Broadband radiation generator based on hollow-core photonic crystal fiber

Abstract

A broadband light source device configured to generate broadband output radiation upon receiving pump radiation includes a hollow-core photonic crystal fiber (HC-PCF) having one or more main sections and at least one structural variation section having at least one structural parameter that varies relative to the one or more main sections. The at least one structural variation section is disposed downstream at a position along the length of the HC-PCF, and includes at least a first structural variation section that spectrally broadens the pump radiation by a nonlinear optical process dominated by modulational instability. The at least one structural variation section is constructed and arranged such that the broadband output radiation has a wavelength in the ultraviolet region.

Description

[Technical Field]

[0001] [CROSS REFERENCE TO RELATED APPLICATIONS] This application claims priority to European Application No. 20213013.4, filed December 10, 2020, and European Application No. 21178292.5, filed June 8, 2021, which are incorporated herein by reference in their entireties.

[0002] [Technical field] The present invention relates to a broadband radiation generator based on hollow-core photonic crystal fiber, particularly for metrology applications in integrated circuit manufacturing. [Background technology]

[0003] A lithographic apparatus is a machine configured to apply a desired pattern onto a substrate. Lithographic apparatus can 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 a substrate (e.g., a 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 with wavelengths 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 with a wavelength of, for example, 193 nm.

[0005] Low-k1 lithography may be used to process features with dimensions smaller than the classical resolution limit of a lithographic apparatus. In such processes, the resolution equation may be expressed as "CD = k1 × λ / NA," where λ is the wavelength of the radiation used, NA is the numerical aperture of the projection optical elements in the lithographic apparatus, CD is the "critical dimension" (typically the smallest feature size to be printed, in this case the half pitch), and k1 is an empirical resolution factor. Generally, the smaller k1, the more difficult it becomes to reproduce on a substrate a pattern resembling the shape and dimensions planned by the circuit designer to achieve a specific 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, NA optimization, customized illumination schemes, the use of phase-shifting patterning devices, various optimizations of the design layout, optical proximity correction (OPC, sometimes expressed as "optics and process correction"), and other methods commonly defined as "resolution enhancement techniques" (RET). Alternatively, a tight control loop for controlling the stability of the lithographic apparatus may be used to improve the reproducibility of patterns at low k1. Summary of the Invention [Problem to be solved by the invention]

[0006] Metrology tools are used at many stages in the IC manufacturing process, for example, as alignment tools for proper positioning of the substrate before exposure, leveling tools for measuring the surface topology of the substrate for focus control, etc., and scatterometry-based tools for inspecting / measuring exposed and / or etched products in process control. In each case, a radiation source is required. For various reasons, including measurement robustness and accuracy, broadband or white light radiation sources are increasingly being used in such metrology applications. It would be desirable to improve upon the present devices for generating broadband radiation. [Means for solving the problem]

[0007] In a first aspect of the invention, a broadband light source device is provided that is configured to generate broadband output radiation upon receiving pump radiation. The broadband light source device includes a hollow-core photonic crystal fiber (HC-PCF) having one or more main sections and at least one structural variation section having at least one structural parameter that varies relative to the one or more main sections. The at least one structural variation section is disposed downstream from a position along the length of the HC-PCF, and includes at least a first structural variation section that spectrally broadens the pump radiation by a nonlinear optical process dominated by modulational instability. The at least one structural variation section is constructed and arranged such that the broadband output radiation has a wavelength in the ultraviolet spectral region.

[0008] In a second aspect of the invention, there is provided a method for optimizing a position of at least a first structural variation along a length of a hollow-core photonic crystal fiber (HC-PCF) such that broadband output radiation is generated from the HC-PCF following excitation with input radiation having a wavelength in the ultraviolet region, the method comprising determining a position along the length of the HC-PCF at which pump radiation is spectrally broadened by a nonlinear optical process dominated by modulational instability, and locating a first structural variation downstream of the determined position.

[0009] In another aspect of the invention, there is provided a measurement device comprising the broadband light source device of the first aspect. [Brief explanation of the drawings]

[0010] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which: FIG. 1 is a schematic diagram of a lithographic apparatus. FIG. 2 is a schematic diagram of a lithography cell. Figure 3 is a schematic diagram of holistic lithography, illustrating the collaboration between three key technologies to optimize semiconductor manufacturing. FIG. 4 is a schematic illustration of a scatterometry apparatus used as a metrology device which may include a radiation source according to embodiments of the invention. FIG. 5 is a schematic diagram of a level sensor device, which may include a radiation source according to an embodiment of the invention. FIG. 6 is a schematic diagram of an alignment sensor apparatus which may include a radiation source according to an embodiment of the invention. FIG. 7 is a schematic cross-section, in a transverse plane (ie perpendicular to the axis of the optical fiber), of a hollow core optical fiber that may form part of a radiation source according to an embodiment. FIG. 8 is a schematic diagram of a radiation source according to an embodiment for providing broadband output radiation. 9(a) and (b) show schematic cross-sections of example hollow-core photonic crystal fiber (HC-PCF) designs for supercontinuum generation. FIG. 10 is a plot of point spread power spectral density (PSD) versus wavelength λ describing three simulated output spectra generated from a fiber with a 30 μm core diameter, a fiber with a 20 μm core diameter, and a fiber with a 30 μm core diameter operating at a lower pressure, respectively. FIG. 11(a) shows a schematic diagram of a single-waist hollow-core optical fiber configured for the production of broadband output radiation with a smooth spectral profile and an extended short-wavelength edge. FIG. 11(b) shows a schematic representation of an alternative configuration of the single-waist hollow-core optical fiber shown in FIG. 11, in which the single-waist region does not include a central waist. Figure 12(a) shows a plot of wavelength λ-energy (or signal sig(dB)) spectral density versus position P along the fiber length for a simulation describing the spectral evolution of a pulse of input radiation in a single-neck hollow-core optical fiber (e.g., as shown in Figure 11(b)) with a neck region beginning at an optimized position along the fiber length (e.g., where the taper begins). Figure 12(b) shows an equivalent plot to Figure 12(a) for a simulation of the spectral evolution of a pulse of radiation in the single-neck hollow-core optical fibre shown in Figure 11(b) when the neck region is in a non-optimised position (i.e., the position where MI-dominated spectral broadening begins at the taper). FIG. 13 shows two simulations of the output spectrum of the radiation source with the same parameters as the simulations shown in FIGS. 12(a) and 12(b), respectively. FIG. 14(a) shows a schematic of how the fiber core diameter varies along the length of an example single-waist hollow-core optical fiber optimized via simulation for short wavelength extension and a balanced spectral profile of the output radiation. FIG. 14(b) shows two measured output spectra emitted from a non-tapered hollow-core optical fiber and a single-waist hollow-core optical fiber (such as that shown in FIG. 14(a)), respectively. Figure 14(c) shows three measured power transfer curves describing how the integrated output power varies with input pump pulse energy for different hollow-core optical fibers (e.g., a uniform hollow-core optical fiber and a tapered hollow-core optical fiber) under different operating conditions (e.g., different pump pulse repetition rates). FIG. 15 illustrates schematically a double-waisted hollow-core optical fiber configured for the production of broadband output radiation with a smooth spectral profile and an extended short-wavelength edge. Figure 16(a) shows a plot equivalent to Figure 12 for a simulation of the spectral evolution of a pulse of radiation in a tapered hollow-core optical fiber having two constriction regions (e.g., as shown in Figure 15), the first constriction region being applied to control modulation instability processes and the second constriction region being applied to control dispersive-wave generation. FIG. 16(b) shows a simulation of the output spectrum of the radiation source with the same parameters as the simulation shown in FIG. 16(a). FIG. 17 illustrates schematically an alternative single-waist hollow-core optical fiber configured for soliton trapping of dispersive waves, according to one embodiment. Figures 18(a) and 18(b) show two simulated spectrograms describing the temporal and spectral distribution of a pulse of input radiation after propagation through a uniform hollow-core optical fiber at distances of 70 cm and 110 cm, respectively. Figures 18(c) and 18(d) show two simulated spectrograms describing the temporal and spectral distribution of a pulse of input radiation after propagation through a single-waist hollow-core optical fiber (e.g., the one shown in Figure 17). FIG. 19 illustrates schematically a further alternative single-waist hollow-core optical fiber configured for soliton trapping of dispersive waves, according to one embodiment. Figures 20(a) and 20(b) show two simulated spectrograms describing the temporal and spectral distribution of a pulse of input radiation after propagation through a uniform hollow-core optical fiber at distances of 27 cm and 42 cm, respectively. Figures 20(c) and 20(d) show two simulated spectrograms describing the temporal and spectral distribution of a pulse of input radiation after propagation through a single-waist hollow-core optical fiber (e.g., the one shown in Figure 19) at distances of 27 cm and 42 cm, respectively. FIG. 21 is a block diagram of a computer system for controlling a broadband radiation source. DETAILED DESCRIPTION OF THE INVENTION

[0011] 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 nm, 248 nm, 193 nm, 157 nm, 126 nm) and EUV (e.g., extreme ultraviolet radiation having wavelengths in the range of about 5-100 nm).

[0012] The terms "reticle," "mask," and "patterning device," as used herein, may be broadly interpreted to refer to any patterning device that can be used to impart an incident beam with a patterned cross-section, which corresponds to the pattern to be produced 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 such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0013] 1 schematically shows a lithographic apparatus LA, comprising: an illumination system (also referred to as an illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation, EUV radiation), a mask support (e.g., a mask table) MT configured to support a patterning device (e.g., a 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., a wafer table) WT configured to hold a substrate (e.g., a 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., a 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.

[0014] 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, such as refractive, reflective, magnetic, electromagnetic, electrostatic and / or other types of optical components, or any combination thereof, for directing, shaping and / or controlling the radiation. The illuminator IL may be used to condition the radiation beam B so that it has a desired spatial and angular intensity distribution in its cross-section in the plane of the patterning device MA.

[0015] 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, as appropriate for the exposure radiation used and / or other factors such as the use of an immersion liquid or the use of a vacuum. The term "projection lens" as used herein may be considered as synonymous with the more general term "projection system" PS.

[0016] The lithographic apparatus LA may also be of a type in which at least part of the substrate is covered by a liquid having a relatively high refractive index, such as water, filling a space between the projection system PS and the substrate W (also referred to as immersion lithography). More information about immersion techniques is given in US6952253, which is incorporated herein by reference.

[0017] The lithographic apparatus LA may be of a type having two or more substrate supports WT (also known as "dual stage"), in which the substrate supports WT may be used in parallel and / or a preparation step for the next exposure of a substrate W located on one substrate support WT may be performed while another substrate W on the other substrate support WT is being used to expose a pattern onto that other substrate W.

[0018] In addition to the substrate support WT, the lithographic apparatus LA may also comprise a measurement stage. The measurement stage is provided for holding a sensor and / or a cleaning device. The sensor may be provided for measuring a property of the projection system PS or a property of the radiation beam B. The measurement stage may hold multiple sensors. The cleaning device may be provided for cleaning part of the lithographic apparatus, for example part of the projection system PS or part of the system for providing immersion liquid. When the substrate support WT is remote from the projection system PS, the measurement stage may move below the projection system PS.

[0019] In operation, the radiation beam B is incident on a patterning device MA, such as a mask held on a mask support MT, and is patterned according to a pattern (design layout) present on the patterning device MA. Passing through 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. With the aid of a second positioner PW and a position measurement system IF, the substrate support WT is 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 optionally other position sensors (not explicitly shown in FIG. 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. While the illustrated substrate alignment marks P1, P2 occupy dedicated target portions, they may also be located in spaces between the target portions. Substrate alignment marks P1, P2 located between target portions C are known as scribe-line alignment marks.

[0020] As shown in FIG. 2 , the lithography apparatus LA may form part of a lithography cell LC, which may also be referred to as a lithocell or (litho)cluster and may 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, and a chill plate CH and 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 equipment, and delivers the substrates W to a loading bay LB of the lithography apparatus LA. The devices in the lithocell, sometimes collectively referred to as a track, are typically under the control of a track control unit TCU, which may itself be controlled by a supervisory control system SCS, which may control the lithography apparatus LA, e.g., via a lithography control unit LACU.

[0021] To ensure that substrates W exposed by lithographic apparatus LA are exposed accurately and consistently, it is desirable to inspect the substrates 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 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 substrate W.

[0022] The inspection apparatus, which may also be referred to as a metrology apparatus, is used to determine the properties of the substrate W, in particular the variations in the properties of different substrates W, or the layer-to-layer variations in 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 a lithography apparatus LA, or may be a stand-alone device. The inspection apparatus may measure properties of the latent image (the image in the resist layer after exposure), the semi-latent image (the image in the resist layer after a post-exposure bake step PEB), the developed resist image (from which exposed or unexposed portions of the resist have been removed), and the etched image (after a pattern transfer step such as etching).

[0023] Typically, the patterning process in a lithography apparatus LA is one of the most critical steps in processing, requiring high accuracy in the dimensions and placement of structures on a substrate W. To achieve this high accuracy, three systems may be combined in a so-called "holistic" control environment, as shown schematically in FIG. 3. One of these systems is a lithography apparatus LA (virtually) connected to a metrology tool MT (second system) and a computer system CL (third system). The essence of such a "holistic" environment is optimizing 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 lithography apparatus LA remains within the process window. The process window defines the range of process parameters (e.g., dose, focus, overlay) within which a specific manufacturing process produces a defined result (e.g., a functional semiconductor device). Typically, within this range, variations in the process parameters are tolerated during the lithography or patterning process.

[0024] The computer system CL may use (a portion of) the design layout to be patterned to predict which resolution enhancement techniques to use and perform computational lithography simulations and calculations to determine which mask layout and lithography apparatus settings will achieve the largest overall process window of the patterning process (shown in FIG. 3 by the double-headed arrow at a first scale SC1). Typically, resolution enhancement techniques are provided to match the patterning capabilities of the lithography apparatus LA. The computer system CL may also be used to detect (e.g., using input from the metrology tool MT) where within the process window the lithography apparatus LA is currently operating, for example, to predict whether defects will be present due to suboptimal processing (shown in FIG. 3 by the arrow pointing to "0" at a second scale SC2).

[0025] The metrology tool MT may provide input to the computer system CL to enable accurate simulations and predictions, 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 Figure 3 by multiple arrows at the third scale SC3).

[0026] In lithography processes, it is frequently desirable to perform measurements of the structures produced, e.g., for process control and verification. Tools for performing such measurements are typically called metrology tools MT. Different types of metrology tools MT are known for performing such measurements, including scanning electron microscopes or various forms of scatterometry tools MT. Scatterometers are versatile instruments that allow the measurement of parameters of the lithography process by placing a sensor in the pupil or in a plane conjugate to the pupil of the scatterometer object (measurements typically referred to as pupil-based measurements), or by placing a sensor in the image plane or in a plane conjugate to the image plane (measurements in this case typically referred to as image- or field-based measurements). Such scatterometers and associated measurement techniques are further described in patent applications US20100328655, US2011102753A1, US20120044470A, US20110249244, US20110026032 or EP1628164A, each of which is incorporated herein by reference in its entirety. The aforementioned scatterometers may measure gratings using soft x-rays and light from the visible to near-infrared wavelength range.

