, the pre-sample dispersive optic comprising: a substrate 206; a focusing structure 208 disposed on the substrate and that focuses the incident beam of light onto the sample; and a dispersive structure 210 disposed on the substrate and that imparts a structure onto the incident beam of light such that the incident beam of light spectrally disperses after it interacts with the sample.91 . The pre-sample dispersive optic of claim 90, wherein the focusing structure comprises a zoneplate.

92. The pre-sample dispersive optic of claim 90, wherein the dispersive structure comprises a grating.

93. The pre-sample dispersive optic of claim 90, wherein the focusing structure and the dispersive structure are substantially co-located on the substrate.

94. The pre-sample dispersive optic of claim 90, wherein the focusing structure focuses multiple spectral components of the incident beam of light onto substantially the same location on the sample.

95. The pre-sample dispersive optic of claim 90, wherein the dispersive structure disperses the beam of light onto a detector 204.

96. The pre-sample dispersive optic of claim 90, wherein the pre-sample dispersive optic produces a plurality of focal spots on the sample.

97. The pre-sample dispersive optic of claim 96, wherein each of the plurality of focal spots is spectrally dispersed by the dispersive structure.

98. The pre-sample dispersive optic of claim 90, wherein the pre-sample dispersive optic operates in reflection.

99. The pre-sample dispersive optic of claim 90, wherein the pre-sample dispersive optic operates in transmission.

100. An alignment-assisted optic 212 that modifies a short-wavelength light (SWL) beam of light, the alignment-assisted optic comprising: a substrate 214; a diffractive structure 231 disposed on the substrate and that diffracts the SWL beam of light; and an alignment structure 230 disposed on the substrate and that diffracts or reflects a beam of alignment light 221 having a wavelength different from a wavelength of the SWL beam of light, wherein the beam of alignment light is collinear with the SWL beam of light.101 . The alignment-assisted optic of claim 100, wherein the diffractive structure comprises a zoneplate, a grating, or a combination comprising at least one of the foregoing optics.

102. The alignment-assisted optic of claim 100, wherein the alignment structure comprises a grating that diffracts the beam of alignment light in a selected direction.

103. The alignment-assisted optic of claim 102, wherein the grating diffracts the beam of alignment light at an angle selected from the group consisting of: retroreflection, 90 degrees from the incident beam, 90 degrees from an output beam of the diffractive structure, a few degrees from the output beam, and substantially in a vertical direction.

104. The alignment-assisted optic of claim 100, wherein the alignment structure comprises a two-dimensional grating.

105. The alignment-assisted optic of claim 104, wherein the two-dimensional grating has a unit cell selected from the group consisting of: square and hexagonal.

106. The alignment-assisted optic of claim 100, wherein the alignment structure comprises a zoneplate that focuses the beam of alignment light.

107. The alignment-assisted optic of claim 100, wherein the alignment structure is sensitive a position or an orientation of the optic relative to the beam of alignment light.

108. The alignment-assisted optic of claim 100, wherein the alignment structure is positioned on a region of the substrate different from a region of the substrate on which the diffractive structure is positioned.

109. The alignment-assisted optic of claim 100, wherein the alignment structure is at a depth relative to a surface of the substrate different from a depth of the diffractive structure relative to the surface of the substrate.

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