Waveguide and manufacturing method thereof

Abstract

Described herein is a waveguide comprising a first section configured to generate, by a nonlinear optical process, an expanded wavelength spectrum of pulsed radiation provided to an input end of the waveguide, and a second section comprising an output end of the waveguide and configured to exhibit a greater absolute value of group velocity dispersion than the first section, the length of the second section configured to reduce a peak intensity of one or more peaks in the expanded wavelength spectrum by at least 20%. Methods for manufacturing the waveguide are also described herein.

Description

[Technical field]

[0001] [CROSS REFERENCE TO RELATED APPLICATIONS] This application claims priority to European Application 21217158.1, filed December 22, 2021, which is incorporated herein by reference in its entirety.

[0002] [Technical field] The present invention relates to waveguides such as optical fibers. [Background technology]

[0003] A lithographic apparatus is a machine that is configured to apply a desired pattern onto a substrate. Lithographic apparatus may be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may project a pattern (often also referred to as a "design layout" or "design") in a patterning device (e.g., mask) onto a layer of radiation-sensitive material (resist) provided on the substrate (e.g., wafer).

[0004] To project a pattern onto a substrate, a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features that can be formed on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm and 13.5 nm. Lithographic apparatus using extreme ultraviolet (EUV) radiation having a wavelength in the range of 4-20 nm (e.g., 6.7 nm or 13.5 nm) may be used to form smaller features on a substrate than lithographic apparatus using radiation having a wavelength of, for example, 193 nm.

[0005] Low-k 1 Lithography may be used. In such processes, the resolution equation is: CD = k 1where λ is the wavelength of the radiation used, NA is the numerical aperture of the projection optics in the lithographic apparatus, CD is the "critical dimension" (generally the smallest feature size to be printed, but in this case the half pitch), and k 1 is an empirical resolution factor. In general, k 1 As the size of the lithographic projection apparatus becomes smaller, it becomes more difficult to reproduce on the substrate a pattern resembling the shape and dimensions planned by the circuit designer to achieve a particular electrical function and performance. To overcome these difficulties, sophisticated fine-tuning steps may be applied to the lithographic projection apparatus and / or the design layout. These include (but are not limited to) optical proximity correction (OPC, sometimes denoted as "optical and process correction") in the design layout, such as optimizing the NA, customized illumination schemes, use of phase-shifting patterning devices, various optimizations of the design layout, or other methods commonly defined as "resolution enhancement techniques" (RET). Alternatively, tight control loops to control the stability of the lithographic apparatus may be used to improve the repeatability of patterns at low k1.

[0006] In the field of lithography, many measurement systems may be used both inside and outside the lithographic apparatus. Typically, such measurement systems may use a radiation source for irradiating a target with radiation, and a detection system capable of measuring at least one property of a portion of the incident radiation scattered from the target. An example of a measurement system external to the lithographic apparatus is an inspection or metrology apparatus that may be used to determine properties of a pattern previously projected onto a substrate by the lithographic apparatus. Such an external inspection apparatus may comprise, for example, a scatterometer. Examples of measurement systems that may be provided within the lithographic apparatus include topography measurement systems (also known as level sensors), position measurement systems (e.g. interferometric devices) for determining the position of a reticle or wafer stage, and alignment sensors for determining the position of alignment marks. These measurement devices may use electromagnetic radiation to perform the measurements.

[0007] Different types of radiation may be used to characterize different types of patterns. Some measurement systems may use a broadband radiation source. Such a broadband radiation source may be a supercontinuum source and may comprise a waveguide having a nonlinear medium (e.g., an optical fiber) through which a pulsed pump radiation beam is transmitted to broaden the spectrum of the radiation. Summary of the Invention [Problem to be solved by the invention]

[0008] One challenge in implementing such a supercontinuum source is the lifetime of the waveguide, and one factor that can severely limit the lifetime of the waveguide is the damage that can occur as the light exits the waveguide due to the high peak intensity of the extended emission spectrum.

[0009] In the case of optical fibers, the damage at the exit can take the form of particles of deposited fiber material produced by ionization, resulting in the "growth" of glass-like structures at the output of the fiber due to sputtering. Without wishing to be bound by theory, for the example of a hollow-core photonic crystal fiber (HC-PCF) typically comprising fused silica glass filled with a nonlinear optical medium in gas form, such as that described in WO2018127266A1 (hereby incorporated by reference), such damage can result from the ionization of the gas caused by the intense pump radiation. The ions produced etch the glass, which can be preferentially redeposited at edges and protrusions. The density of such edges and protrusions can be particularly high at the ends of the fiber due to the fact that the fiber is produced by a cleaving process, introducing defect centers and structural defects. In addition, plasma is confined within the fiber, meaning that the electrons produced in the ionization process quickly recombine at nearby walls. However, at the exit of the fiber the electrons are no longer confined and form a plasma with a higher density of free electrons, which may absorb more power from the radiation pulse traveling through the plasma, which has an amplification effect leading to more plasma and, consequently, more etching of the fiber and further redeposition of the etched glass.

[0010] It would therefore be desirable to provide an alternative waveguide (e.g., optical fiber) for receiving input radiation and expanding the frequency range of the input radiation to provide (broadband) output radiation that at least partially overcomes one or more problems related to the background art (whether or not identified herein). [Means for solving the problem]

[0011] Described herein is a waveguide comprising a first section configured to generate, by a nonlinear optical process, a broadened wavelength spectrum of pulsed radiation provided to an input end of the waveguide, and a second section comprising an output end of the waveguide and configured to exhibit a greater absolute value of group velocity dispersion than the first section, wherein the length of the second section is between 0.5 cm and 20 cm and configured to reduce a peak intensity of one or more peaks in the broadened wavelength spectrum by at least 20%.

[0012] Advantageously, reducing the peak intensity of one or more peaks in the broadened wavelength spectrum can lead to reduced damage at the output end of the waveguide caused by a strong peak. Reducing the damage caused by an individual spectral peak can advantageously increase the number of spectral peaks that can pass through the output of the waveguide before the waveguide is damaged to the point where it becomes unusable, thereby increasing the lifespan of the waveguide.

[0013] In some examples, the peak intensity of one or more peaks in the expanded wavelength spectrum may be further reduced by the second section of waveguide, for example, by 25%, 50%, or 75%.

[0014] In some examples, the waveguide may be an optical fiber, e.g., a hollow-core optical fiber, such as a hollow-core photonic crystal fiber (HC-PCF). In embodiments in which the waveguide is a HC-PCF, the second section may be configured to exhibit normal group velocity dispersion. In some examples, the waveguide may be a solid-core optical fiber.

[0015] It is understood that the first section of the waveguide may be configured to generate an expanded wavelength spectrum by interaction between the pulsed radiation provided at the input end of the waveguide and a nonlinear medium within the waveguide. In some examples, the nonlinear medium may be a gas. In some examples, generating the expanded wavelength spectrum may comprise one or more of four-wave mixing, modulation instability, ionization of the working gas, Raman effect, Kerr nonlinearity, soliton formation, soliton splitting, and / or soliton self-compression.

[0016] "Normal variance" is β 2 In some examples, the first section of the waveguide may correspond to a regime of “anomalous dispersion”, i.e., negative group velocity dispersion (β 2 ). It is further understood that the peak intensity of the peaks in the expanded wavelength spectrum generally decreases over the length of the second section as the peaks propagate through the second section of the waveguide. It is understood that the decrease in the intensity of the peaks is caused by the stretching of the peaks in time due to normal dispersion in the second section.

[0017] In some examples, the waveguide comprises a core extending axially along first and second sections of the waveguide, where a diameter of the core in the second section is greater than a diameter of the core in the first section, which may alternatively be referred to as an inner diameter of the waveguide.

[0018] Varying the core diameter between the first and second sections of the waveguide advantageously changes the dispersion characteristics of the waveguide for a propagating radiation pulse such that the pulse is stretched in time and the peak intensity is reduced.