[0027] In a first embodiment, the scatterometer MT is an angle-resolved scatterometer. In such a scatterometer, a reconstruction method may be applied to the measured signals to reconstruct or calculate the properties of the grating. Such reconstruction may be performed, for example, by simulating the interaction of the scattered radiation with a mathematical model of the target structure and comparing the simulated results with the measurements. Parameters of the mathematical model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from a real target.

[0028] In a second embodiment, the scatterometer MT is a spectroscopic scatterometer MT. In such a spectroscopic scatterometer MT, radiation from a radiation source is directed onto a target and reflected or scattered radiation from the target is directed to a spectrometer detector which measures the spectrum of the specularly reflected radiation (i.e., a measurement of intensity as a function of wavelength). From this data, the structure or profile of the target on which the detected spectrum is based may be reconstructed, for example by RCWA and non-linear regression, or by comparison with a library of simulated spectra.

[0029] In a third embodiment, the scatterometer MT is an ellipsometric scatterometer. Ellipsometric scatterometers enable the determination of parameters of a lithography process by measuring scattered radiation for each polarization state. Such metrology instruments emit polarized light (linear, circular, elliptical, etc.), for example, by using appropriate polarizing filters in the illumination section of the metrology instrument. A source suitable for the metrology instrument may provide the polarized radiation. Various embodiments of existing ellipsometric scatterometers are described in U.S. patent applications 11 / 451,599, 11 / 708,678, 12 / 256,780, 12 / 486,449, 12 / 920,968, 12 / 922,587, 13 / 000,229, 13 / 033,135, 13 / 533,110, and 13 / 891,410, each of which is incorporated herein by reference in its entirety.

[0030] In one embodiment of the scatterometer MT, the scatterometer MT is adapted to measure the overlay of two misaligned gratings or periodic structures by measuring asymmetry related to the degree of overlay in the reflectance spectra and / or detection configuration. The two (typically overlapping) grating structures may be applied to two different (not necessarily consecutive) layers and may be formed at substantially the same location on the wafer. The scatterometer may have a symmetric detection configuration, such as that described in co-owned patent application EP1628164A, so that any asymmetry is clearly identifiable. This provides a straightforward way to measure misalignment in the gratings. Further examples for measuring the overlay error between two layers containing periodic structures as targets through the asymmetry of the periodic structures are described in PCT Patent Application Publication No. WO2011 / 012624 or U.S. Patent Application No. US20160161863, each of which is incorporated herein by reference in its entirety.

[0031] Other parameters of interest include focus and dose. Focus and dose may be determined simultaneously by scatterometry (or by scanning electron microscopy), as described in U.S. Patent Application No. US2011-0249244, the entire contents of which are incorporated herein by reference. A single structure may be used that has a unique combination of critical dimension and sidewall angle measurements for each point in the focus-energy matrix (also referred to as the focus-exposure matrix (FEM)). If these unique combinations of critical dimension and sidewall angle are available, values ​​for focus and dose may be uniquely determined from these measurements.

[0032] Metrology targets are typically formed in resist by a lithography process, but may also be ensembles of composite gratings, which may be formed after, for example, an etching process. Typically, the pitch and linewidth of structures in a grating strongly depend on the measurement optics (particularly the NA of the optics) to enable detection of diffraction orders from the metrology target. As previously described, the diffraction signal may be used to determine the shift between two layers (also referred to as "overlay") and to reconstruct at least a portion of the original grating formed by the lithography process. This reconstruction may be used to provide guidance on the quality of the lithography process and to control at least a portion of the lithography process. The target may have smaller subsegments configured to mimic the dimensions of features in the design layout at the target. This subsegment allows the target to behave more similarly to the features in the design layout, so that overall process parameter measurements better represent the features in the design layout. The target may be measured in underfill mode or overfill mode. In underfill mode, the measurement beam generates a spot smaller than the entire target. In overfill mode, the measurement beam creates a spot larger than the entire target, and in such overfill mode, different targets can be measured simultaneously to simultaneously determine different process parameters.

[0033] The measurement quality of an overall lithography parameter using a specific target is determined at least in part by the measurement recipe used to measure that lithography parameter. The term "substrate measurement recipe" may include one or more parameters of the measurement itself, one or more parameters of one or more patterns being measured, or both. For example, if the measurement used in the substrate measurement recipe is a diffraction-based optical measurement, the one or more parameters of the measurement may include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation relative to the substrate, the direction of the radiation relative to the pattern on the substrate, etc. One of the selection criteria for a measurement recipe may be, for example, the sensitivity of one measurement parameter to process variations. Many more examples are described in U.S. Patent Application US2016-0161863 and Published U.S. Patent Application US2016 / 0370717A1, each of which is incorporated herein by reference in its entirety.

[0034] A metrology device such as a scatterometer is shown in FIG. 4. It comprises a broadband (white light) radiation projector 2 that projects radiation onto a substrate 6. Reflected or scattered radiation reaches a spectrometer detector 4, which measures the spectrum 10 of the specularly reflected radiation (i.e., a measurement of intensity as a function of wavelength). From this data, the structure or profile underlying the detected spectrum may be reconstructed by a processing unit PU, for example, by Rigorous Coupled Wave Analysis (RCWA) and nonlinear regression, or by comparison with a library of simulated spectra such as that shown at the bottom of FIG. 3. Typically, for reconstruction, the approximate morphology of the structure is known, some parameters are assumed from knowledge of the process that forms the structure, and only a few structure parameters remain to be determined from the scatterometry data. Such a scatterometer may be configured as a normal-incidence scatterometer or an oblique-incidence scatterometer.

[0035] The measurement quality of an overall lithography parameter through measurement of a metrology target is determined at least in part by the measurement recipe used to measure the lithography parameter. The term "substrate measurement recipe" may include one or more parameters of the measurement itself, one or more parameters of one or more patterns being measured, or both. For example, if the measurement used in the substrate measurement recipe is a diffraction-based optical measurement, the one or more parameters of the measurement may include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation relative to the substrate, the direction of the radiation relative to the pattern on the substrate, etc. One of the selection criteria for a measurement recipe may be, for example, the sensitivity of one measurement parameter to process variations. Many more examples are described in U.S. Patent Application US2016 / 0161863 and Published U.S. Patent Application US2016 / 0370717A1, each of which is incorporated herein by reference in its entirety.

[0036] Other types of metrology tools used in IC manufacturing are topography measurement systems, level sensors, or height sensors. Such tools may be integrated into lithography apparatus to measure the topography of the top surface of a substrate (or wafer). A map of the substrate's topography, also referred to as a height map, may be generated from these measurements, showing the substrate's height as a function of position on the substrate. This height map may subsequently be used to correct the substrate's position during transfer of a pattern onto the substrate in order to provide an aerial image of the patterning device at the proper focus position on the substrate. "Height" in this context is understood to refer broadly to a dimension out of the substrate plane (also referred to as the Z-axis). Typically, a level or height sensor performs measurements at a fixed position (relative to its optical system), and relative movement between the substrate and the optical system of the level or height sensor results in height measurements at positions across the substrate.

[0037] One known example of a level or height sensor LS is shown schematically in FIG. 5, illustrating only the principle of operation. In this example, the level sensor comprises an optical system including a projection unit LSP and a detection unit LSD. The projection unit LSP comprises a radiation source LSO providing a beam of radiation LSB provided by a projection grating PGR of the projection unit LSP. The radiation source LSO may be a narrowband or broadband light source, such as a polarized or unpolarized laser beam, a pulsed or continuous supercontinuum light source, or the like. The radiation source LSO may also include multiple radiation sources, such as multiple LEDs with different colors or wavelength ranges. The radiation source LSO of the level sensor LS is not limited to visible radiation but may additionally or alternatively encompass UV and / or IR radiation or any range of wavelengths suitable for reflection from the surface of the substrate.

[0038] The projection grating PGR is a periodic grating with a periodic structure, which results in a beam of radiation BE1 with a periodically varying intensity. The beam of radiation BE1 with a periodically varying intensity, having an angle of incidence ANG between 0 and 90 degrees, typically between 70 and 80 degrees, with respect to an axis orthogonal to the incident substrate surface (Z-axis), is directed towards a measurement location MLO on the substrate W. At the measurement location MLO, the patterned beam of radiation BE1 is reflected by the substrate W (indicated by arrow BE2) and directed towards a detection unit LSD.

[0039] To determine the height level at the measurement position MLO, the level sensor further comprises a detection system comprising a detection grid DGR, a detector DET and a processing unit (not shown) for processing an output signal of the detector DET. The detection grid DGR may be the same as the projection grid PGR. The detector DET generates a detector output signal indicative of the received light, e.g., indicative of the intensity of the received light as in a photodetector, or indicative of the spatial distribution of the received intensity as in a camera. The detector DET may comprise any combination of one or more detector types.

[0040] By means of triangulation techniques, the height level at the measurement location MLO can be determined. The detected height level is typically related to the signal intensity measured by the detector DET. This signal intensity has a periodicity that depends, inter alia, on the design of the projection grating PGR and the (oblique) angle of incidence ANG.

[0041] The projection unit LSP and / or the detection unit LSD may include further optical elements, such as lenses and / or mirrors (not shown), along the path of the beam of patterned radiation between the projection grating PGR and the detection grating DGR.

[0042] In one embodiment, the detection grating DGR may be omitted and the detector DET may be arranged at the position where the detection grating DGR is arranged, such a configuration providing a more direct detection of the image of the projection grating PGR.

[0043] To effectively cover the surface of the substrate W, the level sensor LS may be configured to project an array of measurement beams BE1 onto the surface of the substrate W to generate an array of spots covering the measurement area MLO or a larger measurement range.

[0044] Various height sensors of the general type are disclosed, for example, in US7265364 and US7646471, both of which are incorporated herein by reference. A height sensor that uses UV radiation instead of visible or infrared radiation is disclosed in US2010233600A1, which is incorporated herein by reference. WO2016102127A1, which is incorporated herein by reference, describes a compact height sensor that uses a multi-element detector to detect and recognize the position of a grating image without the need for a detection grating.

[0045] Another type of metrology tool used in IC manufacturing is an alignment sensor. A key aspect of a lithography apparatus' performance is its ability to accurately and precisely align an applied pattern with respect to features deposited on a previous layer (by the same or a different lithography apparatus). For this purpose, one or more sets of marks or targets are provided on the substrate. Each mark is a structure whose position can be subsequently measured using a position sensor, typically an optical position sensor. The position sensor may also be referred to as an "alignment sensor" and the marks may also be referred to as "alignment marks."

[0046] A lithographic apparatus may include one or more (e.g., multiple) alignment sensors capable of precisely measuring the positions of alignment marks provided on a substrate. Alignment (or position) sensors may use optical phenomena such as diffraction and interference to derive position information from alignment marks formed on the substrate. One example of an alignment sensor used in current lithographic apparatuses is based on a self-referencing interferometer, such as that described in US6961116. Various improvements and modifications to position sensors have been made, for example, as disclosed in US2015261097A1, the entire contents of which are incorporated herein by reference.

[0047] 6 is a schematic block diagram of an embodiment of a known alignment sensor AS, for example as described in US 6,961,116, which is incorporated herein by reference. A radiation source RSO provides a beam of radiation RB of one or more wavelengths that is directed by directing optics as an illumination spot SP onto a mark, such as a mark AM arranged on a substrate W. In this example, the directing optics comprises a spot mirror SM and an objective lens OL. The illumination spot SP that illuminates the mark AM may be slightly smaller in diameter than the width of the mark itself.

[0048] Radiation diffracted by the alignment mark AM is collimated (in this example via an objective lens OL) into an information-bearing beam IB. The term "diffracted" is intended to include zero-order diffraction (which may also be referred to as reflection) from the mark. After a self-referencing interferometer SRI, for example of the type disclosed in the aforementioned US Pat. No. 6,961,116, causes the beam IB to interfere with itself, the beam is received by a photodetector PD. If multiple wavelengths are produced by the radiation source RSO, additional optical elements (not shown) may be included to provide the separate beams. The photodetector may be a single element or may comprise multiple pixels, if desired. The photodetector may comprise a sensor array.

[0049] The guiding optics, which in this example comprises a spot mirror SM, may serve to block the zero-order radiation reflected from the mark, so that the information-bearing beam IB contains only higher-order diffracted radiation from the mark AM (this is not essential for the measurement, but improves the signal-to-noise ratio).

[0050] The intensity signal SI is fed to a processing unit PU. The combination of optical processes in block SRI and computational processes in unit PU outputs values ​​for the X and Y position on the substrate relative to a reference frame.

[0051] A single measurement of the type shown merely fixes the position of the mark within a certain range corresponding to one pitch of the mark. Coarser measurement techniques are used in conjunction with this to determine which period of the sine wave contains the marked position. The same process, at coarser and / or finer levels, may be repeated at different wavelengths for improved accuracy and / or robust detection of the mark, regardless of the material the mark is made from or the material on which it is provided. Wavelengths may be optically multiplexed and demultiplexed to be processed simultaneously, and / or multiplexed by time or frequency division.

[0052] In this example, the alignment sensor and spot SP remain stationary, while the substrate W moves. Therefore, the alignment sensor can be rigidly and precisely mounted to a reference frame and can effectively scan the mark AM in a direction opposite to the direction of movement of the substrate W. In this movement, the substrate W is controlled by being mounted on a substrate support and a substrate positioning system that controls the movement of the substrate support. A substrate support position sensor (e.g., an interferometer) measures the position of the substrate support (not shown). In one embodiment, one or more (alignment) marks are provided on the substrate support. Measuring the positions of the marks provided on the substrate support allows for calibration of the position of the substrate support (e.g., relative to a frame to which the alignment system is connected) as determined by the position sensor. Measuring the positions of the alignment marks provided on the substrate allows for determination of the position of the substrate relative to the substrate support.

[0053] Metrology tools MT, such as the aforementioned scatterometers, topography measurement systems, and position measurement systems, 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 off the metrology target with zero or minimal interference with other frequencies. Thus, different frequencies may be used, for example, to simultaneously acquire more metrology data. Different radiation frequencies can probe and identify different characteristics of the metrology target. Broadband radiation is useful in metrology systems MT, such as level sensors, alignment mark measurement systems, scatterometry tools, and inspection tools. The broadband radiation source may be a supercontinuum source.

[0054] High-quality broadband radiation, such as supercontinuum radiation, is difficult to generate. One method for generating broadband radiation is to magnify high-power narrowband or single-frequency input or pump 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. Alternatively, the input radiation may be referred to as seed radiation. To obtain high-power radiation for the magnification effect, the radiation may be confined to a small area so 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 high-intensity radiation areas, different materials and / or structures may be used to achieve and / or improve radiation magnification by providing a suitable nonlinear media.

[0055] In some implementations, broadband output radiation is generated in a photonic crystal fiber (PCF). In some embodiments, such a photonic crystal fiber has a microstructure around its fiber core that serves to confine radiation propagating through the fiber within the fiber core. The fiber core can be made of a solid material with nonlinear properties that can generate broadband radiation when high-intensity pump radiation passes through the fiber core. Although broadband radiation can be generated in a solid-core photonic crystal fiber, the use of solid materials comes with some drawbacks. For example, if UV radiation is generated in the solid core, this radiation may not be present in the output spectrum of the fiber because the radiation is absorbed by most solid materials.

[0056] In some implementations, as discussed further below with reference to FIG. 8, methods and apparatus for expanding input radiation may use a fiber to confine and expand the input radiation to output broadband radiation. The fiber may be a hollow-core fiber and may include an internal structure to achieve effective guiding and confinement of the radiation within the fiber. The fiber may be a hollow-core photonic crystal fiber (HC-PCF), which is particularly suitable for achieving high radiation intensity due to strong radiation confinement primarily within the hollow core of the fiber. The hollow core of the fiber may be filled with a gas, which serves as a expanding medium for expanding the input radiation. Such a fiber and gas arrangement may be used to generate a supercontinuum radiation source. The radiation input to the fiber may be electromagnetic radiation, such as radiation in one or more of the infrared, visible, UV, and extreme UV spectrums. The output radiation constitutes or comprises broadband radiation, which may be described as white light.

[0057] Some embodiments relate to new designs of broadband radiation sources comprising such optical fibers. The optical fiber is a hollow-core photonic crystal fiber (HC-PCF). In particular, the optical fiber may be a type of hollow-core photonic crystal fiber that is equipped with an anti-resonance structure for radiation confinement. Fibers with such anti-resonance structures are known as anti-resonance fibers, tubular fibers, single-ring fibers, negative curvature fibers, or coupling-disruption fibers. Various different designs of such fibers are known. Alternatively, the optical fiber may be a photonic bandgap fiber (HC-PBF, such as a Kagome fiber).

[0058] Many types of HC-PCFs are possible, each based on a different physical guiding mechanism. Two such HC-PCFs include hollow-core photonic bandgap fiber (HC-PBF) and hollow-core antiresonant reflecting fiber (HC-ARF). Details on the design and fabrication of HC-PCFs can be found in U.S. Patent US2004 / 015085A1 (HC-PBF) and International PCT Patent Application WO2017 / 032454A1 (Hollow-Core Antiresonant Reflecting Fiber), both of which are incorporated herein by reference. Figure 9(a) shows a Kagome fiber with a Kagome lattice structure.

[0059] An example of an optical fiber for use in a radiation source will now be described with reference to Figure 7, which is a schematic cross-section of an optical fiber OF. Further embodiments similar to the example fiber of Figure 7 are disclosed in WO2017 / 032454A1.

[0060] The optical fiber OF comprises an elongated body having one dimension that is longer than the other two dimensions of the fiber OF. This elongated dimension may be referred to as the axial direction and may define the axis of the optical fiber OF. The two other dimensions define a plane that may be referred to as the transverse plane. Figure 7 shows a cross-section of the optical fiber OF in this transverse plane (i.e., perpendicular to the axis), referred to as the xy plane. The transverse cross-section of the optical fiber OF may be substantially uniform along the fiber axis.

[0061] It is understood that the optical fiber OF has a degree of flexibility and therefore the axial direction is generally not uniform along the length of the optical fiber OF. Terms such as optical axis, cross section, etc. are understood to mean the local optical axis, local cross section, etc. Furthermore, when a component is described as cylindrical or tubular, these terms are understood to encompass the shape that the optical fiber OF is distorted into when it is bent.

[0062] It is understood that the optical fiber OF may have any length and the length of the optical fiber OF may vary depending on the application. The optical fiber OF may have a length between 1 cm and 10 m, for example, the optical fiber OF may have a length between 10 cm and 100 cm.

[0063] The optical fiber OF comprises a hollow core HC, a cladding portion surrounding the hollow core HC, and a support portion SP surrounding and supporting the cladding portion. The optical fiber OF may be interpreted as comprising a body (comprising the cladding portion and the support portion SP) having the hollow core HC. The cladding portion comprises a plurality of anti-resonant elements for guiding radiation through the hollow core HC. In particular, the plurality of anti-resonant elements are provided to confine radiation propagating through the optical fiber OF primarily within the hollow core HC and to guide the radiation along the optical fiber OF. The hollow core HC of the optical fiber OF may be disposed in a substantially central region of the optical fiber OF such that the axis of the optical fiber OF may also define the axis of the hollow core HC of the optical fiber OF.

[0064] The cladding comprises a plurality of anti-resonant elements for guiding radiation propagating through the optical fiber OF. In particular, in this embodiment, the cladding comprises a single ring of six tubular capillary caps, each of which functions as an anti-resonant element.

[0065] The capillary CAP may be described as a tube. The cross section of the capillary CAP may be circular or have other shapes. Each capillary CAP generally includes a cylindrical wall WP that at least partially defines a hollow core HC of the optical fiber OF and separates the hollow core HC from the capillary cavity CC. It is understood that the wall WP may function as an anti-reflection Fabry-Perot resonator for radiation propagating through the hollow core HC (which may be incident on the wall WP at an oblique incidence angle). The thickness of the wall WP is appropriately set to ensure that reflection back into the hollow core HC is promoted and conduction into the capillary cavity CC is suppressed. In some embodiments, the capillary wall WP may have a thickness between 0.01 and 10.0 μm.

[0066] The term "cladding" as used herein is understood to mean the portion of the optical fiber OF intended to guide radiation propagating therethrough (i.e., the capillary CAP that confines the radiation within the hollow core HC). The radiation may be confined in the form of transverse modes propagating along the fiber axis.

[0067] The support portion is generally tubular and supports six capillary CAPs of the cladding portion. The six capillary CAPs are equally spaced around the inner surface of the inner support portion SP. The six capillary CAPs may be generally described as being arranged in a hexagonal configuration.

[0068] The capillary CAPs are arranged so that each capillary does not contact the other capillary CAPs. Each capillary CAP contacts the inner support SP and is spaced apart from adjacent capillary CAPs in the ring structure. This arrangement is advantageous for increasing the transmission bandwidth of the optical fiber OF (e.g., compared to an arrangement in which the capillaries contact each other). Alternatively, in some embodiments, each capillary CAP may contact adjacent capillary CAPs in the ring structure.

[0069] The six capillary caps of the cladding are arranged in a ring structure around the hollow core HC. The inner surfaces of the ring structure of the capillary caps at least partially define the hollow core HC of the optical fiber OF. The diameter d of the hollow core HC (which may be defined as the smallest dimension between opposing capillaries, indicated by arrow d) may be between 10 and 1000 μm. The diameter d of the hollow core HC may affect the mode field diameter, shock loss, dispersion, mode diversity, and nonlinear properties of the hollow-core HC optical fiber OF.

[0070] In this embodiment, the cladding comprises a single ring arrangement of capillary CAPs (which act as anti-resonant elements), so that any radial line from the center of the hollow core HC to the exterior of the optical fiber OF passes through at most one capillary CAP.

[0071] It is understood that other embodiments may be provided with different arrangements of anti-resonant elements. These may include arrangements with multiple rings of anti-resonant elements or arrangements with nested anti-resonant elements. FIG. 9(a) shows an embodiment of an HC-PCF with three rings of capillary caps stacked radially on top of each other. In this embodiment, each capillary cap contacts other capillaries in the same ring and in different rings. Furthermore, while the embodiment shown in FIG. 7 includes six rings of capillaries, other embodiments may provide one or more rings in the cladding with any number of anti-resonant elements (e.g., 4, 5, 6, 7, 8, 9, 10, 11, or 12 capillaries).

[0072] Figure 9(b) shows a variation of the aforementioned HC-PCF with a single ring of tubular capillaries. In the example of Figure 9(b), there are two concentric rings of tubular capillaries 21. A support tube ST may be included in the HC-PCF to hold the inner and outer rings of tubular capillaries 21. The support tube may be made of silica.

[0073] The tubular capillaries of the examples of Figures 7 and 9(a) and (b) may have a circular cross-sectional shape. Other shapes, such as oval or polygonal cross-sections, are also possible for the tubular capillaries. Additionally, the solid material of the tubular capillaries of the examples of Figures 7 and 9(a) and (b) may include plastic materials such as PMA, glasses such as silica and soft glass.

[0074] Figure 8 shows a radiation source RDS for providing broadband output radiation. The radiation source RDS comprises a pulsed pump radiation source PRS or any other type of source capable of generating short pulses of a desired length and energy level, an optical fiber OF having a hollow core HC (e.g., of the type shown in Figure 7), and a working medium WM (e.g., a gas) provided within the hollow core HC. In Figure 8, the radiation source RDS comprises the optical fiber OF shown in Figure 7, although in alternative embodiments other types of hollow-core HC optical fiber OF may be used.

[0075] The pulsed pump radiation source PRS is configured to provide input radiation IRD. The hollow core HC of the optical fiber OF is arranged to receive the input radiation IRD from the pulsed pump radiation source PRS and expand it to provide output radiation ORD. The working medium WM enables expanding the frequency range of the received input radiation IRD to provide broadband output radiation ORD.

[0076] The radiation source RDS further includes a reservoir RSV. The optical fiber OF is disposed inside the reservoir RSV. The reservoir RSV may be referred to as a housing, a container, or a gas cell. The reservoir RSV is configured to contain a working medium WM. The reservoir RSV may include one or more known features for controlling, regulating, and / or monitoring the composition of the working medium WM (which may be a gas) within the reservoir RSV. The reservoir RSV may include a first transparent window TW1. During operation, the optical fiber OF is disposed within the reservoir RSV such that the first transparent window TW1 is disposed near an input end IE of the optical fiber OF. The first transparent window TW1 may form part of a wall of the reservoir RSV. The first transparent window TW1 may be transparent to at least the received input radiation frequency such that the received input radiation IRD (or at least a majority thereof) may be coupled into the optical fiber OF disposed within the reservoir RSV. It is understood that an optical element (not shown) may be provided for coupling the input radiation IRD into the optical fiber OF.

[0077] The reservoir RSV includes a second transparent window TW2 that forms part of a wall of the reservoir RSV. During operation, when the optical fiber OF is disposed within the reservoir RSV, the second transparent window TW2 is located near the output end OE of the optical fiber OF. The second transparent window TW2 may be transparent to at least the frequencies of the broadband output radiation ORD of the device 120.

[0078] Alternatively, in other embodiments, two opposite ends of the optical fiber OF may be disposed in different reservoirs. The optical fiber OF may have a first end configured to receive input radiation IRD and a second end for outputting broadband output radiation ORD. The first end may be disposed in a first reservoir containing the working medium WM. The second end may be disposed in a second reservoir, which may also contain the working medium WM. The reservoirs may have the functions described above with respect to FIG. 8. The first reservoir may have a first transparent window configured to be transparent to the input radiation IRD. The second reservoir may have a second transparent window configured to be transparent to the broadband output broadband radiation ORD. The first and second reservoirs may have sealable openings, allowing one portion of the optical fiber OF to be disposed inside the reservoir and another portion to be disposed outside the reservoir, such that a gas can be sealed within the reservoir. The optical fiber OF may further have an intermediate portion not contained within the reservoir. Such an arrangement using two separate gas reservoirs is particularly suitable for embodiments in which the optical fiber OF is relatively long (e.g., greater than 1 m in length). For such an arrangement using two separate gas reservoirs, it is understood that the two reservoirs (which may include one or more known features for controlling, regulating, and / or monitoring the composition of the gases in the two reservoirs) may be construed as providing an apparatus for providing the working medium WM within the hollow core HC of the optical fiber OF.

[0079] In this context, a window is said to be transparent to a frequency if at least 50%, 75%, 85%, 90%, 95% or 99% of radiation incident on the window at that frequency is transmitted through the window.

[0080] Both the first and second transparent windows TW1 and TW2 may form an airtight seal within the wall of the reservoir RSV such that a working medium WM (which may be a gas) may be contained within the reservoir RSV. It is understood that the gas WM may be contained within the reservoir RSV at a pressure in the reservoir RSV that is different from atmospheric pressure.

[0081] The working medium WM may contain a noble gas such as argon, krypton, or xenon; a Raman-active gas such as hydrogen, deuterium, or nitrogen; or a gas mixture such as an argon / hydrogen mixture, a xenon / deuterium mixture, a krypton / nitrogen mixture, or a nitrogen / hydrogen mixture. Depending on the type of filling gas, nonlinear optical processes may include modulation instability (MI), soliton self-compression, soliton splitting, the Kerr effect, the Raman effect, and dispersive wave generation (DWG). These are described in detail in WO 2018 / 127266 A1 and US 9160137 B1 (both incorporated herein by reference). By varying the pressure of the working medium WM in the reservoir RSR (i.e., the gas cell pressure), the dispersion of the filling gas can be adjusted, and thus the dynamics and associated spectral broadening characteristics of the generated broadband pulses can be tailored to optimize frequency conversion.

[0082] In one implementation, the working medium WM may be provided within the hollow core HC at least while the optical fiber OF is receiving input radiation IRD to generate the broadband output radiation ORD. It is understood that the gas WM may be wholly or partially absent from the hollow core HC while the optical fiber OF is not receiving input radiation IRD to generate the broadband output radiation.

[0083] To achieve frequency broadening, high-intensity radiation is desirable. An advantage of having a hollow-core HC optical fiber OF is that high-intensity radiation (high localized radiation intensity) can be achieved through the strong spatial confinement of radiation propagating through the optical fiber OF. For example, the radiation intensity within the optical fiber OF may be high due to a high received input radiation intensity and / or the strong spatial confinement of radiation within the optical fiber OF. An advantage of hollow-core optical fibers is that they can guide radiation having a wider wavelength range than solid-core fibers. In particular, hollow-core optical fibers can guide radiation in both the ultraviolet and infrared ranges.

[0084] An advantage of using a hollow-core HC optical fiber OF may be that a large portion of the radiation guided within the optical fiber OF is confined to the hollow core HC, and thus a large portion of the interaction of the radiation within the optical fiber OF occurs with the working medium WM provided within the hollow core HC of the optical fiber OF, resulting in an enhanced magnifying effect of the working medium WM on the radiation.

[0085] The received input radiation IRD may be electromagnetic radiation. The input radiation IRD may be received as pulsed radiation. For example, the input radiation IRD may comprise ultrafast pulses generated by a laser or the like.

[0086] The input radiation IRD may be coherent radiation. The input radiation IRD may be collimated radiation. This has the advantage of facilitating coupling of the input radiation IRD into the optical fiber OF, increasing efficiency. The input radiation IRD may comprise a single frequency or a narrow range of frequencies. The input radiation IRD may be generated by a laser. Similarly, the output radiation ORD may be collimated and / or coherent.

[0087] The broadband range of the output radiation ORD may be a continuous range, including a continuous range of radiation frequencies. The output radiation ORD may be supercontinuum radiation. Continuum radiation is advantageous for use in many applications, such as metrology applications. For example, a continuous range of frequencies may be used to probe a large number of properties. A continuous range of frequencies may be used, for example, to determine and / or eliminate frequency dependence of a property being measured. The supercontinuum output radiation ORD may include electromagnetic radiation over a wavelength range of, for example, 100 nm-4000 nm. The frequency range of the broadband output radiation ORD may be, for example, 400 nm-900 nm, 500 nm-900 nm, or 200 nm-2000 nm. The supercontinuum output radiation ORD may include white light.