[0019] In some examples, the diameter of the core in the second section is constant over the length of the second section. Advantageously, a waveguide with a second section having a constant core diameter over its length may be easily manufactured. For example, if the waveguide is an optical fiber, the first and second sections of the waveguide may be formed by attaching two pieces of optical fiber together.

[0020] In some examples, the diameter of the core in the second section increases with increasing distance from the first section over at least a portion of the second section, For example, the second section may include an upwardly tapered section.

[0021] Since the peak intensity of the peaks in the broadened spectrum is proportional to the inverse square of the inner diameter of the waveguide (core), even a weaker upwardly tapered second section advantageously leads to a significantly reduced peak intensity, resulting in a further improvement in the lifetime of the waveguide.

[0022] In some examples, the waveguide further comprises a plurality of anti-resonant elements surrounding the core in the first section. The anti-resonant elements are understood to function to confine radiation traveling through the waveguide and guide the radiation along the waveguide. The anti-resonant elements may further function to suppress coupling of the fundamental optical mode to higher order optical modes, reducing losses in the waveguide. In some examples, the anti-resonant elements may be capillaries.

[0023] In some examples, a plurality of anti-resonant elements may surround the core in at least a portion of the second section, and a cross-sectional area of ​​each of the anti-resonant elements may decrease with increasing distance in the second section from the first section. For example, the anti-resonant elements may be collapsed over at least a portion of the length of the second section of the waveguide.

[0024] It will be appreciated that the decreasing cross-sectional area of ​​the anti-resonant element may correspond to alternative forms of an upwardly tapered inner diameter of the waveguide. Advantageously, a second section comprising an anti-resonant element with a decreasing cross-sectional area may be readily manufactured, for example, by heating and stretching an existing portion of the waveguide comprising the anti-resonant element.

[0025] In some examples, the cross-sectional area of ​​the anti-resonant element may decrease over at least a portion of the length of the second section at a rate sufficient to meet an adiabaticity criterion to prevent coupling of the fundamental optical mode to higher order modes, which would occur as a result of an abrupt change in the inner diameter of the waveguide and result in losses in the waveguide.

[0026] In some examples, the first section may comprise a plurality of anti-resonant elements surrounding the core, and the second section may not be provided with any anti-resonant elements.

[0027] Advantageously, the second section, which is not provided with any anti-resonant element, can be easily manufactured, for example, by attaching a portion of a baseline optical fiber to a portion of an optical fiber carrying the anti-resonant element.

[0028] Also described herein is a method of manufacturing a waveguide comprising: forming a first section of a waveguide configured to broaden a wavelength spectrum of pulsed radiation provided to an input end of the waveguide by a nonlinear optical process; and forming a second section of the waveguide having an output end and configured to exhibit a greater absolute value of group velocity dispersion than the first section, wherein the length of the second section is between 0.5 cm and 20 cm and configured to reduce a peak intensity of one or more peaks in the broadened wavelength spectrum by at least 20%.

[0029] Advantageously, reducing the peak intensity of one or more peaks in the broadened wavelength spectrum can lead to reduced damage at the output end of the waveguide caused by a strong peak. Reducing the damage caused by an individual spectral peak can advantageously increase the number of spectral peaks that can pass through the output of the waveguide before the waveguide is damaged to the point where it becomes unusable, thereby increasing the lifespan of the waveguide.

[0030] In some examples, the peak intensity of one or more peaks in the expanded wavelength spectrum may be further reduced by the second section of waveguide, for example, by 25%, 50%, or 75%.

[0031] In some examples, the method may be a method of manufacturing a waveguide that is an optical fiber, e.g., a hollow core optical fiber, such as a hollow core photonic crystal fiber (HC-PCF). In embodiments where the waveguide is a HC-PCF, the second section may be configured to exhibit normal group velocity dispersion. In some examples, the method may be applied to the manufacture of a waveguide that is a solid core optical fiber.

[0032] It is understood that the first section of the waveguide may be configured to generate an expanded wavelength spectrum by interaction between the pulsed radiation provided at the input end of the waveguide and a nonlinear medium within the waveguide. In some examples, the nonlinear medium may be a gas. In some examples, generating the expanded wavelength spectrum may comprise one or more of four-wave mixing, modulation instability, ionization of the working gas, Raman effect, Kerr nonlinearity, soliton formation, soliton splitting, and / or soliton self-compression.

[0033] "Normal variance" is β 2 In some examples, the first section of the waveguide may correspond to a regime of “anomalous dispersion”, i.e., negative group velocity dispersion (β 2). It is further understood that the peak intensity of the peaks in the expanded wavelength spectrum generally decreases over the length of the second section as the peaks propagate through the second section of the waveguide. It is understood that the decrease in the intensity of the peaks is caused by the stretching of the peaks in time due to normal dispersion in the second section.

[0034] In some examples, forming the first and second sections of waveguide may comprise receiving a waveguide and modifying a section of the waveguide with an output end, It will be appreciated that modifying the section of the waveguide with an output end may comprise further attaching a section of waveguide to the output end of the waveguide and / or making adjustments directly to the output end of the received waveguide.

[0035] In some examples, forming the second section of the waveguide may comprise attaching the second section to the first section, for example, by splicing the second section to the first section and / or bonding the second section to the first section.

[0036] Advantageously, attaching the second section to the first section allows for a simplified manufacturing process, e.g., two waveguide sections can be manufactured separately according to the specific specifications of the two sections and then combined at the end of the manufacturing process.

[0037] Alternatively or additionally, forming the second section of the waveguide may comprise directly conditioning an output end of the received waveguide. For example, if the received waveguide comprises a plurality of anti-resonant elements surrounding a core, directly conditioning the output end of the received waveguide may comprise collapsing the anti-resonant elements to form the second section.

[0038] In some examples, the first and second sections of the waveguide may comprise a plurality of anti-resonant elements surrounding the core, and forming the second section may comprise collapsing the plurality of anti-resonant elements in the second section.

[0039] In some examples, collapsing the plurality of anti-resonant elements in the second section may comprise heating the second section and stretching the second section by applying a tensile force.

[0040] Advantageously, collapsing the anti-resonant element in the second section allows the first and second sections to be formed from a single pre-existing piece of waveguide that includes the anti-resonant element. [Brief description of the drawings]

[0041] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which: FIG. 1 shows a schematic overview of a lithographic apparatus. FIG. 2 shows a schematic overview of a lithography cell. FIG. 3 shows a schematic representation of Holistic Lithography, which illustrates the collaboration between three key technologies to optimize semiconductor manufacturing. FIG. 4A shows a schematic representation of a waveguide according to one embodiment of the present invention in a cross-section (ie, a plane perpendicular to the axis of the optical fiber). FIG. 4B is a schematic cross-sectional view of an optical fiber according to one embodiment of the present invention, taken along a plane including the axis of the optical fiber. FIG. 5A illustrates an optical fiber comprising multiple anti-resonant elements according to one embodiment of the present invention. FIG. 5B is a schematic cross-sectional view of an optical fiber with multiple anti-resonant elements according to one embodiment of the present invention, taken in a transverse plane (ie, perpendicular to the axis of the optical fiber). FIG. 6 is a schematic cross-sectional view of a background optical fiber having an anti-resonant element crushed over a length of several hundred μm. FIG. 7A is a schematic cross-sectional view of an optical fiber with a straight second section according to an embodiment of the invention, taken along a plane containing the axis of the optical fiber. FIG. 7B is a schematic cross-sectional view of an optical fiber with an upwardly tapered second section in accordance with an embodiment of the present invention, taken along a plane containing the axis of the optical fiber. FIG. 7C is a schematic cross-sectional view of an optical fiber with a second section having a straight portion and an upwardly tapered portion in a plane containing the axis of the optical fiber according to one embodiment of the present invention. FIG. 7D is a schematic cross-sectional view of an optical fiber with a second section having a collapsed anti-resonant element in accordance with an embodiment of the present invention, taken along a plane containing the axis of the optical fiber. FIG. 7E is a schematic cross-sectional view of an optical fiber having a second section according to one embodiment of the present invention, the second section including a portion having a collapsed anti-resonant element and a straight portion without an anti-resonant element, in a plane including the axis of the optical fiber. Figure 8 illustrates a numerical simulation of the (a) full-width-at-half-maximum pulse duration and (b) peak intensity evolution of a 2.5-fs-long peak of approximately 50 nJ energy traveling along a 5-cm-long section of hollow-core optical fiber without an antiresonant element. FIG. 9 illustrates a method for manufacturing a waveguide according to one embodiment of the present invention. 10a, 10b and 10c illustrate the reduction in peak intensity at a central wavelength of 1030 nm of a spectrally broadened radiation pulse as a function of the length of a section of a hollow-core optical fiber without an antiresonant element for three different pulse lengths (2.5, 4 and 7 fs). DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0042] In this document, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having wavelengths of 365, 248, 193, 157 or 126 nm) and EUV (e.g., extreme ultraviolet radiation having a wavelength in the range of about 5-100 nm).