[0088] The input radiation IRD provided by the pulsed pump radiation source PRS may be pulsed. The input radiation IRD may include electromagnetic radiation at one or more frequencies between 200 nm and 2 μm. The input radiation IRD may, for example, include electromagnetic radiation having a wavelength of 1.03 μm. The repetition rate of the pulsed radiation IRD may be on the order of 1 kHz to 100 MHz. The pulse energy may be on the order of 0.1 μJ to 100 μJ, for example, on the order of 1-10 μJ. The pulse duration for the input radiation IRD may be between 10 fs and 10 ps, ​​for example, 300 fs. The average power of the input radiation IRD may be between 100 mW and several hundred W. The average power of the input radiation IRD may, for example, be 20-50 W.

[0089] The pulsed pump radiation source PRS may be a laser. Spatiotemporal transfer characteristics, such as spectral amplitude and phase, of laser pulses transmitted along such an optical fiber OF can be varied and adjusted through adjustment of (pump) laser parameters, operating component WM variations, and optical fiber OF parameters. The spatiotemporal transfer characteristics may include one or more of output power, output mode profile, output temporal profile, width of output temporal profile (or output pulse width), output spectral profile, and bandwidth of output spectral profile (or output spectral bandwidth). Parameters of the pulsed pump radiation source PRS may include one or more of pump wavelength, pump pulse energy, pump pulse width, and pump pulse repetition rate. Parameters of the optical fiber OF may include one or more of optical fiber length, size and shape of the hollow core HC, size and shape of the capillary, and wall thickness of the capillary surrounding the hollow core HC. Parameters of the operating component WM, such as a fill gas, may include one or more of gas type, gas pressure, and gas temperature.

[0090] The broadband output radiation ORD provided by the radiation source RDS may have an average output power of at least 1 W. The average output power may be at least 5 W. The average output power may be at least 10 W. The broadband output radiation ORD may be a pulsed broadband output radiation ORD. The broadband output radiation ORD may have a power spectral density of at least 0.01 mW / nm across the entire wavelength range of the output radiation. The power spectral density of the broadband output radiation across the entire wavelength range may be at least 3 mW / nm.

[0091] In many applications requiring broadband output radiation ORDs, such as the aforementioned metrology applications, there is growing interest in further extending the short-wavelength edge of broadband output radiation ORDs, particularly into the ultraviolet (UV) wavelength region. The desired wavelength region may include, for example, wavelengths down to 400 nm, down to 350 nm, down to 300 nm, down to 200 nm, down to 100 nm, down to 50 nm, or down to 10 nm. Radiation sources RDS capable of emitting broadband output radiation ORDs (e.g., supercontinuum or white light) with a smooth (or flat) spectral profile and an extended short-wavelength edge are particularly desirable for applications requiring better multi-wavelength capability and greater flexibility. For example, a smoothly extended supercontinuum into the UV is particularly useful in overlay metrology applications where the demand for targets with smaller pitch sizes and more layers cannot be met by existing light sources. The extended UV wavelength can resolve smaller target gratings and penetrate more target layers. The spectral profile, which extends smoothly into the UV, allows precise and reliable wavelength switching between different spectral ranges for different applications or optimization of measurement performance.

[0092] Currently, several methods are being employed to further extend the short-wavelength edge of the broadband output radiation ORD generated in an optical fiber OF. These methods include a) using a longer optical fiber OF, b) using an optical fiber with a smaller core diameter, and c) using lower gas pressure. Used individually or in combination, these methods facilitate the generation of UV wavelengths by ensuring that the phase-matching condition is met in the UV region. However, these methods have many drawbacks. For example, a longer hollow-core HC optical fiber OF (e.g., HC-PCF) typically requires a larger reservoir RSV, leading to larger physical dimensions and higher manufacturing costs for the broadband radiation source RDS. Radiation sources with large footprints are unsuitable for many applications where only limited space is provided to accommodate the radiation source. Reducing the core diameter of a hollow-core HC optical fiber OF increases propagation losses within the fiber, resulting in lower conversion efficiency and an undesirable (e.g., unbalanced or thin) spectral profile. In addition, fabricating hollow-core HC optical fibers OF with smaller core diameters in a drawing tower is very difficult, resulting in higher manufacturing costs. Lowering the gas pressure significantly reduces nonlinearities in gas-filled hollow-core HCs, resulting in lower conversion efficiencies and undesirable (e.g., unbalanced or thin) spectral profiles. To maintain the same level of nonlinearity at lower gas pressures, pulsed pump radiation sources (PRS) with higher pulse energies are required. However, such high-pulse-energy pump radiation sources (PRS) are very expensive.

[0093] Figure 10 is a plot of point spread power spectral density (PSD) versus wavelength λ illustrating simulations of three output spectra generated from a fiber with a 30 μm core diameter, a fiber with a 20 μm core diameter, and a fiber with a 30 μm core diameter operating at a lower pressure. As shown in Figure 10, the first output spectrum SP1 is generated in a first HC-PCF with a 30 μm core diameter and filled with a working medium of krypton gas at a pressure of 25.7 bar. The pulse energy and pulse repetition rate of the input radiation IRD are 5.3 μJ and 5 MHz, respectively. The second output spectrum SP2 is generated in a second HC-PCF with a 20 μm core diameter and filled with the same working medium of krypton gas at the same pressure of 25.7 bar. The pulse energy and pulse repetition rate of the input radiation IRD are 2.4 μJ and 10.6 MHz, respectively. The third output spectrum SP3 is generated in the first HC-PCF filled with the same working medium but at a lower pressure (i.e., lower than 25.7 bar). The pulse energy and pulse repetition rate of the input radiation IRD are 9.7 μJ and 2.7 MHz, respectively. In the simulation, as the pulse energy is changed, the pulse repetition rate is adjusted to maintain a constant average power of the input radiation IRD.

[0094] In contrast to the first output spectrum SP1, the second and third output spectra SP2 and SP3 both have sharp spectral peaks located on the short-wavelength side around 350 nm. Because most of the pump power is converted into the sharp spectral peaks, the PSD of spectral components in other spectral regions, such as the visible and near-infrared regions, is very low. For many applications requiring a smooth, broadband spectrum (e.g., scatterometry-based metrology applications), such an unbalanced or thin spectral profile is problematic and unreliable. For example, in metrology applications, when a sample is illuminated in the UV spectral band (e.g., the range between 300 nm and 400 nm) selected from the second or third output spectrum SP2 and SP3 in FIG. 10, the measurement data becomes very sensitive to small changes in the spectrum. Small shifts in the sharp spectral peaks can lead to large variations in wavelength and / or intensity relative to the sample, resulting in unreliable measurement data (e.g., large measurement errors, lack of reproducibility).

[0095] As mentioned above, there are many nonlinear optical processes involved in generating broadband output radiation ORD (e.g., supercontinuum or white light). Which nonlinear optical process has the greater spectral broadening effect depends on how the operating parameters are set. For example, by selecting the pump wavelength and / or optical fiber so that the pump pulse propagates through the fiber in the normal dispersion region (positive group velocity dispersion (GVD)), self-phase modulation becomes the dominant nonlinear optical process and is responsible for the spectral broadening of the pump pulse. However, in most cases, the spectral broadening of the input radiation IRD provided by the pulsed pump radiation source PRS is driven by soliton dynamics, which requires the pump pulse to propagate through the optical fiber OF in the anomalous dispersion region (negative GVD). This is because in the anomalous dispersion region, the effects of Kerr nonlinearity and dispersion act against each other. If the pulse parameters of a pump pulse entering an optical fiber (e.g., HC-PCF) with anomalous chromatic dispersion do not exactly match those of the soliton, the pump pulse will transform into a soliton pulse with a specific soliton order and dispersive wave.

[0096] Soliton fission and modulation instability (MI) are known to be the two main mechanisms for spectral broadening in soliton-driven broadband radiation generation. The difference between the two mechanisms is that the soliton fission process applies to low soliton orders, while the MI process applies to high soliton orders. MI is a physical process that describes the spontaneous growth of strong narrow-band (compared to the MI modulation frequency) spectral sidebands of a pump pulse in a nonlinearly dispersive medium. MI typically occurs in the anomalous dispersion regime, but it can also occur in the normal dispersion regime if certain conditions are met, such as the presence of higher-order dispersion. In the MI process, small perturbations in the electric field (or envelope) of the pulse, due to quantum fluctuations, are exponentially amplified under the Kerr nonlinearity. The amount of amplification is determined by the MI gain. In such an MI process, the temporal pulse envelope is decomposed into multiple short temporal substructures, or fundamental solitons. In parallel, spectral sidebands are generated symmetrically on both sides of the peak pump wavelength, resulting in a continuously broadening spectral profile.

[0097] The modulation frequency is expressed as: Δω MI = √(2γP / |β2|) (Equation 1) And the corresponding MI period is given by: T MI = 2π / Δω MI = 2π / (√(2γP / |β2|)) (Equation 2) where γ represents the nonlinear coefficient, P represents the pump power, and β represents the fiber propagation constant. For the MI process to be dominant, the pump pulse must be delivered with an MI period of T MI However, the pump pulse duration alone does not indicate whether the soliton fission or MI process is the dominant mechanism for spectral broadening in broadband radiation generation, because the pump pulse duration scales with the pump peak power, affecting the nonlinear coefficient and therefore the modulation period.

[0098] For a given pump pulse with pulse duration τ, the equivalent soliton order N is given by N = (√2)πτ0) / T MI (Formula 3)

[0099] In Equation 1, the soliton for N = 1 is the fundamental soliton. All other solitons for N > 1 are higher-order solitons. As mentioned above, for the MI process to become the dominant spectral broadening mechanism, the pump pulse must be driven with an MI period of T MI " (or, τ0>> T MI ) is required. It has been found that, typically when N >> 20, spectral broadening is dominated by MI processes, while, typically when N << 20, spectral broadening is dominated by soliton splitting. Therefore, for configurations using MI processes, it is desirable to generate input radiation IRD with a high soliton order N. Furthermore, as can be seen from Equation 3, the soliton order of the input radiation IRD is proportional to the pulse duration τ of the input radiation IRD. Thus, for typical prior art configurations dominated by MI processes, the pulse duration τ of the input radiation IRD is typically in the range of 100 femtoseconds (fs) to several tens of picoseconds (ps), with pulse energies in the range of 1 microjoule (μJ) to 20 μJ.

[0100] It should be noted that other nonlinear optical processes, such as the Raman process, can also contribute to nonlinear spectral broadening. The Raman process depends on the type of gas medium. For example, when broadband output radiation ORD is generated in an HC-ARF filled with a noble gas or gas mixture (e.g., argon, krypton, or xenon), MI is the dominant process for spectral broadening of the pump pulse, and the Raman effect is absent. Similarly, when broadband output radiation ORD is generated in an HC-ARF filled with a Raman-active gas or gas mixture (e.g., hydrogen, deuterium, and nitrogen), MI remains the dominant process if the pump pulse is shorter than the oscillation time of the dominant (i.e., higher gain) molecular vibration. However, the Raman effect plays a dominant role when the pump pulse is longer than the oscillation time of the dominant Raman-active mode. The Raman effect induces soliton self-frequency shifts and soliton collisions. It has been found that the interplay between Raman and MI processes can extend the long wavelength edge of the broadband output radiation ORD.

[0101] In addition to the initial pumping process, dispersive waves can also be generated by subsequent nonlinear optical processes. For example, dispersive waves can be formed when solitons are perturbed by localized losses in the fiber or by transitions into fibers with altered parameters. If the generated dispersive waves are phase-matched and spectrally overlap with the solitons, the soliton energy is partially converted into dispersive waves. Dispersive waves are formed in the normal dispersion region with wavelengths shifted from those of the solitons, so dispersive wave generation (DWG) can be utilized for short wavelength extension. For efficient generation of dispersive waves, it is desirable for the solitons to have a relatively broad spectrum and propagate near the zero-dispersion wavelength of the optical fiber OF.

[0102] Returning to FIG. 10, the inventors have found that the sharp spectral peaks in both the second and third output spectra SP2 and SP3 are primarily due to uncontrolled DWG. Therefore, it is proposed to better control the various nonlinear optical processes mentioned above to extend the short-wavelength edge of the broadband output radiation while maintaining a smooth spectral profile. The proposed method and device aim to generate an output spectrum such as the first output spectrum SP1. In particular, such an output spectrum may be such that it does not vary by more than 75%, 50%, 40%, or 30% (in terms of PSD) from the average over a broad wavelength range of interest (e.g., a range with a lower limit between 10 nm and 400 nm and an upper limit between 1000 nm and 3000 nm, a range between 400 nm and 1000 nm, a range between 400 nm and 2000 nm, or a range between 200 nm and 2000 nm). Additionally or alternatively, such output spectrum may be such that it does not contain peaks with a PSD greater than two, three, four or five times the average PSD for the spectrum.

[0103] In this disclosure, methods and apparatus are proposed to overcome the aforementioned problems with existing methods. The methods and apparatus specifically proposed in the following examples extend the broadband output radiation ORD generated from a radiation source RDS based on a hollow-core HC optical fiber OF further into the UV region while maintaining a balanced spectral profile. This may be achieved by applying one or more necks or reduced diameter regions to the hollow-core HC optical fiber OF in which the broadband output radiation ORD is generated. The purpose of applying one or more necks to the hollow-core HC optical fiber OF is to carefully manipulate one or more nonlinear optical processes within the fiber (e.g., the intensity and onset of MI processes and DWG) so that short wavelength extension is effectively achieved in a controlled manner.

[0104] Fiber tapering is known as a useful technique for modifying the local properties of an optical fiber to achieve different optical characteristics. Fiber tapers are used in a wide range of applications, including optical communications and sensing. In these applications, fiber tapers are used to improve mode matching between optical waveguides, provide mode filtering for higher-order guided modes, and increase nonlinearity. Because fiber tapers reduce the core and cladding diameters, the same pump pulse passing through a fiber taper has a higher peak intensity and therefore higher nonlinearity in a more confined fiber taper. In the publication "TA Birks et al., "Supercontinuum generation in tapered fibers," Opt. Lett. 25 (19), 1415 (2000)," fiber tapering is applied to increase the nonlinearity in standard communications fibers. The use of tapered fibers allows unamplified pump pulses to be broadened to a spectrum greater than two octaves wide.