[0043] The terms "reticle," "mask," or "patterning device" as used in this text may be broadly interpreted to refer to a general patterning device that may be used to impart an incident radiation beam with a patterned cross-section that corresponds to the pattern to be created in a target portion of a substrate. The term "light valve" may also be used in this context. Besides the classic mask (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0044] 1 illustrates diagrammatically a lithographic apparatus LA, which includes an illumination system (also denoted illuminator) IL configured to condition a radiation beam B (e.g. UV, DUV or EUV radiation), a mask support (e.g. mask table) MT configured to support a patterning device (e.g. mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g. wafer table) WT configured to hold a substrate (e.g. resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support according to certain parameters, and a projection system (e.g. refractive projection lens system) PS configured to project a pattern formed in the radiation beam B by the patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[0045] In operation, the illumination system IL receives a radiation beam from the radiation source SO, for example via the beam delivery system BD. The illumination system IL may include various types of optical components, or any combination thereof, such as refractive, reflective, magnetic, electromagnetic, electrostatic and / or other types of optical components, for directing, shaping and / or controlling the radiation. The illuminator IL may be used to condition the radiation beam B such that it has a desired spatial and angular intensity distribution in its cross-section at the plane of the patterning device MA.

[0046] The term "projection system" PS as used herein should be interpreted broadly to encompass various types of projection systems including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, appropriate for the exposure radiation being used, and / or other factors such as the use of an immersion liquid or vacuum. Use of the term "projection lens" herein may be interpreted as synonymous with the more general term "projection system" PS.

[0047] The lithographic apparatus LA may be of a type (also referred to as immersion lithography) in which at least a part of the substrate may be covered by a liquid having a relatively high refractive index, such as water, to fill a space between the projection system PS and the substrate W. More information about immersion techniques is given in US6952253, which is incorporated herein by reference.

[0048] The lithographic apparatus LA may be of a type having two or more substrate supports WT (also referred to as "dual stage") In such a "multi-stage" apparatus, the substrate supports WT may be used in parallel and / or preparation steps for a subsequent exposure of a substrate W may be performed on a substrate W located on one substrate support WT while another substrate W on the other substrate support WT is being used to expose a pattern onto another substrate W.

[0049] In addition to the substrate support WT, the lithographic apparatus LA may comprise a measurement stage. The measurement stage is provided to hold a sensor and / or a cleaning device. The sensor may be provided to measure a property of the projection system PS or a property of the radiation beam B. The measurement stage may hold a number of sensors. The cleaning device may be provided to clean parts of the lithographic apparatus, for example parts of the projection system PS or parts of a system for providing immersion liquid. The measurement stage may move underneath the projection system PS when the substrate support WT is spaced apart from the projection system PS.

[0050] In operation, the radiation beam B is incident on a patterning device, such as a mask MA, which is held on a mask support MT, and is patterned by a pattern (design layout) present on the patterning device MA. After the mask MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of a substrate W. By means of the second positioner PW and the position measurement system IF, the substrate support WT may be accurately driven, for example to position different target portions C at focusing and alignment positions in the path of the radiation beam B. Similarly, the first positioner PM and suitable other position sensors (not explicitly shown in Figure 1) may be used to accurately position the patterning device MA with respect to the path of the radiation beam B. The patterning device MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the illustrated substrate alignment marks P1, P2 occupy dedicated target portions, they may also be located in spaces between the target portions. The substrate alignment marks P1, P2 located between the target portions C are known as scribe-line alignment marks.

[0051] As shown in FIG. 2, the lithographic apparatus LA may form part of a lithographic cell LC, which may also be denoted a lithocell or (litho)cluster and may also include apparatus for performing pre-exposure and post-exposure processing on a substrate W. Conventionally, these include a spin coater SC for forming a resist layer, a developer DE for developing the exposed resist, a cooling plate CH and a bake plate BK for adjusting the temperature of the substrate W, e.g. to adjust the solvent in the resist layer. A substrate handler or robot RO picks up substrates W from input / output ports I / O1, I / O2, moves them between different processing devices, and delivers the substrates W to a loading bay LB of the lithographic apparatus LA. The devices in the lithocell, which may also be collectively referred to as a track, are typically under the control of a track control unit TCU, which may itself be controlled, e.g., by a supervisory control system SCS, which may control the lithographic apparatus LA via a lithography control unit LACU.

[0052] In order for a substrate W to be exposed by the lithographic apparatus LA to be exposed accurately and consistently, it is desirable to inspect the substrate in order to measure properties of the patterned structures, such as overlay error between successive layers, line thickness, critical dimensions (CD), etc. For this purpose, an inspection tool (not shown) may be included in the lithocell LC. If an error is detected, particularly if inspection is performed before other substrates W of the same batch or lot are exposed or processed, adjustments may be made, for example, to the exposure of subsequent substrates or to other processing steps performed on the substrate W.

[0053] The inspection apparatus, which may also be denoted as metrology apparatus, is used to determine the properties of the substrate W, in particular the variation of the properties of different substrates W or the layer-to-layer variation of the properties for different layers of the same substrate W. The inspection apparatus may alternatively be configured to identify defects on the substrate W and may for example be part of a lithocell LC, integrated in the lithographic apparatus LA or may be a stand-alone device. The inspection apparatus may measure properties of the latent image (image in the resist layer after exposure), the semi-latent image (image in the resist layer after a post-exposure bake step PEB), the developed resist image (from which exposed or unexposed parts of the resist have been removed) and the etched image (after a pattern transfer step such as etching).

[0054] Typically, the patterning process in the lithographic apparatus LA is one of the most critical steps in the process, requiring high accuracy of the dimensions and placement of the structures on the substrate W. To achieve this high accuracy, three systems may be combined in a so-called "holistic" control environment, as shown diagrammatically in FIG. 3. One of these systems is the lithographic apparatus LA, which is (virtually) connected to a metrology tool MT (second system) and a computer system CL (third system). The essence of such a "holistic" environment is to optimize the cooperation between these three systems to improve the overall process window and provide a tight control loop so that the patterning performed by the lithographic apparatus LA stays within the process window. The process window defines the range of process parameters (e.g. dose, focus, overlay) within which a specific manufacturing process leads to a defined result (e.g. a functional semiconductor device). Typically, within that range, variations of the process parameters in the lithographic or patterning process are allowed.

[0055] The computer system CL may use (part of) the design layout to be patterned to predict the resolution enhancement technique to be used and perform computational lithography simulations and calculations to determine which mask layout and lithography apparatus settings will achieve the maximum overall process window of the patterning process (indicated in FIG. 3 by the double-headed arrow at the first scale SC1). Typically, the resolution enhancement technique is provided to match the patterning capabilities of the lithography apparatus LA. The computer system CL may be used to detect (e.g., using input from the metrology tool MT) where in the process window the lithography apparatus LA is currently operating, for example, to predict whether defects are present due to non-optimal processing (indicated in FIG. 3 by the arrow pointing to "0" at the second scale SC2).