[0105] Tapered fibers may have a waist region with a tapered section where the fiber diameter decreases, a central section of constant diameter, and a flared section where the fiber diameter increases back to the original diameter. The length of the tapered waist region can extend, for example, from a few millimeters to tens of centimeters. If fiber parameters are varied during fiber drawing, tapered waist regions with lengths of, for example, tens of meters are also possible. Typically, tapered fibers are created by heating the fiber (e.g., scanning a heat source or oxybutane flame along the length of the fiber) while a pulling force is gently applied at both ends. Precise control of the drawing in the heated area during the drawing process allows for the production of arbitrary taper profiles and waist lengths. The publication "R. Pennetta et al., "Fabrication and non-destructive characterization of tapered single-ring hollow-core photonic crystal fiber," APL Photonics 4, 056105 (2019)" discloses that a single-ring HC-PCF can be tapered by selectively withdrawing the outer capillary region to balance surface tension using a standard flame brush technique. In the following embodiment, a hollow-core HC optical fiber OF may be tapered adiabatically so that fundamental mode propagation is substantially maintained through the tapered fiber.

[0106] Although higher nonlinearity is advantageous for enhancing the spectral broadening effect, the inventors have found that there is an upper limit to power scalability, beyond which the broadband radiation (e.g., supercontinuum) generation process in tapered hollow-core HC optical fibers OF becomes unstable. Unstable supercontinuum generation is manifested by power and spectral instabilities. It is desirable to optimize the fiber taper to prevent power instabilities and provide the desired spectrum with low pump pulse energy.

[0107] 11 shows schematically two examples of single-waist hollow-core optical fibers configured for producing broadband output radiation with a smooth spectral profile and an extended short-wavelength edge. The single-waist hollow-core optical fiber may comprise a single tapered waist region TP, TP'.

[0108] In some embodiments, the waist region may comprise a central region having a substantially constant diameter between the tapered regions, as illustrated in Figure 11(a). Thus, the single waist hollow core optical fiber STF may comprise five sections: a first non-tapered section FU, a tapered section TD, a central waist section CW (having a substantially or relatively constant diameter), a tapered section TU, and a second non-tapered section SU. Also, a single waist region or reduced diameter region may be interpreted as a fiber section comprising the tapered section TD, the central waist section CW, and the tapered section TU.

[0109] For each section, there may be a corresponding set of parameters defining, for example, section length, core diameter, capillary diameter, etc. Specifically, the first non-tapered section FU may have a first length L1, a first core diameter D1, and a first capillary diameter (not shown), the tapered section TD may have a second length L2, a second core diameter D2 that varies (or decreases) along the tapered section, and a second capillary diameter (not shown) that varies (or decreases) along the tapered section, the central waist section CW may have a third length L3, a third core diameter D3, and a third capillary diameter (not shown), the converging section TU may have a fourth length L4, a fourth core diameter D4, and a fourth capillary diameter (not shown), and the second non-tapered section SU may have a fifth length L5, a first core diameter D1, and a first capillary diameter (not shown). At the location where the convergent portion TD and the central waist portion CW meet, the second core diameter D2 may be the same as the third core diameter D3, and the second capillary core diameter may be the same as the third capillary core diameter. Similarly, at the location where the central waist portion CW and the divergent portion TU meet, the third core diameter D3 may be the same as the fourth core diameter D4, and the second capillary core diameter may be the same as the fourth capillary core diameter.

[0110] It should be noted that the aforementioned fiber parameters are examples of parameters that are particularly appropriate for a tapered single-ring HC-ARF. Other different types of optical fibers may have different or additional fiber parameters. For example, in some embodiments, the optical fiber may comprise a different type of HC-ARF, such as a Kagome fiber, whose cladding structure comprises a set of concentric hexagonal rings. In such cases, the aforementioned capillary diameter may be replaced by the distance between two opposing edges of the hexagonal rings.

[0111] It should be noted that a central waist CW is not necessarily required for a tapered optical fiber or taper. In some embodiments, the optical fiber may be tapered, with a converging portion TU immediately following the tapering portion TD. Thus, a tapered optical fiber may not have a central waist CW, or the central waist CW may be so short that its presence is substantially negligible. Figure 11(b) schematically illustrates another configuration of a single-waist hollow-core optical fiber, in which the single-waist region TP' may not have a central waist. The optical fiber OF used in the embodiment of Figure 11(b) may be the same as that in the embodiment of Figure 11(a). The main difference is that the single waist TP' of the tapered optical fiber STF' shown in Figure 11(b) does not include a central waist CW. At the location where the tapered portion TD and the flared portion TU meet (or at the taper waist location), the second core diameter D2 may be the same as the fourth core diameter D4, and the second capillary core diameter (not shown) may be the same as the fourth core diameter (not shown). It should also be understood that one or more other portions of the single waist hollow core optical fiber STF may be omitted. For example, in other embodiments, the single waist hollow core optical fiber may not include the flared portion TU or the second non-tapered portion SU. In different embodiments, the single waist hollow core optical fiber may not include the first non-tapered portion FU or the tapered portion TD.

[0112] In the tapering section TD, the structural dimensions of the fiber may gradually and continuously decrease along the axial or length of the single-waist hollow-core optical fiber STF, STF'. For example, the first core diameter D1 and the first capillary diameter may gradually decrease to the second core diameter D2 and the second capillary diameter, respectively. Similarly, in the expanding section TU, the structural dimensions of the fiber may gradually and continuously increase along the axial or length of the single-waist hollow-core optical fiber SFT, STF'. For example, the fourth core diameter D4 and the fourth capillary diameter may gradually and continuously increase to the first core diameter D1 and the first capillary diameter, respectively. The rate at which the structural dimensions, such as the core diameters, increase or decrease may depend on the tapering process, such as the rate at which the fiber is drawn during tapering.

[0113] The first non-tapered section FU may be the input end of the tapered hollow optical fiber STF, STF′, and the second non-tapered section SU may be the output end of the tapered optical fiber STF, STF′. The first non-tapered section FU may have a first fiber face FF, and the second non-tapered section SU may have a second fiber face SF. Returning to FIG. 8 , in operation, the tapered optical fiber STF, STF′ may be completely surrounded by a reservoir RSV filled with a suitable medium WM, such as a noble gas or a noble gas-dominated gas mixture. After entering the reservoir RSV, input pump pulses emitted from the pulsed pump radiation source PRS may be coupled into the first non-tapered section FU through the first fiber face FF. The generated broadband output radiation ORD may then exit the second non-tapered section SU through the second fiber face SF. It should be understood that the configuration in FIG. 8 is merely an example. In different configurations, the tapered fiber may be partially surrounded by the reservoir RSV. In other configurations, the reservoir RSV in FIG. 8 may not be used. For example, the hollow core of the tapered optical fiber STF, STF' may first be filled with a noble gas or a noble gas-dominated gas mixture WM. The gas-filled hollow core HC may then be sealed, for example, by attaching optical mirrors to each fiber face (e.g., the first fiber face FF and the second fiber face SF). In this way, the use of a reservoir RSV may be omitted.

[0114] In some embodiments, the non-tapered or uniform optical fiber OF may comprise one of the HC-PCFs described above (e.g., a single ring HC-ARF as illustrated in FIG. 7). When used for generating broadband output radiation ORD, the single-waist hollow-core optical fiber STF, STF' may be provided in a broadband radiation source RDS as shown in FIG. 8. In some embodiments, the single-waist hollow-core optical fiber STF, STF' may be filled with a noble gas or a noble gas-dominant mixture. As mentioned above, a noble gas or a noble gas-dominant mixture may enable the MI process to become the dominant nonlinear optical process for spectral broadening.

[0115] Figure 12(a) shows a plot of wavelength λ-energy (or signal sig(dB)) spectral density versus position P along the fiber length for a simulation describing the spectral evolution of a pulse of input radiation in a single-waist hollow-core optical fiber (e.g., as shown in Figure 11(b)) with a waist region beginning at an optimized position along the fiber length (e.g., where the tapering begins). The optimized position may be where MI-dominated spectral broadening has already begun. The single-waist hollow-core optical fiber may be located within a radiation source, for example, as shown in Figure 8. The white line "0 GVD" indicates the wavelength at which group velocity dispersion becomes zero. Since the zero-dispersion wavelength varies with the local fiber core diameter (e.g., shorter zero-dispersion wavelengths correspond to smaller core diameters), the white line "0 GVD" also indicates the variation in fiber core diameter along the length of the single-waist hollow-core optical fiber STF'. In this example simulation, the total length of the single-waist hollow-core optical fiber STF' is 42 cm. The lengths of the first non-tapered portion FU, the tapered portion TD, the converging portion TU, and the second non-tapered portion SU are 20 cm, 9 cm, 9 cm, and 4 cm, respectively. The diameter of the hollow core in the non-tapered portions FU and SU is 30 μm, and the minimum diameter of the hollow core (or the tapered waist diameter) where the tapered and converging portions meet is 20 μm. In the simulation, the diameter of the hollow core in the tapered portion TD is treated as decreasing linearly from 30 μm to 20 μm, and the diameter of the hollow core in the converging portion TU is treated as increasing linearly from 20 μm to 30 μm (this is for the sake of simplicity; in reality, a taper with a linearly varying diameter is unlikely due to the manufacturing process).

[0116] The hollow core of the single-waist hollow-core optical fiber STF' may be filled with a working medium of krypton gas at a pressure of 25.7 bar. The input radiation may be a train of pump pulses with a repetition rate of 5 MHz and a center wavelength of 1030 nm. The full-width at half maximum (FWHM) pulse duration may be 300 fs, and the pulse energy may be 5.3 μJ. The pulsed input radiation (or pump pulse) IRD entering the single-waist hollow-core optical fiber STF' transforms into a high-order soliton with a soliton order of N = 110. The soliton order varies with the core diameter, so that the initial soliton order decreases to N = 75 when the core diameter is reduced to 20 μm. As mentioned above, the soliton order of the pump pulse is a convenient parameter that can be used to distinguish between conditions in which the spectral broadening is dominated by MI and conditions in which the spectral broadening is dominated by soliton splitting. Since the soliton order is significantly higher than “20”, which is interpreted as the lower limit of the MI process, the spectral broadening observed in the first untapered section FU (or the first 20 cm of the single-neck hollow-core optical fiber STF′) is mainly due to the MI process.

[0117] As shown in Figure 12(a), the MI process begins at a distance of approximately 13 cm from the first fiber face FF of the single-waist hollow-core optical fiber STF'. The MI process results in significant spectral broadening, extending the long-wavelength edge to approximately 1600 nm and the short-wavelength edge to approximately 500 nm. When the spectrally broadened pulse enters the tapered section (i.e., at a distance of 20 cm from the first fiber face FF), the decreasing core diameter changes the conditions of the previously established nonlinear optical process, facilitating the efficient generation of wavelength-shifted dispersive waves. This results in additional short-wavelength extension. This additional short-wavelength extension is evident in Figure 12(a), where the short-wavelength edge of the spectrum extends from approximately 500 nm at a distance of 20 cm from the first fiber face FF to less than 300 nm at a distance of 28 cm from the first fiber face FF. The maximum short-wavelength extension is achieved around the tapered waist location, or the point where the tapered section TD and the diverging section TU meet.

[0118] The location of the taper, defined as the point where tapering begins, is important for simultaneously obtaining maximum short wavelength extension and a smooth overall spectral profile, such as the example spectral profile shown in Figure 12(a). For a single-neck hollow-core optical fiber STF, STF', the taper location may be precisely determined via simulation. Alternatively or additionally, the taper location may be determined using a cut-back method, which may comprise, for example, the following four steps: step 1) measuring the output spectrum and power in a length of (e.g., a long) untapered hollow-core optical fiber; step 2) cutting the untapered fiber at a point near the input end to obtain a shortened length; step 3) performing the same measurements on the shortened length of the untapered fiber; and step 4) repeating steps 2) through 3) until the measured output spectrum confirms that MI-dominated spectral broadening has occurred. The corresponding remaining length of the untapered fiber may be used to set the length of the first untapered portion FU of the single-neck hollow-core optical fiber STF, STF'. In this way, the single taper, more specifically the tapered portion TD, may start immediately after the determined length.

[0119] It should be understood that different sets of operating parameters (e.g., parameters of the input radiation IRD, the optical fiber OF, the working medium WM, etc.) lead to different nonlinear conditions and require different taper parameters (e.g., taper position, tapering rate, taper waist, etc.). For example, for different sets of operating parameters, the single-waist hollow-core optical fiber STF of Figure 11(a) with an additional central waist CW may be used to obtain a smoothly elongated spectral profile. The central waist CW further improves the nonlinearity for the propagating pulse (due to the smaller core diameter) and increases the efficiency of the DWG.

[0120] A hollow-core optical fiber tapered with a single taper is an effective approach for generating broadband output radiation ORDs with a spectral profile that smoothly extends into the UV. However, the primary function of the single taper is to control the onset of the DWG. The onset of the MI process, which is enabled primarily by providing a sufficient length of the first non-tapered section FU, cannot be controlled. If the length of the first non-tapered section FU is insufficient for a given set of operating parameters, the resulting output spectrum will not have the desired spectral profile.

[0121] Figure 12(b) shows a plot equivalent to Figure 12(a) for a simulation of the spectral evolution of a pulse of radiation in the single-waist hollow-core optical fiber shown in Figure 11(b) when the single-waist region is in a non-optimized position (i.e., the position where MI-dominated spectral broadening begins at the taper). The simulation shown in Figure 12(b) is based on the same tapered hollow-core optical fiber used in the simulation shown in Figure 12(a). The main difference between the two simulations is that the pulse energy of the input radiation IRD in the simulation of Figure 12(b) is 2.4 μJ instead of 5.3 μJ. The same length of the first non-tapered section FU is not sufficient to trigger the onset of the MI process due to the lower pulse energy. As shown in Figure 12(b), the onset of MI-dominated spectral broadening is delayed until the pulse enters the tapering region (e.g., the tapered section TD and the flared section TU). In this simulation example, the delay in the MI process prevents the occurrence of DWG, resulting in an output spectrum with a lean profile and no short wavelength extension.

[0122] Figure 13 shows simulations of two output spectra of a radiation source with the same parameters as those shown in Figures 12(a) and 12(b), respectively. The unoptimized output spectrum USP, generated from a radiation source in which the hollow-core fiber is tapered at a non-optimized position, has a spectral bandwidth similar to the first output spectrum SP1 (generated from the same but uniform optical fiber) and, like the second output spectrum SP2, has two pronounced, sharp peaks (e.g., one around 450 nm and the other around 1000 nm). Such a spectral profile is undesirable for metrology applications. In contrast, the output spectrum OSP, generated from a radiation source in which the hollow-core fiber is tapered at an optimized position, has an extended short-wavelength edge and a smoother spectral profile (or a more balanced PSD profile).

[0123] In addition to the simulations described above, the inventors also conducted experiments to prove the concept. FIG. 14(a) schematically illustrates how the fiber core diameter varies along the length of an exemplary single-waist hollow-core optical fiber optimized via simulation for short-wavelength extension of the output radiation ORD and maintaining a balanced spectral profile. Note that the illustrated fiber design is only one specific example of the hollow-core optical fiber STF shown in FIG. 11(a). The fiber design is also used as a target for manufacturing the fiber. Therefore, the final or manufactured fiber dimensions (e.g., dimensions of the waist region including the tapered portion TD, the central waist portion CW, and the bulged portion TU) may deviate slightly from the designed values ​​within a manufacturing tolerance. It is understood that the size of the manufacturing tolerance depends on many factors, such as the method by which the fiber is tapered and the tools used for such fiber tapering. The manufacturing tolerance for a single-waist hollow-core optical fiber according to the design of FIG. 14(a) may be about ±5%, about ±10%, about ±15%, or about ±20% of each target dimension.