[0056] The metrology tool MT may provide input to the computer system CL to enable accurate simulation and prediction, and may provide feedback to the lithographic apparatus LA, for example to identify possible drifts in the calibration status of the lithographic apparatus LA (indicated in FIG. 3 by multiple arrows at the third scale SC3).

[0057] A metrology tool MT (e.g. a scatterometer, a topography measurement system, or a position measurement system) may use radiation from a radiation source to perform measurements. The characteristics of the radiation used by the metrology tool may affect the type and quality of measurements that may be performed. In some applications, it is advantageous to use multiple radiation frequencies to measure the substrate, for example broadband radiation may be used. Multiple different frequencies can propagate, illuminate, and scatter to the metrology target with zero or minimal interference with other frequencies. Thus, different frequencies may be used, for example, to simultaneously obtain more metrology data. Different radiation frequencies may also probe and find different characteristics of the metrology target. Broadband radiation is useful in metrology systems MT, such as, for example, level sensors, alignment mark measurement systems, scatterometry tools, or inspection tools. The broadband radiation source may be a supercontinuum source.

[0058] One way to generate broadband radiation is to magnify high power narrow band or single frequency input radiation, for example by utilizing nonlinear, higher order effects. The input radiation (which may be generated using a laser) may be referred to as pump radiation. To obtain high power radiation for the magnification effect, the radiation may be confined in small areas (e.g., in a waveguide) such that a strongly localized high intensity radiation is realized. In these areas, the radiation may interact with materials that form magnifying structures and / or nonlinear media to generate broadband output radiation. In this high intensity radiation area, different materials and / or structures may be used to enable and / or improve the magnification of the radiation by providing a suitable nonlinear medium.

[0059] As mentioned above, many nonlinear optical processes are involved in the generation of broadband output radiation (e.g., supercontinuum or white light). Which nonlinear optical processes have a more pronounced spectral broadening effect than others depends on how the operating parameters are set. For example, if the pump pulse is in the normal dispersion region (β 2By selecting the pump wavelength and / or the waveguide to propagate through the waveguide in the positive group velocity dispersion (GVD) represented by β, self-phase modulation becomes the dominant nonlinear optical process and is responsible for the spectral broadening of the pump pulse. In most cases, however, the spectral broadening of the input radiation provided by a pulsed pump radiation source occurs when the pump pulse propagates through the waveguide in the anomalous dispersion region (negative β 2 ) in the anomalous dispersion regime, the effects of Kerr nonlinearity and dispersion work against each other. If the pulse parameters of the pump pulses introduced in the waveguide, such as optical fiber (e.g., HC-PCF), along with the anomalous chromatic dispersion, do not exactly match those of the soliton, the pump pulses will transform into soliton pulses with specific soliton orders and dispersive waves. Further details of the mechanism for spectral broadening in soliton-driven broadband radiation generation are provided in pending PCT Application No. PCT / EP2021 / 081952, which is incorporated herein by reference in its entirety.

[0060] As an example, one particular method known in the background art for generating broadband output radiation by interaction between input radiation and a nonlinear medium is modulation instability. In a particular example, modulation instability of a very short (e.g., on the order of a few hundred fs) infrared laser pulse (represented as pump radiation) may be realized by directing the laser pulse into a waveguide (e.g., a hollow-core optical fiber) that is filled with a nonlinear medium (e.g., Kr gas at a pressure of 25 bar). Such a waveguide produces a weak anomalous (e.g., β 2 =-7fs 2 / cm) group velocity dispersion (i.e., the situation where the shorter wavelength components of the pulse travel faster than the longer wavelength components) and can be exploited to access the soliton regime. As an example, the pump radiation entering the waveguide typically has a pulse duration of about 300 fs. At this point, the bandwidth of the radiation is relatively small (on the order of a few nm) and the peak intensity (e.g., about 10 TW / cm) is low. 2) is insufficient to ionize the gas. During broadband radiation generation due to modulation instability progressing as the pulse travels along the waveguide, the temporal structure of the pulse forms very sharp peaks with durations of only a few femtoseconds or even hundreds of attoseconds, resulting in a broad optical spectrum (tens to hundreds of nm) and high peak intensities that can ionize the gas and lead to damage to the waveguide (such as glass deposition at the output of the fiber) as described above.

[0061] An embodiment of the present disclosure relates to a waveguide modified to confine input radiation for use in a broadband radiation source. An example of a waveguide 10 is illustrated in FIG. 4A. Generally, a waveguide 10 according to the present disclosure comprises an elongated body that is longer in one dimension of the waveguide 10 than the other two dimensions. In use, the waveguide 10 may include a nonlinear optical medium (such as a gas) that is pumped by the input radiation to generate broadband output radiation.

[0062] The received input radiation may be electromagnetic radiation. The input radiation may be received as pulsed radiation. For example, the input radiation may comprise ultrafast pulses. The mechanism for broadening the spectrum as the radiation interacts with the nonlinear medium may be, for example, one or more of four-wave mixing, modulation instability, ionization of the working gas, Raman effect, Kerr nonlinearity, soliton formation, or soliton splitting. In particular, the spectral broadening may be achieved through one or both of soliton formation or soliton splitting. In some examples, generating the broadband output radiation may comprise soliton self-compression.

[0063] The input radiation may be coherent radiation. The input radiation may be collimated radiation, which has the advantage of facilitating and improving the efficiency of coupling the input radiation into the waveguide 10. The input radiation may comprise a single frequency, or a narrow range of frequencies. The input radiation may be generated by a laser. Similarly, the output radiation may be collimated and / or coherent.

[0064] The broadband range of output radiation may be a continuous range comprising a continuous range of radiation frequencies. The output radiation may comprise supercontinuum radiation. Continuum radiation is beneficial for use in many applications, such as metrology applications. For example, a continuous range of frequencies may be used to probe multiple properties. A continuous range of frequencies may be used, for example, to determine and / or remove frequency dependence of a property being measured. The supercontinuum output radiation may comprise electromagnetic radiation over a wavelength range, for example, 100 nm to 4000 nm. The broadband output radiation frequency range may be, for example, 400 nm to 900 nm, 500 nm to 900 nm, or 200 nm to 2000 nm. The supercontinuum output radiation may comprise white light.

[0065] As illustrated in FIG. 4B, in some examples, the waveguide may be an optical fiber 100 forming part of an apparatus 120 for receiving input radiation 122 (i.e., pump radiation) and expanding the frequency range of the input radiation 122 to provide broadband output radiation 124.

[0066] In the example illustrated in Figure 4B, the waveguide is a hollow-core optical fiber 100, specifically a hollow-core photonic crystal fiber (HC-PCF) that comprises a hollow core 102 for guiding radiation traveling through the optical fiber 100. It will be understood that the fiber illustrated in Figure 4B is shown in cross section.

[0067] In use, a nonlinear optical medium in the form of a gas 126 is disposed within the hollow core 102. The gas 126 comprises a working component that allows for broadening of the frequency range of the received input radiation 122 to provide a broadband output radiation 124. The working component of the gas 126 may be a noble gas. The working component may comprise one or more of argon, krypton, neon, helium and xenon. Alternatively or in addition to a noble gas, the working component may be a molecular gas (e.g., N 2 , O 2 , C.H. 4 ,SCIENCE FICTION 6In some examples, the apparatus 120 may further include a reservoir containing the gas 126, and the optical fiber 100 may be disposed within the reservoir. The reservoir may be configured to control, regulate, and / or monitor the composition of the gas 126 within the reservoir.

[0068] It is understood that the optical fiber 100 may have any length, and the length of the optical fiber 100 may depend on the application (e.g., the amount of spectral broadening desired in the application in a supercontinuum radiation source). The optical fiber 100 may have a length between 1 cm and 10 m, for example, the optical fiber 100 may have a length between 10 cm and 100 cm.

[0069] A further example of an HC-PCF (fiber) 100 is illustrated in FIG. 5A. The fiber 100 illustrated in FIG. 5A comprises a plurality of anti-resonant elements 104 surrounding a hollow core 102. The anti-resonant elements 104 are arranged to confine radiation traveling through the optical fiber 100 primarily within the hollow core 102 and guide the radiation along the optical fiber 100. The hollow core 102 of the optical fiber 100 may be disposed substantially in a central region of the optical fiber 100 such that the axis of the optical fiber 100 may also define the axis of the hollow core 102 of the optical fiber 100. Further details of the function of the anti-resonant elements 104 are provided in EP3136143A1 and WO2018127266A1 (both of which are incorporated herein by reference). In the examples illustrated in the present disclosure, the anti-resonant elements 104 take the form of a capillary (e.g., a tubular capillary) surrounding the hollow core 102. Thus, in this disclosure, the terms "anti-resonant element" and "capillary" are used interchangeably. The anti-resonant element 104 may also be referred to as a tube.

[0070] FIG. 5B illustrates a cross-section of the optical fiber 100 illustrated in FIG. 5A. The cross-section illustrated in FIG. 5B is understood to be in a transverse plane (i.e., a plane perpendicular to the axis of the optical fiber) designated as the xy plane, and the cross-section illustrated in FIG. 4B is understood to be in the zy plane. It is further understood that the optical fiber 100 has a degree of flexibility, and therefore the orientation of the axis of the optical fiber 100 is generally not uniform along the length of the optical fiber 100. Thus, terms such as axis and transverse section are understood to mean local axis, local transverse section, etc. Furthermore, when a component is described as being cylindrical or tubular, these terms are understood to encompass bent and distorted shapes of the optical fiber 100.

[0071] As illustrated in FIG. 5B, hollow core optical fiber 100 may comprise a hollow core 102, an inner cladding region surrounding hollow core 102, and a jacket region 110 that surrounds and supports the inner cladding region.

[0072] The inner cladding region may comprise a plurality of capillaries 104 (e.g., tubular capillaries) surrounding the hollow core 102. Each of the capillaries 104 functions as an anti-resonant element for guiding radiation traveling through the optical fiber 100. In particular, in the example illustrated in Figures 5A and 5B, the inner cladding region comprises a single ring of six tubular capillaries 104.

[0073] The capillary 104 is generally configured to suppress higher order modes in the fiber 100 and prevent coupling of the higher order modes with the (desired) fundamental optical mode, thereby reducing losses in the fiber 100 .

[0074] The capillaries 104 may be circular in cross section or may have other shapes. Each capillary 104 may comprise a generally cylindrical wall portion 105 that at least partially defines the hollow core 102 of the optical fiber 100 and separates the hollow core 102 from the cavity 106. It is understood that the wall portion 105 may act as an anti-reflective Fabry-Perot resonator for radiation traveling through the hollow core 102 (and that may be incident on the wall portion 105 at an oblique incidence angle). The thickness 160 of the wall portion 105 may be appropriate to ensure that reflection into the hollow core 102 is generally promoted while transmission into the cavity 106 is generally suppressed. In some embodiments, the capillary wall portion 105 may have a thickness 160 less than 400 nm, less than 300 nm, or less than 150 nm.

[0075] As used herein, the term inner cladding region is understood to be intended to mean the region of the optical fiber 100 for guiding radiation propagating through the optical fiber 100 (i.e., the capillary 104 that confines said radiation within the hollow core 102). The radiation may be confined in the form of a transverse mode that propagates along the fiber axis.

[0076] The jacket region 110 may be generally tubular and may support the inner cladding region capillaries 104. The capillaries 104 may be uniformly distributed about the inner surface of the jacket region 110. Six capillaries 104 may be described as surrounding the hollow core 102 in a symmetrical arrangement. In an embodiment including six capillaries 104, the capillaries 104 may be described as generally arranged in a hexagonal shape.

[0077] The capillaries 104 may be arranged such that each capillary does not contact any of the other capillaries 104. Each of the capillaries 104 may contact the jacket region 110 and may be separated from nearby capillaries 104 in a ring configuration. Such an arrangement may be beneficial because it may increase the transmission bandwidth of the optical fiber 100 (e.g., compared to an arrangement in which the capillaries are in contact with each other). Alternatively, in some embodiments, each of the capillaries 104 may contact nearby capillaries 104 in a ring configuration.

[0078] The capillaries 104 of the inner cladding region may be arranged in a ring structure around the hollow core 102. The inner surface of the ring structure of capillaries 104 at least partially defines the hollow core 102 of the optical fiber 100. In some embodiments, the diameter of the hollow core 102 (which in embodiments comprising capillaries 104 may be defined as the smallest dimension between opposing capillaries, indicated by arrows 114) may be between 5 μm and 100 μm. In some embodiments, the diameter 114 of the hollow core 102 may be between 5 μm and 50 μm. In some embodiments, the diameter 114 of the hollow core 102 may be between 30 μm and 40 μm. The diameter 114 of the hollow core 102 may affect the mode field parameters and may affect the loss, dispersion, modal multiplicity, and nonlinearity properties of the hollow-core optical fiber 100.

[0079] 5A and 5B, the inner cladding region comprises a single ring arrangement of capillaries 104 (which function as anti-resonant elements). Thus, any radial line from the center of the hollow core 102 to the outer periphery of the optical fiber 100 passes through at most one capillary 104.

[0080] It will be appreciated that in other embodiments, different arrangements of anti-resonant elements may be provided. These may include arrangements having multiple rings of anti-resonant elements and arrangements having nested anti-resonant elements. Furthermore, while the embodiment shown in Figures 5A and 5B includes six rings of capillaries 104 with wall portion 105, in other embodiments, one or more rings including any number of anti-resonant elements (e.g., 4, 5, 6, 7, 8, 9, 10, 11 or 12 capillaries) may be provided in the inner cladding region.

[0081] In the embodiment illustrated in Figures 5A and 5B, the inner cladding region has a circular cross-section. However, it is understood that in other embodiments, an inner cladding region having a cross-section other than circular may be provided. For example, in one embodiment of the present invention, the inner cladding region may have a hexagonal cross-section. A hexagonal cross-section may advantageously facilitate symmetrical placement of the capillaries 104. For example, six capillaries 104 may be disposed at vertices of each hexagonal cross-section, providing an arrangement of capillaries 104 with hexagonal symmetry.

[0082] The ability of the optical fiber 100 to provide effective guiding and confinement of radiation in the fiber 100 can be greatly influenced by the internal dimensions of the fiber 100: the hollow core diameter 114, the geometry of the capillary 104, the thickness 160 of the capillary wall portion 105, and / or the shape and dimensions of the anti-resonant cavity 106. These parameters are therefore generally understood to be limited within certain ranges of acceptable values ​​outside which the HC-PCF will not function properly. Examples of such possible constraints on these parameters are described in EP 3 136 143 A1.

[0083] The jacket region 110 may be formed from a material comprising glass. That is, the material may comprise an amorphous (i.e., non-crystalline) material that exhibits a glass transition when heated to a transition temperature. For example, the material may comprise fused silica. For example, portions of the optical fiber 100 (e.g., the capillary 104 and the jacket region 110) may be made of high purity silica (SiO 2 ) (e.g. F300 material as sold by Heraeus Holding GmbH, Germany), soft glasses such as lead silicate glasses (e.g. SF6 glass sold by Schott AG, Germany), or other special glasses such as chalcogenide glasses or heavy metal fluoride glasses (also designated ZBLAN glasses). Advantageously, glass materials do not outgas. Detailed examples of methods for producing HC-PCFs are known, for example as described in EP 3136143 A1.