[0124] Returning to FIG. 14(a), in this example design, the first non-tapered section FU, the tapered section TD, the flared section TP, and the second non-tapered section SU are approximately 29 cm, 4 cm, 2 cm, 4 cm, and 3 cm long, respectively. The fiber core diameter FCD at the first non-tapered section FU or the second non-tapered section SU is approximately 32 μm. The fiber core diameter FCD at the tapered section TD or the flared section TU varies substantially linearly along the fiber length. The fiber core diameter FCD at the central waist CW is approximately 21.5 μm. In this case, the tapering ratio, defined as the ratio of the fiber core diameter FCD at the central waist CW to the fiber core diameter FCD of the first or second non-tapered section FU or SU, is calculated to be approximately 0.67. The length of the first untapered section FU (in this case about 29 cm) is intentionally chosen to ensure that, for a given set of operating parameters, the MI undergoes dominant spectral broadening before the pump pulse enters the neck region of the fiber.

[0125] Figure 14(b) shows two measured output spectra, "SP_REF" and "SP_SW," emitted from a uniform hollow-core optical fiber and a single-waist hollow-core optical fiber (e.g., the one shown in Figure 14(a)), respectively. The spectrum "SP_REF" corresponds to a baseline situation in which a set of operating parameters is carefully selected for a given hollow-core optical fiber. In this particular experiment, the uniform fiber was a single-ring HC-ARF (e.g., the one illustrated in Figure 7) with a core diameter of 32 μm. The working medium WM that filled the hollow core of the uniform fiber was a gas mixture containing 98% argon and 2% hydrogen in molar ratios. The pressure of the working medium WM was set to 40 bar. The pulsed pump radiation PRS emitted a train of pump pulses with a repetition rate of 1 MHz. The pump pulses had a center wavelength of approximately 1030 nm, a pulse duration of approximately 300 fs, and a pulse energy of approximately 4.16 μJ. As can be seen, the baseline spectrum has a very thin (or non-smooth / flat) spectral profile, especially in the wavelength range between 300 and 600 nm, which is not suitable for practical use.

[0126] In contrast, spectrum "SP_SW" was generated from a tapered hollow-core optical fiber made from the same uniform fiber (or a different fiber with the same design) used to generate spectrum "SP_REF," but post-processed (i.e., tapered) to the design shown in FIG. 14(a). To fine-tune the output spectrum to balance short-wavelength extension and spectral shape, the pump pulse energy was adjusted (e.g., increased from 4.16 μJ to 5.36 μJ) while other operating parameters remained the same. It is clear from the comparison that the implementation of a single waist region (or single taper) not only further extends the short-wavelength edge (e.g., from about 350 nm to 300 nm), but also significantly smooths the original thin spectral profile, especially in the wavelength range between 300 and 600 nm (e.g., the valley region around 400 nm no longer exists).

[0127] Figure 14(c) shows three measured power transfer curves, "P_REF," "P_SW1," and "P_SW2," describing how the integrated output power varies with input pump pulse energy for different hollow-core optical fibers under different operating conditions. Specifically, the power transfer curve "P_REF" was obtained based on the same uniform hollow-core optical fiber and the same operating parameters (except that the input pump pulse energy was intentionally varied in this measurement) as those used to generate the spectrum "SP_REF" shown in Figure 14(b). Similarly, the power transfer curve "P_SW1" was obtained based on the same tapered hollow-core optical fiber and the same operating parameters (except that the input pump pulse energy was intentionally varied in this measurement) as those used to generate the spectrum "SP_SW" shown in Figure 14(b). The power transfer curve "P_SW2" was obtained based on the same tapered hollow-core optical fiber and the same operating parameters (except that the pump pulse repetition rate was increased from 1 MHz to 2 MHz) as those used to generate the power transfer curve "P_SW1."

[0128] Here, the integrated output power is the power integrated over a specific wavelength range or spectral bandwidth of the output radiation ORD emitted from the fiber. As can be seen, for all three power transfer curves (P_REF, P_SW1, and P_SW2), the output power increases as the input pump pulse energy increases without a significant inversion at the high-energy end. Thus, it was confirmed that, up to pulse energies of at least approximately 7 μJ, the implementation of a single-waist region (or a single taper) has no or negligible adverse effect on the energy scaling capability of the radiation source RDS when a single-waist hollow-core optical fiber is used for broadband radiation generation. A comparison between the power transfer curves (P_REF and P_SW1) indicates that at the same pump pulse repetition rate (e.g., 1 MHz), the pump energy threshold for generating output radiation ORD is lower in the single-waist hollow-core optical fiber than in the uniform hollow-core optical fiber. Furthermore, a comparison between the power transfer curves "P_SW1" and "P_SW2" shows that a higher pump pulse repetition rate results in a higher pump energy threshold and a higher slope efficiency (the gradient of the curve).

[0129] According to the simulation shown in Figure 12(b), fiber tapering is beneficial in triggering the onset of the MI process. Thus, an additional necked or reduced-diameter region may be applied to the single-necked hollow-core optical fiber STF, STF' to provide better active control over the MI process (e.g., the onset of the MI process) rather than relying on the MI process being passively triggered in the first non-tapered portion FU. The use of an additional necked region is also advantageous in that it allows the MI-dominated spectral broadening to begin even at low pulse energies. In this way, the power and spectral instabilities mentioned above for high pulse energies may be avoided.

[0130] 15 schematically illustrates a double-waisted hollow-core optical fiber DTF configured for producing broadband output radiation with a smooth spectral profile and an extended short-wavelength edge. The double-waisted hollow-core optical fiber DTF may comprise a first waist region or reduced diameter region TP1 and a second waist region or reduced diameter region TP2, each located at two different positions along the fiber.

[0131] Each of the two tapers may be configured as a single taper as shown in FIG. 11( a) (i.e., with a central waist as illustrated here), a single taper as shown in FIG. 11( b) (i.e., without a central waist), or a combination thereof (e.g., the first waist region may have a central waist and the second waist region may not have a central waist, or vice versa). In some embodiments, the non-tapered hollow-core optical fiber may comprise one of the HC-PCFs described above (e.g., a single ring HC-ARF as illustrated in FIG. 7). When used for generating broadband output radiation ORD, the double-waist hollow-core optical fiber DTF shown in FIG. 15 may be provided in the radiation source RDS shown in FIG. 8. The double-waist hollow-core optical fiber DTF may be filled with a noble gas or a noble-gas-dominant mixture. As mentioned above, a noble gas or a noble-gas-dominant mixture enables the MI process to become the dominant nonlinear optical process for spectral broadening.

[0132] In the embodiment of Figure 15, the double waist hollow core optical fiber DTF may comprise nine sections: a first non-tapered section UT1, a first tapered section TD1, a first central waist CW1, a first tapered section TU1, a second non-tapered section UT2, a second tapered section TD2, a second central waist CW2, a second tapered section TU1, and a third non-tapered section UT3. For each section, there may be a set of parameters defining, for example, the section length, core diameter, and capillary diameter. Specifically, the first non-tapered section UT1 may have a first length L1', a first core diameter D1', and a first capillary diameter (not shown), and the first tapered section TD1 may have a second length L2', a second core diameter D2' that varies (or decreases) along the tapered section, and The first central waist portion CW1 may have a third length L3′, a third core diameter D3′, and a third capillary diameter (not shown), the first converging portion TU1 may have a fourth length L4′, a fourth core diameter D4′, and a fourth capillary diameter (not shown), the second non-tapered portion UT2 may have a fifth length L5′, a first core diameter D1′, and a first capillary diameter, and the second The tapered portion TD2 may have a sixth length L6', a sixth core diameter D6', and a sixth capillary diameter (not shown), the second central waist portion CW2 may have a seventh length L7', a seventh core diameter D7', and a seventh capillary diameter (not shown), the second converging portion may have an eighth length L8', an eighth core diameter D8', and an eighth capillary diameter (not shown), and the third non-tapered portion UT3 may have a ninth length L9', a first core diameter D1', and a first capillary diameter. In different embodiments, the double waist hollow core optical fiber DTF may have either of two central waist portions TW1, TW2. In other embodiments, the double waist hollow core optical fiber DTF may not have a central waist portion.

[0133] In some embodiments, a first taper TP1 near the first fiber face FF' may be used to trigger the initiation of the MI process, and a second taper TP2 located downstream of the first taper TP1 and near the second fiber face SF' may be configured to trigger the initiation of DWG. The term "downstream" describes a position closer to the output end of the fiber, and "upstream" describes a position closer to the input end of the fiber. The above-mentioned configurations of radiation source RDS applicable to the single-waist hollow-core optical fiber STF, STF' are equally applicable to the double-waist hollow-core optical fiber DTF.

[0134] Figure 16(a) shows a plot equivalent to Figure 12 for a simulation of the spectral evolution of a pulse of radiation in a tapered hollow-core optical fiber having two neck regions (e.g., as shown in Figure 15), with a first neck region applied to control modulation instability processes and a second neck region applied to control dispersive-wave generation. The white line "0 GVD" indicates the zero-dispersion wavelength and the variation of the fiber core diameter along the length of the double-necked hollow-core optical fiber DTF. In this simulation example, the total length of the double-necked hollow-core optical fiber DTF is 42 cm, the same as, for example, the single-necked hollow-core optical fiber STF, STF' shown in Figures 11(a) and 11(b). The lengths of the first non-tapered portion UT1, first tapered portion TD1, first converging portion TU1, second non-tapered portion UT2, second tapered portion TD2, second central waisted portion CW2, second converging portion TU2, and third non-tapered portion UT3 are 4 cm, 5 cm, 7 cm, 5 cm, 5 cm, 5 cm, 4 cm, 5 cm, and 2 cm, respectively. The diameter of the hollow core in the non-tapered portions UT1, UT2, and UT3 is 30 μm, and the minimum diameter of the hollow core (or the tapered waist diameter) in the first central waisted portion CW1 and second central waisted portion CW2 is 20 μm. In the simulation, the diameter of the hollow core in the tapered sections TD1 and TD2 is treated as linearly decreasing from 30 μm to 20 μm, and the diameter of the hollow core in the expanded sections TU1 and TU2 is treated as linearly increasing from 20 μm to 30 μm.

[0135] The hollow core of the double-neck hollow-core optical fiber DTF may be filled with a working medium of krypton gas at a pressure of 25.7 bar. The input radiation may be a train of pump pulses with a repetition rate of 10.6 MHz and a center wavelength of 1030 nm. The full-width at half maximum (FWHM) pulse duration is 300 fs, and the pulse energy is 2.4 μJ. Upon entering the double-neck hollow-core optical fiber DTF, the pulsed input radiation (or pump pulse) IRD is transformed into a high-order soliton with a soliton order of N = 80. Since the soliton order varies with the core diameter, the initial soliton order decreases to N = 54 when the core diameter is reduced to 20 μm. This high soliton order ensures that the input radiation IRD is spectrally broadened in the MI region.

[0136] As shown in FIG. 16(a), the MI process begins at the first constriction TU1 of the first constriction region TP1. The first constriction region TP1 initiates (or at least supports) MI-dominated spectral broadening at a distance of approximately 16 cm from the first fiber face FF' (or input fiber end). This contrasts with the case shown in FIG. 12(b), where input radiation IRD with the same pulse energy of 2.4 μJ does not undergo MI-dominated spectral broadening even at a distance of 25 cm. Thus, the first constriction region TP1 facilitates the initiation of the MI process. Before entering the second constriction region TP2, the spectrum of the input radiation is significantly broadened to cover the spectral range between approximately 450 nm and 1700 nm.

[0137] The DWG-induced short wavelength extension begins when the pulsed input radiation IRD reaches the second waist region TP2 (more specifically, the second central waist portion CW2 of this second waist region). This results in the spectral short wavelength edge being extended from approximately 450 nm to a minimum of approximately 300 nm. The first tapered waist region effectively provides the DWG-induced short wavelength extension. This is in contrast to the case shown in Figure 12(b), where the input radiation IRD with the same pulse energy of 2.4 μJ does not provide the DWG-induced short wavelength extension itself due to a delay in the onset of the MI process.

[0138] Figure 16(b) shows a simulation of the output spectrum of the radiation source with the same parameters as the simulation shown in Figure 16(a). In contrast to the unoptimized generated output spectrum USP shown in Figure 13, even with the same pump pulse energy, the double-waisted hollow-core optical fiber DTF can significantly extend the short-wavelength edge of the spectrum DSP while maintaining a much smoother spectral profile (or a more balanced PSD profile).

[0139] To design a double-neck hollow-core optical fiber (DTF) for broadband radiation generation, it is important to ensure that the location and parameters of the first neck are optimized to control the onset and intensity of MI-induced spectral broadening, and that the location and parameters of the second neck are optimized to control the onset and intensity of MI-induced spectral broadening. MI-induced spectral broadening can begin between 5 cm and 30 cm from the first facet FF' of the double-neck hollow-core optical fiber (DTF). For example, the MI onset can be between 10 cm and 20 cm, 14 cm and 16 cm, 15 cm and 35 cm, 20 cm and 30 cm, or 24 cm and 28 cm from the first facet FF'. For example, if the first central neck portion CW1 of the first neck region TP1 is inappropriately long, dispersive waves will be generated within the first neck region. In such a case, the desired short wavelength extension is achieved, but the output spectral profile will be unbalanced, resulting in a sharp UV peak similar to the second output spectrum SP2. Therefore, in addition to optimizing each waist region for each step, it is also important to ensure that the first waist region ends before the start of the DWG. In some embodiments, the first cone portion TU1 may be located within a short distance from the start of the MI step. Such a short distance may be, for example, between -10 and 10 cm, between -5 and 5 cm, between -2.5 and 2.5 cm, or between -1 and 1 cm.

[0140] It should be noted that the term "taper" used in the previous embodiments should be broadly interpreted to refer to a portion of an optical fiber where the structural dimensions of the fiber (e.g., internal core diameter, internal and / or external capillary diameters) change along the fiber length. Thus, a taper may be interpreted as a structural change portion of the optical fiber OF, and a non-tapered portion of the optical fiber OF may be interpreted as comprising one or more main portions. A waist region does not necessarily have to comprise all three portions: the tapered portion TD, the central waist portion CW, and the flared portion TU. It should be understood that the double waist hollow-core optical fiber DTF is merely one example. In other embodiments, one or more portions of the double waist hollow-core optical fiber DTF may be omitted. For example, in one embodiment, the double waist hollow-core optical fiber may not comprise the third non-tapered portion UT3. In a different embodiment, the double waist hollow-core optical fiber may not comprise the first non-tapered portion UT1 and the first tapered portion TD1. In this case, input radiation IRD may be directly coupled into the first central waist portion CW1. It should also be understood that more than one waist region may be applied to a hollow-core optical fiber. More waist regions may provide additional flexibility for effectively controlling a variety of different nonlinear optical processes. It should be noted that the application of more than one waist region to a hollow-core optical fiber to improve broadband radiation generation is not limited to controlling MI processes and DWG. More than one waist region may also be applied to control other nonlinear processes in gas-filled hollow-core optical fibers.