[0084] As discussed above, in the case of optical fibers, damage (such as glass particle deposition) may occur where the output radiation 124 (see FIG. 4B) exits the waveguide (e.g., optical fiber). Such damage may be limited to the exit point, at least in part, as a result of a high concentration of edges and protrusions, caused in part by structural imperfections at the end of the waveguide. This problem may therefore be partially solved by smoothing the end of the waveguide.

[0085] FIG. 6 illustrates an example of a background optical fiber 600 adapted to solve the problem of damage caused by the deposition of glass particles. It is understood that the optical fiber 600 may be almost the same as the optical fiber 100 illustrated in FIGS. 5A and 5B. In the first (main) section 612, the optical fiber 600 illustrated in FIG. 6 comprises a plurality of anti-resonant elements 604 distributed around the inner surface of the jacket region 610 and surrounding the core such that the core diameter is defined by the inner surface of the anti-resonant elements 604, as shown in the first inset 680 in the cross section at the point indicated by the arrow (the inner cladding region of the optical fiber 600 in FIG. 6 has a hexagonal cross section, but in light of the above description, it is understood that, like the optical fiber illustrated in FIGS. 5A and 5B, the optical fiber 600 may equally have a circular cross section or any other suitable cross section). However, the optical fiber 600 further comprises a section 615 at one or both ends (i.e., the end where the output radiation 124 exits the fiber 600 and / or the end where the input radiation 122 enters the fiber 600, see also FIG. 4B ) in which the anti-resonant element 604 is collapsed (604X). As shown in the second inset 690 of the cross section at the end of the fiber 600, the total surface area of ​​the end of the fiber is reduced compared to a fiber having the end cross section shown in the first inset 680. The reduced surface area reduces the deposition of glass etched according to the ionization process discussed above, since the surface on which glass can be deposited is reduced. Importantly, the length 675 of the section 615 comprising the collapsed anti-resonant element 604X is very short (typically on the order of a few hundred μm).

[0086] While it has been discovered that optical fiber 600 of the type illustrated in Figure 6 exhibits improved lifetime under certain conditions, the inventors have discovered that the lifetime of such fibers is limited to about 100 days under many realistic operating conditions, and that damage at the output due to gas ionization remains dominant. Thus, further improvements to lifetime through reduction of damage at the output of the fiber are needed.

[0087] Thus, in the present disclosure it is proposed to provide a waveguide for use in generating broadband radiation that achieves a reduction in the peak intensity of the generated broadband radiation (supercontinuum) pulse before the broadband radiation pulse exits the waveguide. Although the examples described herein relate primarily to hollow core optical fibers (in particular HC-PCF filled with gas as the nonlinear medium to achieve spectral broadening), it is understood that the principles described herein may be similarly applied to any type of waveguide suitable for use in broadening the wavelength spectrum of pulsed radiation applied to the input end of the waveguide. For example, the waveguide may be a solid core optical fiber.

[0088] In summary, the present disclosure aims to rapidly reduce the intensity of the generated broadband radiation by stretching the spectral peak in time. This is achieved by including a section of the waveguide that exhibits normal dispersion characteristics before the exit of the waveguide. This results in a lower peak intensity and, since the density of free electrons generated depends nonlinearly on the peak intensity, a strongly reduced ionization.

[0089] To approximate a "true" pulse, a Gaussian shape is often used. The peak intensity of a Gaussian pulse undergoing group velocity dispersion is given by:

number

[0090] 7A-7E illustrate various examples of a waveguide 700 comprising a first section 712 and a second section 716A-E. The first section 712 is configured to expand an input radiation pulse by a nonlinear process, such as any of the processes discussed above. For example, the waveguide 700 may be filled with a nonlinear optical medium, such as a gas. In the examples illustrated in FIGS. 7A-7E, the first section 712 has a particular inner diameter (e.g., core diameter) that is defined by the distance between opposing inner surfaces of the waveguide 700. The inner diameter and other characteristics of the first section 712 are configured such that an input radiation pulse that reaches the first section is expanded by a nonlinear process. For example, the waveguide 700 may be a hollow-core optical fiber comprising a jacket region 710 and a plurality of anti-resonant elements 704 distributed around the inner surface of the jacket region 710 and surrounding the core, similar to the examples illustrated in FIGS. 5A and 5B. However, it is understood that the waveguide 700 may be any type of waveguide (e.g., a solid-core optical fiber) in which the first section 712 is configured to expand the wavelength spectrum of the pulsed radiation provided to the input end of the waveguide 700. In the example illustrated in Figures 7A-7E, the illustrated portion of the first section 712 is shown as having a constant inner (core) diameter, however, it is understood that the first section 712 may in some cases comprise one or more tapered or waist sections having a smaller inner diameter, as described in PCT / EP2021 / 081952. In contrast to the first section 712, the second sections 716A-E are configured to exhibit normal dispersion at the central wavelength of the input radiation, resulting in a temporal stretching of the radiation pulse.

[0091] As a first example illustrated in FIG. 7A, the second section 716A of the waveguide 700 may comprise a straight section having a larger inner (core) diameter than the first section 712. That is, the core diameter in the second section 716A is constant over the length of the second section 716A. For example, if the waveguide 700 is a hollow-core fiber with an anti-resonant element 704 in the first section 712, the second section 716A may comprise a portion of hollow-core fiber without an anti-resonant element. To form the waveguide 700 illustrated in FIG. 7A, the second section 716A may be spliced ​​or butt-coupled to the output end of an existing fiber. As an example, according to equation (1) (above), a waveguide with a core diameter of about 40 TW / cm at "z=0" (where it is understood that "z=0" may correspond to the dotted lines in FIGS. 7A-E) may have a core diameter of about 40 TW / cm. 2 The intensity of the peak with a length of about 4 fs in the expanded spectrum with a peak intensity of β 2 = 5.5fs 2 3. Following propagation through the second section 716A of fiber (corresponding to "1 / cm" and a length 776 of about 4 cm), the optical fiber optics is reduced by a factor of 4.

[0092] There may be a maximum length 776 of the second section 716A-E of the waveguide 700 beyond which the power of the radiation pulse traveling through the waveguide 700 falls below a usable level. In the case of a hollow core optical fiber second section 716A without an anti-resonant element, losses are caused by light leaking through the wall surrounding the core and / or coupling into higher order optical modes that are suppressed by the anti-resonant element 704 in the first section 712. The above-mentioned example of a fiber second section 716A having a core diameter of 60 μm and filled with 30 bar Kr gas exhibits a power loss of 73 dB / m, so half of the power of the expanded radiation is lost over a length of approximately 4 cm.

[0093] In a second example of the waveguide 700 illustrated in FIG. 7B, the second section 716B may comprise an upwardly tapered section. That is, the diameter of the core in the second section 716B increases with increasing distance from the first section over at least a portion of the second section 716B. The peak intensity of the peak in the broadened spectrum is proportional to the inverse square of the inner (core) diameter of the waveguide 700. Thus, even a weakly upwardly tapered second section 716B leads to a strongly reduced ionization of the optical medium (gas), resulting in a further improvement in the lifetime of the waveguide.

[0094] It is understood that straight and tapered sections may be combined to form second section 716C, as illustrated in the example of Figure 7C. The diameters, lengths, and tapering of the different sections making up second section 716C may be selected depending on the required temporal stretching and reduction in peak intensity of the expanded radiation. It is understood that the total length 776 of second sections 716A-E must be considered to balance the need to maximize the reduction in peak intensity while minimizing power loss.

[0095] Although not shown, it will be understood that the example illustrated in FIGS. 7A-7C may comprise a collapsed (over hundreds of μm) anti-resonant element 604X of the type illustrated in FIG.

[0096] In a further example illustrated in FIG. 7D, where the waveguide 700 comprises an anti-resonant element 704, an upwardly tapered second section 716D may be formed by collapsing the anti-resonant element 704Y over the length 775 of the waveguide 700. That is, the cross-sectional area of ​​each of the anti-resonant elements 704Y in the second section 716D decreases as the distance from the first section 712 increases. It is understood that the second section 716D with the collapsed anti-resonant element 704Y may be interpreted as an alternative form of upwardly tapered section, such as the second section 716B illustrated in FIG. 7B. As discussed above, the anti-resonant element 704 serves the function of preventing undesired coupling of the fundamental optical mode to higher order modes. By ensuring that the fiber region gradually collapses to meet the adiabaticity criteria, undesired coupling of the (desired) fundamental optical mode to higher order modes may be suppressed. For an upwardly tapered core (i.e., a gradually collapsed “single-ring” photonic structure), the adiabaticity criterion is the maximum angle θ over which the fiber core diameter is allowed to increase, as follows: max Expresses.

number

number

[0097] FIG. 7E illustrates an example of a waveguide 700, such as an optical fiber, with an anti-resonant element 704, where the second section 716E includes both a collapsed anti-resonant element 704Y as illustrated in FIG. 7D in a first portion 716EA of the second section 716E, and a straight section of fiber without an anti-resonant element in a second portion 716EB of the second section 716E. It is understood that the second section 716E may similarly be formed from a combination of a section with a collapsed anti-resonant element of the type illustrated in FIG. 7D, a straight section of the type illustrated in FIG. 7A, and / or a tapered section of the type illustrated in FIG. 7B. The diameters, lengths, and tapering of the different sections that make up the second section 716C may be selected depending on the required time stretching of the expanded radiation and the reduction in peak intensity of the peak. It is understood that the total length 776 of the second sections 716A-E must be considered to balance the need to maximize the reduction in peak intensity while minimizing power loss.

[0098] FIG. 8 illustrates, as a numerically simulated example, the evolution of (a) the full-width-at-half-maximum pulse duration and (b) the peak intensity of a 2.5 fs long peak of about 50 nJ energy traveling along a 5 cm long section of hollow-core optical fiber without an antiresonant element. More specifically, a single (Fourier transform limited) modulation instability peak (approximated as a Gaussian pulse) with a duration of 2.5 fs produces a bandwidth (full-width at half-maximum) of about 510 nm at a central wavelength of 1030 nm. If this spike contains 1% of the original pulse energy of 5 μJ, its peak power is 19 MW. If the spike travels in a hollow fiber with an inner diameter of 62 μm (with normal group velocity dispersion, β 2 =1fs 2 / cm), with a peak intensity of approximately 2.2TW / cm 2 After propagation over a length of only 5 cm (without nonlinear effects), the pulse is stretched to about 6 fs and has a wavelength of about 0.5 TW / cm 2As can be clearly seen, the pulse duration has more than doubled and the peak intensity is reduced by a factor of about 4 over a length of 5 cm. Based on this modeling, it is estimated that the reduction in peak intensity at the output of the fiber could increase the fiber lifetime from about 100 days to about 1000 days due to reduced ionization induced damage.

[0099] The simulated example of FIG. 8 shows a power loss of about 40 dB / m (caused by coupling of the fundamental mode to higher order modes as discussed above), leading to a power loss of about 2 dB over the simulated 5 cm length.

[0100] As discussed above, to reduce or prevent damage to the waveguide as the light exits the waveguide, it is necessary to reduce the intensity of the peaks in the broadened spectrum by an amount that corresponds to a reduction in damage appropriate to extend the life of the waveguide by a desired amount. As discussed above with respect to equation (1), the reduction in intensity of the peaks in the broadened spectrum at the output end of the waveguide depends on a particular characteristic (i.e., a particular β 2 ) is determined by the length of the second section of the waveguide. For example, the length of the second section may be configured to reduce the peak intensity of one or more peaks in the broadened wavelength spectrum by at least 20%. In some examples, the length of the second section may be configured to reduce the peak intensity of one or more peaks in the broadened spectrum by at least 25%, preferably at least 50%, and more preferably at least 75%. A reduction in peak intensity is beneficial because ionization scales highly nonlinearly with intensity.

[0101] To ensure that the power of the expanded radiation upon exiting the waveguide is maintained at a usable level, the maximum length of the second section of the waveguide may be defined as a length that corresponds to a power reduction of less than 6 dB in the expanded radiation spectrum. Thus, depending on the particular characteristics of the waveguide, the maximum length of the second section may be defined as about 20 cm, preferably about 15 cm, more preferably about 10 cm.

[0102] Figures 10a, b and c illustrate the simulated reduction in peak intensity of a radiation pulse having a spectrum broadened around a central wavelength of 1030 nm after leaving a waveguide based on a nonlinear hollow-core fiber filled with krypton as the nonlinear medium. In this example, the fiber is provided with an anti-resonant optical confinement element in a first section followed by a second section filled with the same gas at the same pressure but without an anti-resonant element (as sketched in Figure 7A). For clarity, in the simulations of Figures 10a, b and c the total dispersion in the second section of the hollow-core fiber is approximated by pure (second-order) group velocity dispersion. The second section has a diameter of about twice the core diameter of the first section of the hollow-core fiber. The length of the second section varies between 0 and 5 cm for three different pulse durations of the input (pump) radiation. Figure 10a corresponds to a pulse duration of 2.5 fs, Figure 10b corresponds to a pulse duration of 4 fs and Figure 10c corresponds to a pulse duration of 7 fs. Figure 10a shows that for a second section length of 1 cm, the peak intensity is reduced by 56% compared to a configuration without a second section. For longer pump pulse durations, the reduction in peak intensity is smaller, down to 7% for a 1 cm long second section when the pump pulse has a duration of 7 fs. In practical cases, pump pulses typically have durations of 1-10 fs, and a minimum second section length of 0.5 cm is typically sufficient to significantly reduce the peak intensity by 20-30% for pulse durations of, for example, approximately 2.5 fs.

[0103] In the following, a method of manufacturing a waveguide 700 according to the present disclosure is described.

[0104] Fabricating a waveguide 700 according to the present disclosure comprises forming a first section of a waveguide and forming a second section of a waveguide. An example of a method 900 for fabricating a waveguide according to the present disclosure is illustrated in FIG. 9. In a first step S901, the method 900 comprises forming a first section of a waveguide configured to broaden a wavelength spectrum of pulsed radiation provided to an input end of the waveguide by a nonlinear optical process. In a second step S902, the method 900 further comprises forming a second section of a waveguide comprising an output end of the waveguide and configured to exhibit a greater absolute value of group velocity dispersion than the first section, wherein the length of the second section is configured to reduce a peak intensity of one or more peaks in the broadened wavelength spectrum by at least 20%.

[0105] In some examples, forming the second section of waveguide may comprise receiving the waveguide and modifying the section of the waveguide with the output end, it being understood that modifying the section of the waveguide with the output end may comprise attaching a further section of waveguide to the output end of the waveguide and / or making adjustments directly to the output end of the received waveguide.

[0106] In some examples, the first and second sections of waveguide 700 may be formed by attaching two sections of waveguide together.

[0107] In some examples, attaching the second section to the first section may comprise splicing the second section to the first section. For example, splicing the second section to the first section may comprise splicing together two ends of a waveguide section having the same outer diameter. In some examples, splicing together the first and second sections may provide a continuous coupling between the first and second sections.

[0108] In some examples, attaching the second section to the first section may comprise bonding the second section to the first section (e.g., butt bonding the second section to the first section). In some examples, bonding the second section to the first section may result in a very small gap (e.g., less than 300 μm, less than 200 μm, or less than 100 μm) between the first and second sections.

[0109] In some examples, the first and second sections may comprise a plurality of anti-resonant elements, for example of the type described above. Forming the second section (particularly the type of second section illustrated in Figures 7D and 7E) may comprise stretching the second section by heating the second section and applying a tensile force. For example, in the case of optical fiber, the second section may be formed by heating the fiber (e.g., scanning a heat source or oxybutane flame along the length of the fiber) while gently applying a tensile force at both ends. Precise control of the stretching of the heated area during the stretching process allows for the creation of any profile (e.g., tapering) of the anti-resonant element and length of the collapsed portion.