[0141] As described in the previous embodiment, applying one or more necks or reduced-diameter regions to the hollow-core HC optical fiber OF from which broadband output radiation ORD is generated allows for the careful manipulation of one or more nonlinear optical processes within the fiber (e.g., the intensity and onset of MI processes and DWG) so that short-wavelength extension is effectively achieved in a controlled manner. The degree of short-wavelength extension or the position of the short-wavelength edge of the output spectrum is primarily determined by the phase-matching condition between the associated solitons and dispersive waves. Further short-wavelength extension can be obtained by further reducing the size of the necks applied to the hollow-core HC optical fiber OF. However, such an approach has limitations because smaller tapered neck sizes lead to reduced light transmission and increased manufacturing difficulties.

[0142] Therefore, a method is desirable that not only allows the short-wavelength edge of the broadband output spectrum to be further extended into the UV region, but also avoids further reduction of the tapered waist. The inventors have identified that soliton trapping of dispersive waves can be used to extend the short-wavelength limit of the broadband output radiation ORD generated in a hollow-core HC optical fiber OF. According to the publication "J.C. Travers, 'Blue extension of optical fiber supercontinuum generation', Journal of Optics, 12 (2010) 113001," the soliton trapping process begins when a soliton of adequate intensity in the anomalous region overlaps in time with a dispersive wave in the normal dispersion region with the same group velocity. In such a case, four-wave mixing within the pulse can slightly blue-shift the dispersive wave and slightly red-shift the soliton. As a result, the dispersive wave and the soliton shift into a region with a lower group velocity, slowing both down. If the temporal overlap between the soliton and the dispersive wave is maintained, the dispersive wave will be captured by the soliton as it continues to blueshift. On the other hand, if the wavelength shift causes a group velocity mismatch between the soliton and the dispersive wave, and if this group velocity mismatch is large enough, the two waves will eventually separate in time and the soliton trapping process will cease. Therefore, the soliton trapping process can be maintained by matching the group velocities of the soliton and the dispersive wave or by minimizing the group velocity mismatch between the soliton and the dispersive wave.

[0143] The inventors have recognized that when broadband output radiation ORD is generated in a non-tapered or uniform hollow-core HC optical fiber OF (e.g., a uniform HC-PCF) with a Raman-free working medium WM (e.g., a noble gas or gas mixture), and the operating parameters (e.g., pump laser parameters) are selected to enable MI-dominated spectral broadening, the solitons have a higher group velocity than the dispersive waves. In this way, the dispersive waves cannot trap the solitons once they are generated, and soliton trapping of the dispersive waves does not occur.

[0144] The inventors have recognized that the soliton trapping process can be initiated and sustained by applying at least one group velocity control mechanism to a hollow-core HC optical fiber OF from which broadband output radiation ORD is generated, because the group velocity control mechanism variably controls the group velocities of the solitons and dispersive waves, minimizing their temporal separation and maintaining their temporal overlap.

[0145] In some embodiments, the group velocity control mechanism may include at least one taper with a specific taper slope. The taper slope of each taper may be carefully optimized to alter the group velocities of solitons and dispersive waves to different degrees. For example, a taper with an optimized taper slope may slow down solitons more than dispersive waves. This effectively compensates for or minimizes the time separation between solitons and dispersive waves before they enter the taper, allowing them to maintain good temporal overlap as they propagate through the fiber. In contrast, the primary purpose of the tapers or waist regions TP, TP', TP1, and TP2 shown in Figures 11(a), 11(b), and 15 is to control the intensity and onset of MI processes and DWG. For this reason, the effect of the taper slope on soliton trapping of dispersive waves may not be considered when implementing these tapers.

[0146] FIG. 17 schematically illustrates a further single-waist hollow-core optical fiber configured for soliton trapping of dispersive waves, according to one embodiment. As shown, the single-waist hollow-core optical fiber TOF1 may comprise a first fiber face FF11 for receiving input radiation IRD and a second fiber face SF11 for outputting broadband output radiation ORD. The single-waist hollow-core optical fiber TOF1 may comprise three fiber sections: a uniform or non-tapered section UT11 having a first length L11, a tapered section TD11 having a second length L12, and a central waist section CW11 having a third length L13. The uniform section UT11 may have a constant first hollow-core diameter D11 along the length of the section. In contrast, the tapered section TD11 may have a second hollow-core diameter D12 that decreases continuously and substantially linearly along the length of the section. The third section, i.e., central waist CW11, may begin immediately after tapered section TD11 and may have a third hollow core diameter D13 that is reduced relative to the first core diameter D11 but constant along the length of the section. Tapered section TD11 and central waist CW11 may form a waisted region or taper TP11 as defined in the previous embodiment.

[0147] In this embodiment, the second hollow core diameter D12 may decrease with a predetermined taper gradient TG11, which may be used to describe the rate at which the hollow core changes size along the length of the fiber and may be defined as: TG = ΔR / ΔL (Equation 4) where ΔR represents the change in hollow core radius at any given portion of the taper TD11 and ΔL represents the fiber length over which the change in hollow core radius ΔR occurs. The inventors have determined that the taper slope may fall within ranges, for example, between 0.01 μm / cm and 10 μm / cm, between 0.05 μm / cm and 5 μm / cm, between 0.1 μm / cm and 1 μm / cm, or between 0.1 μm / cm and 0.5 μm / cm.

[0148] Figures 18(a) and 18(b) are two simulated spectrograms describing the temporal and spectral distribution of a pulse of input radiation after propagation over distances of 70 cm and 110 cm in a uniform hollow-core optical fiber. The horizontal axis represents the time distribution or delay between the spectral components of the input radiation, and the vertical axis represents the spectral distribution of the input radiation. The contrast in the grayscale plots ranges from black for the weakest energy (dB) to white for the strongest.

[0149] In this simulation example, a uniform hollow-core HC optical fiber OF (e.g., a single-ring HC-ARF as illustrated in FIG. 7) may have a length of 110 cm and a core diameter of 30 μm (or a core radius of 15 μm). The position "Pos = 70 cm" corresponds to a position in the fiber 70 cm away from the first fiber face F11, and the position "Pos = 110 cm" corresponds to the position of the second fiber face SF11. The hollow core HC may be filled with a working medium WM of krypton gas at a pressure of 25.7 bar. Pulsed input radiation IRD has a pump pulse duration τ of 150 fs, a pulse energy Ep of 0.5 μJ, and a center wavelength λ of 1030 nm. The pulsed input radiation IRD may be admitted into the fiber via the first fiber face FF11 and may exit the fiber via the second fiber face SF11. This configuration enables pumping in the anomalous dispersion regime. The pulsed input radiation (or pump pulse) IRD entering the single-neck hollow-core optical fiber TOF1 transforms into a high-order soliton with soliton order N = 23, ensuring a MI-dominated nonlinear optical process. As can be seen in Figure 18(a), the delay time between the dispersive wave around 580 nm and the soliton around 1380 nm is less than 100 fs, and they still partially overlap in time. However, after propagating a distance of another 40 cm, the delay time between the dispersive wave and the soliton becomes greater than 300 fs. This large delay time results in a complete time separation between the dispersive wave and the soliton, thereby preventing the soliton trapping process from occurring.

[0150] Figures 18(c) and 18(d) are two simulated spectrograms depicting the temporal and spectral distribution of a pulse of input radiation after propagation of 70 cm and 110 cm distances, respectively, within a single-waist hollow-core optical fiber (e.g., the one shown in Figure 17). This simulation is based on the same operating parameters as those used in the simulations shown in Figures 18(a) and 18(b). The single-waist hollow-core optical fiber TOF1 may have a length of 110 cm. As shown in Figure 17, the waist region may begin just after 70 cm from the first fiber face FF11 of the fiber and may end at the second fiber face SF11. The first hollow-core diameter D11 may be 30 μm, and the taper slope TG11 may be 0.2 μm / cm. In this case, the hollow-core diameter (e.g., the third hollow-core diameter D13) is reduced to 24 μm at the end of the tapered section TD11. This reduced hollow core size may be substantially constant along the length of central waist CW11.

[0151] As can be seen in Figure 18(c), the temporal and spectral distribution of the input radiation IRD is identical to that shown in Figure 18(a), simply due to the fact that the untapered section UT11 of the single-neck fiber TOF1 has the same structural dimensions (except for length) as the uniform fiber (not shown) used in the simulation shown in Figure 18(a). Figure 18(d) confirms that the use of the necked region slows the soliton, and good temporal overlap between the dispersive wave and the soliton is substantially maintained until it exits the fiber through the second fiber face SF11. Good temporal overlap may correspond to, for example, a delay time of less than 50 fs, less than 20 fs, or even less than 10 fs. Such good temporal overlap enables soliton trapping of the dispersive wave, resulting in a further blueshift of the short-wavelength edge from 580 nm, as shown in Figure 18(b), to below 500 nm, as shown in Figure 18(d).

[0152] FIG. 19 schematically illustrates another different single-waist hollow-core optical fiber configured for soliton trapping of dispersive waves, according to one embodiment. The single-waist hollow-core optical fiber TOF2 may comprise a first fiber face FF22 for receiving input radiation IRD and a second fiber face SF22 for outputting broadband output radiation ORD. The fiber may comprise only two sections: a non-tapered / uniform section UT22 having a first length L21 and a tapered section TD22 having a second length L22. The uniform section UT22 may have a constant first hollow-core diameter D21 along the length of the section. The tapered section TD22 may have a second hollow-core diameter D22 that decreases continuously and substantially linearly with a taper slope TG22 along the length of the section. The tapered section TD22 may form a waist region or taper TP22 as defined in the previous embodiment.

[0153] Figures 20(a) and 20(b) are two simulated spectrograms depicting the temporal and spectral distribution of a pulse of input radiation after propagation through a uniform hollow-core optical fiber (HOF) of 27 cm and 42 cm, respectively. In this simulation example, the uniform hollow-core HC optical fiber OF (e.g., a single-ring HC-ARF as illustrated in Figure 7) may have a length of 42 cm and a core diameter of 30 μm (or a core radius of 15 μm). Position "Pos = 27 cm" corresponds to a position in the fiber 27 cm from the first fiber face F11, and position "Pos = 42 cm" corresponds to the position of the second fiber face SF22. The hollow core HC may be filled with a working medium WM of krypton gas at a pressure of 25.7 bar. The pulsed input radiation IRD has a pump pulse duration τ of 280 fs, a pulse energy Ep of 5.3 μJ, and a central wavelength λ of 1030 nm. Pulsed input radiation IRD may be admitted into the fiber via the first fiber face FF11 and may exit the fiber via the second fiber face SF11. This configuration enables pumping in the anomalous dispersion regime. Pulsed input radiation (or pump pulse) IRD entering the single-waist hollow-core optical fiber TOF2 is transformed into high-order solitons with soliton order N = 104, ensuring MI-dominated nonlinear optical processes.

[0154] As can be seen in Figure 20(a), the delay time between the dispersive wave around 400 nm and the soliton around 1800 nm is less than 100 fs, and they still partially overlap in time. However, after propagating a distance of another 15 cm, the delay time between the dispersive wave and the soliton becomes greater than 500 fs. This large delay time results in a complete time separation between the dispersive wave and the soliton, thereby preventing the soliton trapping process from occurring.

[0155] Figures 20(c) and 20(d) are two simulated spectrograms describing the temporal and spectral distribution of a pulse of input radiation after propagation of 27 cm and 42 cm, respectively, within a single-waist hollow-core optical fiber (e.g., as shown in Figure 19). This simulation is based on the same operating parameters as those used in the simulations shown in Figures 20(a) and 20(b). The single-waist hollow-core optical fiber TOF2 may have a length of 42 cm. As shown in Figure 19, the waist region may begin just after 27 cm from the first fiber face FF22 of the fiber and may end at the second fiber face SF22. The first hollow-core diameter D21 may be constant at 30 μm, and the taper slope TG22 may be 0.5 μm / cm. In this case, the hollow-core diameter at the second fiber face SF22 (e.g., the second hollow-core diameter D22 at the second fiber face SF22) is reduced to 15 μm.

[0156] Due to the fact that the untapered section UT22 of the single-neck fiber TOF2 has the same structural dimensions (except for length) as the uniform fiber (not shown) used in the simulation shown in Figure 20(a), the temporal and spectral distributions of the input radiation IRD shown in Figure 20(c) are identical to those shown in Figure 20(a). Figure 20(d) confirms that the use of the necked region slows the soliton, and the temporal overlap between the dispersive wave and the soliton is substantially maintained until it exits the fiber through the second fiber face SF22. This results in a situation where the dispersive wave is temporally and spectrally captured by the soliton, resulting in a further blue-shift of the short-wavelength edge from 400 nm, as shown in Figure 20(b), to below 300 nm, as shown in Figure 20(d).

[0157] In some embodiments, the group velocity control mechanism may comprise a Raman-active working medium WM. The Raman-active working medium may be a gas fill or gas mixture containing at least one Raman-active gas. The Raman-active gas may be, for example, hydrogen, deuterium, or nitrogen. As described above, the inventors have recognized that the Raman-active working medium alone can decelerate solitons relative to dispersive waves, enabling soliton trapping of dispersive waves in non-tapered hollow-core optical fibers, but not in tapered fibers. In some embodiments, the Raman-active working medium may be configured to minimize the time separation between the dispersive wave and the solitons and ensure good temporal overlap between them. Good temporal overlap may correspond to, for example, a delay time of less than 50 fs, less than 20 fs, or less than 10 fs.

[0158] In different embodiments, two or more group velocity control mechanisms may be used together. For example, in one embodiment, a single-neck hollow-core optical fiber, such as the tapered fibers TOF1 and TOF2 shown in Figure 17 or Figure 19, may be filled with a Raman-active working medium. In this case, the fiber neck region and the Raman-active working medium (e.g., a filling gas or gas mixture including at least one Raman-active gas) may be configured to affect the input radiation IRD both to minimize the time separation between dispersive waves and solitons and to preserve the soliton trapping process.

[0159] It should be noted that the single-neck hollow-core optical fibers TOF1 and TOF2 configured for dispersive-wave soliton trapping described above are non-limiting examples. Other hollow-core optical fibers having two or more neck regions are equally applicable. Furthermore, the single neck regions TP11 and TP22 of the single-neck hollow-core optical fibers TOF1 and TOF2 may be configured and arranged not only to trigger the initiation of DWG but also to enable and maintain the soliton trapping process. In a preferred embodiment, a double-neck hollow-core optical fiber (e.g., as shown in FIG. 15 ) may be configured such that the first neck region is optimized to initiate the MI process and the second neck region TP2 is optimized to initiate both the DWG and soliton trapping processes. In another preferred embodiment, the double-neck hollow-core optical fiber may be filled with a Raman-active filling gas. The use of a Raman-active filling gas may add an additional degree of freedom for optimizing the soliton trapping process. In other embodiments, one or more group velocity control mechanisms (e.g., a tapered hollow-core optical fiber and / or a Raman-active filling gas) may be applied to a single-neck or double-neck hollow-core optical fiber (e.g., those shown in Figures 11(a), 11(b), and 15) configured for the production of broadband output radiation with a smooth spectral profile and an extended short-wavelength edge.