[0110] Although the examples described herein relate primarily to hollow-core optical fibers (e.g., HC-PCF), it is understood that the examples and methods described in this disclosure may generally be applied to other types of waveguides. In some examples, the examples and methods described herein may be applied to solid-core optical fibers. As an example, the solid-core fiber may comprise a flexible glass rod. It is understood that the solid-core optical fiber may comprise a hollow structure arranged in an arrangement similar to the solid cylindrical wall portion 105 forming the capillary tube 104 illustrated in FIG. 5B. The hollow channel provides a smaller "average" refractive index of the cladding compared to the (unstructured) core. As a result, such a structure still supports the formation of "total internal reflection".

[0111] Further embodiments of the invention are disclosed in the following numbered item listing: Item 1: a first section configured to generate, by a nonlinear optical process, a broadened wavelength spectrum of pulsed radiation provided to an input end of the waveguide; a second section comprising an output end of the waveguide and configured to exhibit a greater absolute value of group velocity dispersion than the first section; Equipped with the length of the second section is between 0.5 cm and 20 cm and is configured to reduce a peak intensity of one or more peaks in the broadened wavelength spectrum by at least 20%. waveguide. Item 2: Item 2. The waveguide of item 1, wherein the second section is configured to exhibit normal group velocity dispersion. Item 3: a core extending axially along the first and second sections of the waveguide; The diameter of the core in the second section is larger than the diameter of the core in the first section. 3. The waveguide according to item 1 or 2. Item 4: 4. The waveguide of claim 3, wherein the diameter of the core in the second section is constant over the length of the second section. Item 5: 4. The waveguide of claim 3, wherein a diameter of the core in the second section increases with increasing distance from the first section over at least a portion of the second section. Item 6: a plurality of anti-resonant elements surrounding the core in the first section; the plurality of anti-resonant elements surround the core in at least a portion of the second section; a cross-sectional area of ​​each of the anti-resonant elements decreases in the second section as the distance from the first section increases. 6. A waveguide according to any one of items 3 to 5. Item 7: a plurality of anti-resonant elements surrounding the core in the first section; the second section is not provided with any anti-resonant element; 6. A waveguide according to any one of items 3 to 5. Item 8: 8. The waveguide of any one of claims 1 to 7, wherein the waveguide is a hollow core photonic crystal fiber. Item 9: 8. The waveguide according to any one of claims 1 to 7, wherein the waveguide is a solid-core optical fiber. Item 10: 10. The waveguide of any one of the preceding claims, wherein the length of the second section is configured to reduce the power of the expanded radiation spectrum by less than 6 dB. Item 11: 11. The waveguide of any one of items 1 to 10, wherein the length of the second section is less than 10 cm. Item 12: forming a first section of a waveguide configured to broaden a wavelength spectrum of pulsed radiation provided to an input end of the waveguide by a nonlinear optical process; forming a second section of the waveguide comprising an output end of the waveguide, the second section being configured to exhibit a greater absolute value of group velocity dispersion than the first section; Equipped with the length of the second section is between 0.5 cm and 20 cm and is configured to reduce a peak intensity of one or more peaks in the broadened wavelength spectrum by at least 20%. A method for manufacturing a waveguide. Item 13: Forming the first and second sections of the waveguide includes: Receiving a waveguide; and modifying a section of the waveguide comprising the output end; and Item 13. The method according to item 12, comprising: Item 14: Item 14. The method of item 12 or 13, wherein forming the second section of the waveguide comprises attaching the second section to the first section. Item 15: Attaching the second section to the first section comprises: splicing the second section to the first section; and / or coupling said second section to said first section; 15. The method according to item 14, comprising one or more of the following: Item 16: the first and second sections of the waveguide comprising a plurality of anti-resonant elements surrounding a core; forming the second section comprises collapsing the plurality of anti-resonant elements in the second section. 16. The method according to any one of items 12 to 15. Item 17: Collapsing the plurality of anti-resonant elements in the second section includes heating the second section; and stretching the second section by applying a tensile force; and 17. The method according to item 16, comprising: Item 18: 18. The method according to any of items 12 to 17, wherein the waveguide is a hollow core photonic crystal fiber. Item 19: 18. The method according to any of items 12 to 17, wherein the waveguide is a solid-core optical fiber.

[0112] Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0113] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatus. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes objects such as wafers (or other substrates) or masks (or other patterning devices). These apparatus may be generally referred to as lithography tools. Such lithography tools may use vacuum or atmospheric (non-vacuum) conditions.

[0114] Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be understood that the invention is not limited to optical lithography and may be used in other applications, such as imprint lithography, where the context permits.

[0115] Although specific embodiments of the invention have been described above, it will be understood that the invention may be practiced otherwise than as described. The above description is intended to be illustrative and not limiting. Thus, it will be apparent to one skilled in the art that changes may be made to the invention as described without departing from the scope of the following claims.

Claims

1. a first section configured to generate, by a nonlinear optical process, a broadened wavelength spectrum of pulsed radiation provided to an input end of the waveguide; a second section comprising an output end of the waveguide and configured to exhibit a greater absolute value of group velocity dispersion than the first section; Equipped with the length of the second section is between 0.5 cm and 20 cm and is configured to reduce a peak intensity of one or more peaks in the broadened wavelength spectrum by at least 20%. waveguide.

2. The waveguide of claim 1 , wherein the second section is configured to exhibit normal group velocity dispersion.

3. a core extending axially along the first and second sections of the waveguide; a diameter of the core in the second section is greater than a diameter of the core in the first section; 3. A waveguide according to claim 1 or 2.

4. 4. The waveguide of claim 3, wherein a diameter of the core in the second section is constant over the length of the second section.

5. 4. The waveguide of claim 3, wherein a diameter of the core in the second section increases with increasing distance from the first section over at least a portion of the second section.

6. a plurality of anti-resonant elements surrounding the core in the first section; the plurality of anti-resonant elements surround the core in at least a portion of the second section; a cross-sectional area of ​​each of the anti-resonant elements decreases in the second section as the distance from the first section increases.

6. A waveguide according to any one of claims 3 to 5.

7. a plurality of anti-resonant elements surrounding the core in the first section; the second section is not provided with any anti-resonant element; 6. A waveguide according to any one of claims 3 to 5.

8. A waveguide according to any preceding claim, wherein the waveguide is a hollow core photonic crystal fibre.

9. 8. A waveguide according to claim 1, wherein the waveguide is a solid core optical fibre.

10. 10. A waveguide according to claim 1, wherein the length of the second section is configured to reduce the power of the expanded radiation spectrum by less than 6 dB.

11. forming a first section of the waveguide configured to broaden the wavelength spectrum of pulsed radiation provided to an input end of the waveguide by a nonlinear optical process; forming a second section of the waveguide comprising an output end of the waveguide, the second section being configured to exhibit a greater absolute value of group velocity dispersion than the first section; Equipped with the length of the second section is between 0.5 cm and 20 cm and is configured to reduce a peak intensity of one or more peaks in the broadened wavelength spectrum by at least 20%. A method for manufacturing a waveguide.

12. Forming the first and second sections of the waveguide includes: Receiving a waveguide; and modifying a section of the waveguide comprising the output end; and The method of claim 11 , comprising:

13. 13. The method of claim 11 or 12, wherein forming the second section of the waveguide comprises attaching the second section to the first section.

14. the first and second sections of the waveguide comprising a plurality of anti-resonant elements surrounding a core; forming the second section comprises collapsing the plurality of anti-resonant elements in the second section.

14. The method according to any one of claims 11 to 13.

15. Collapsing the plurality of anti-resonant elements in the second section includes heating the second section; and stretching the second section by applying a tensile force; and The method of claim 14 comprising:

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