[0160] 21 is a block diagram illustrating a computer system 2100 that can assist in implementing the methods and flows disclosed herein. The computer system 2100 includes a bus 2002 or other communication mechanism for communicating information and a processor 2104 (or multiple processors 2104 and 2105) coupled to the bus 2002 for processing information. The computer system 2100 also includes a main memory 2106, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 2002 for storing information and instructions to be executed by the processor 2104. The main memory 2106 may be used to store temporary variables or other intermediate information during execution of instructions to be executed by the processor 2104. The computer system 2100 further includes a read-only memory (ROM) 2108 or other static storage device coupled to the bus 2002 for storing static information and instructions for the processor 2104. A storage device 2110, such as a magnetic disk or optical disk, is also provided and coupled to the bus 2002 for storing information and instructions.

[0161] The computer system 2100 may be connected via bus 2002 to a display 2112, such as a cathode ray tube (CRT) or flat panel or touch panel display, for displaying information to a computer user. An input device 2014, including alphanumeric and other keys, is connected to bus 2002 for communicating information and command selections to the processor 2104. Another type of user input device is a cursor control 2116, such as a mouse, trackball, cursor direction keys, etc., for communicating directional information and command selections to the processor 2104 and for controlling cursor movement on the display 2112. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), allowing the device to specify a position on a surface. A touch panel (screen) display may also be used as an input device.

[0162] At least some of the methods described herein may be performed by computer system 2100 in response to processor 2104 executing one or more sequences of one or more instructions contained in main memory 2106. Such instructions may be read into main memory 2106 from another computer-readable medium, such as storage device 2110. Execution of the sequences of instructions contained in main memory 2106 causes processor 2104 to perform the process steps described herein. One or more processors in a multi-processor configuration may be utilized to execute the sequences of instructions contained in main memory 2106. In alternative embodiments, hardware-implemented circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0163] The term "computer-readable medium" refers to any medium that participates in providing instructions to processor 2104 for execution. Such media may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device(s) 2110. Volatile media include dynamic memory, such as main memory 2106. Transmission media include coaxial cables, copper wire, and fiber optics, including the wires that comprise bus 2002. Transmission media also can take the form of sound or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tape, any other physical media with patterns of holes, RAM, PROM, EPROM, FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described below, or any other computer-readable medium.

[0164] Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to the processor 2104 for execution. For example, the instructions may initially be carried on a magnetic disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to the computer system 2100 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to the bus 2002 can receive the data carried in the infrared signal and transmit the data on the bus 2002. The bus 2002 carries the data to the main memory 2106, from which the processor 2104 retrieves and executes the instructions. The instructions received by the main memory 2106 may optionally be stored on a storage device 2110 either before or after execution by the processor 2104.

[0165] Computer system 2100 also includes a communication interface 2118 preferably coupled to bus 2002. The communication interface 2118 provides a two-way data communication connection to a network link 2120 that is connected to a local network 2122. For example, the communication interface 2118 may be an Integrated Services Digital Network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface 2118 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link may also be implemented. In any such implementation, the communication interface 2118 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0166] Network link 2120 typically provides data communication through one or more networks to other data devices. For example, network link 2120 may provide a connection through local network 2122 to a host computer 2124 or to data equipment operated by an Internet Service Provider (ISP) 2126. ISP 2126 provides data communication services through the global packet data communication network now commonly referred to as the "Internet" 2128. Local network 2122 and the Internet 2128 both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks, and the signals on network link 2120 and through communication interface 2118, which carry the digital data to and from computer system 2100, are exemplary forms of carrier-wave-borne information.

[0167] Computer system 2100 may send messages and receive data, including program code, through the network(s), network link 2120, or communication interface 2118. In the Internet example, a server 2030 may send a requested code for an application program through Internet 2128, ISP 2126, local network 2122, or communication interface 2118. One such downloaded application may, for example, provide one or more of the techniques described herein. The received code may be executed by processor 2104 that receives it, and / or stored in storage device 2110 or other non-volatile storage for later execution. In this manner, computer system 2100 may obtain application code in the form of a carrier wave.

[0168] Further embodiments are disclosed in the following list of numbered items: 1. A broadband light source device configured to generate broadband output radiation upon receiving pump radiation, comprising: a hollow-core photonic crystal fiber (HC-PCF) having one or more main sections and at least one structural change section having at least one structural parameter that changes with respect to the one or more main sections; the at least one structural change is located downstream of a position along the length of the HC-PCF and comprises at least a first structural change where the pump radiation is spectrally broadened by a nonlinear optical process dominated by modulation instability; the at least one structural change constructed and arranged such that the broadband output radiation has wavelengths in the ultraviolet spectral region. Broadband light source device. 2. The broadband light source device described in item 1, wherein one or more of the at least one structural change portion each comprises at least one diameter reduction portion having an inner core diameter reduced relative to a main inner core diameter for the one or more main portions of the HC-PCF. 3. Each diameter reduction of the at least one diameter reduction portion comprises a first tapered portion tapered in a first direction; the inner core diameter decreases over the length of the first tapered section from the main inner core diameter to a second inner core diameter that is smaller than the main inner core diameter; Item 3. The broadband light source device according to item 2. 4. One or more of the at least one reduced diameter section comprises a second tapered section tapering in a direction opposite to the first direction; the inner core diameter increases from the second inner core diameter to the main inner core diameter over the length of the second tapered section. Item 3. The broadband light source device according to item 3. 5. One or more of the at least one reduced diameter section comprises a central waist portion between the first tapered section and the second tapered section; the central waist portion having the second inner core diameter along its length; Item 5. The broadband light source device according to item 4. 6. A broadband light source device described in any one of items 1 to 5, wherein one or more of the at least one structural change portion each has different structural dimensions of the inner cladding structure of the HC-PCF relative to the one or more main portions of the HC-PCF. 7. The broadband light source device according to item 6, wherein the different structural dimensions of the inner cladding structure of the HC-PCF are different capillary tube diameters. 8. A broadband light source device described in any one of items 1 to 7, wherein the start point of the first structural change section is located downstream of a position along the length of the HC-PCF at which the pump radiation is spectrally broadened by a nonlinear optical process dominated by modulation instability. 9. A broadband light source device according to any one of items 1 to 8, wherein the first structural change portion is configured to control a second nonlinear optical process. 10. The broadband light source device of item 9, wherein the second nonlinear optical process comprises dispersive wave generation. 11. The at least one structural change section further comprises a second structural change section disposed upstream of the first structural change section; The second structural change portion is configured and arranged to control the MI (modulation instability)-dominated nonlinear optical process. Item 11. The broadband light source device according to item 10. 12. The broadband light source device according to item 11, wherein the second structural change portion is configured so that the second nonlinear optical process does not begin in the first structural change portion. 13. The broadband light source device of item 12, wherein the second structural change portion is constructed and arranged such that the dispersive wave generation further extends the short wavelength limit of the broadband output radiation. 14. Further comprising at least one group velocity control mechanism configured to minimize time separation between at least one soliton and at least one dispersive wave, both of which are generated by the MI-dominated nonlinear optical process; the short wavelength limit of the broadband output radiation is further extended via soliton trapping processes; 14. The broadband light source device according to any one of items 10 to 13. 15. The broadband light source device described in item 14, wherein the at least one group velocity control mechanism comprises at least one diameter reduction section having an inner core diameter that decreases with a taper slope configured to slow down the at least one soliton relative to the at least one dispersive wave and minimize their time separation. 16. The broadband light source device according to item 15, wherein the at least one diameter reduction portion is provided within the first structural change portion. 17. The broadband light source device according to item 15 or 16, wherein the taper slope is in the range between 0.01 μm / cm and 10 μm / cm. 18. A broadband light source device according to any of items 14 to 17, wherein the at least one group velocity control mechanism comprises a Raman-active gas or gas mixture configured to fill the HC-PCF and to decelerate the at least one soliton relative to the at least one dispersive wave and minimize their time separation. 19. A broadband light source device configured to generate broadband output radiation upon receiving pump radiation, comprising: a hollow-core photonic crystal fiber (HC-PCF) having at least a first structural change portion and a second structural change portion; each of the first structural variation section and the second structural variation section has at least one structural parameter of the HC-PCF that varies with respect to one or more main sections of the HC-PCF; At least one of the one or more main portions of the HC-PCF separates the first structural change portion and the second structural change portion. Broadband light source device. 20. A broadband light source device as described in Item 19, wherein each of the first structural change portion and the second structural change portion comprises at least one diameter reduction portion having an inner core diameter reduced relative to a main inner core diameter for the one or more main portions of the HC-PCF. 21. Each diameter reduction of the at least one diameter reduction portion comprises a first tapered portion tapering in a first direction; the inner core diameter decreases over the length of the first tapered section from the main inner core diameter to a second inner core diameter that is smaller than the main inner core diameter; Item 21. The broadband light source device according to item 20. 22. One or more of the at least one reduced diameter section comprises a second tapered section tapering in a direction opposite to the first direction; the inner core diameter increases from the second inner core diameter to the main inner core diameter over the length of the second tapered section. Item 22. The broadband light source device according to item 21. 23. One or more of the at least one reduced diameter section comprises a central waist between the first tapered section and the second tapered section; the central waist portion having the second inner core diameter along its length; Item 23. The broadband light source device according to item 22. 24. A broadband light source device described in any one of items 19 to 23, wherein one or more of the at least one structural change portion each has different structural dimensions of the inner cladding structure of the HC-PCF relative to the one or more main portions of the HC-PCF. 25. The broadband light source device of item 24, wherein the different structural dimensions of the inner cladding structure of the HC-PCF are different capillary tube diameters. 26. The broadband light source device according to item 25. 2. The broadband light source device of claim 1, wherein the first structural change portion and the second structural change portion are configured and arranged to control first and second nonlinear optical processes, respectively, responsible for generating the broadband output radiation. 27. A broadband light source device according to item 26, wherein the first structural change portion is constructed and arranged so that the second nonlinear optical process does not begin in the first structural change portion. 28. The broadband light source device of item 27, wherein the first nonlinear optical process comprises modulation instability and the second nonlinear optical process comprises dispersive wave generation. 29. A broadband light source device as described in item 28, wherein the first structural change section is configured and arranged such that the modulation instability broadens the spectrum of the pump radiation, and the second structural change section is configured and arranged such that the dispersive wave generation further extends the short wavelength edge of the spectrally broadened pump radiation. 30. Further comprising at least one group velocity control mechanism configured to minimize the time separation between at least one soliton and at least one dispersive wave, both of which are generated by the MI-dominated nonlinear optical process; the short wavelength limit of the broadband output radiation is further extended via soliton trapping processes; Item 30. The broadband light source device according to item 29. 31. The at least one group velocity control mechanism comprises at least one diameter reduction section having an inner core diameter that decreases from the main inner core diameter with a taper slope over the length of the at least one diameter reduction section; the tapered gradient is configured to decelerate the at least one soliton relative to the at least one dispersive wave and minimize their time separation. Item 31. The broadband light source device according to item 30. 32. The broadband light source device according to item 31, wherein the at least one diameter reduction section is provided within the second structural change section. 33. The broadband light source device according to item 31 or 32, wherein the taper slope is in the range between 0.01 μm / cm and 10 μm / cm. 34. A broadband light source device according to any of items 30 to 33, wherein the at least one group velocity control mechanism comprises a Raman-active gas or gas mixture configured to fill the hollow core of the HC-PCF in which the broadband output radiation is generated and configured to decelerate the at least one soliton relative to the at least one dispersive wave and minimize their time separation. 35. The broadband light source device according to any one of items 1 to 34, wherein the first structural change section and the second structural change section are further configured to support propagation of substantially a fundamental mode of the pump radiation. 36. A broadband light source device according to any one of items 1 to 35, wherein the wavelength in the ultraviolet region is a minimum of 300 nm. 37. A broadband light source device according to any one of items 1 to 36, wherein the wavelength in the ultraviolet region is a minimum of 200 nm. 38. The broadband light source device according to any one of items 1 to 37, wherein the broadband output radiation has a wavelength of up to 2000 nm. 39. The broadband light source device of any of items 1 to 38, wherein the broadband output radiation has a wavelength of up to 3000 nm. 40. A broadband light source device according to any one of items 1 to 39, wherein at least the first structural variation portion is constructed and arranged so that the point spread power spectral density of the spectrum of the broadband output radiation does not vary by more than 50% from the average over the wavelength range of interest. 41. The broadband light source device according to item 40, wherein the wavelength range of interest includes wavelengths between at least 400 nm and 1000 nm. 42. The broadband light source device according to item 40, wherein the wavelength range of interest includes wavelengths between at least 400 nm and 2000 nm. 43. The broadband light source device according to item 40, wherein the wavelength range of interest includes wavelengths between at least 200 nm and 2000 nm. 44. A broadband light source device according to any one of items 1 to 43, wherein at least the first structural change portion is constructed and arranged such that the point spread power spectral density of the spectrum of the broadband output radiation does not contain a peak whose point spread power spectral density is greater than twice the average of the point spread power spectral density of the spectrum. 45. A broadband light source device according to any of items 1 to 44, further comprising a pump radiation source for generating the pump radiation. 46. ​​The broadband light source device of item 45, wherein the pump radiation source is configured such that the pump radiation has a pulse energy in the range between 1 μJ and 10 μJ. 47. A broadband light source device according to any one of items 1 to 46, wherein the HC-PCF is a single ring HC-PCF. 48. A broadband light source device according to any one of items 19 to 47, wherein the starting point of the first structural change section is located at a position between 5 cm and 30 cm from the input end of the HC-PCF. 49. A broadband light source device according to any one of items 19 to 47, wherein the starting point of the first structural change section is located at a position between 10 cm and 20 cm from the input end of the HC-PCF. 50. A broadband light source device according to any one of items 19 to 47, wherein the starting point of the first structural change section is located at a position between 14 cm and 16 cm from the input end of the HC-PCF. 51. A broadband light source device according to any one of items 19 to 50, wherein the starting point of the second structural change section is located at a position between 15 cm and 35 cm from the input end of the HC-PCF. 52. A broadband light source device according to any one of items 19 to 50, wherein the starting point of the second structural change section is located at a position between 20 cm and 30 cm from the input end of the HC-PCF. 53. A broadband light source device according to any one of items 19 to 50, wherein the starting point of the second structural change section is located at a position between 24 cm and 28 cm from the input end of the HC-PCF. 54. A measurement device comprising a broadband light source device according to any one of items 1 to 53. 55. The measurement device according to item 54, comprising a scatterometer, a level sensor or an alignment sensor. 56. A method of optimizing a position of at least a first structural change along a length of a hollow-core photonic crystal fiber (HC-PCF) such that broadband output radiation is generated from the HC-PCF following excitation with input radiation having a wavelength in the ultraviolet region, comprising: determining a position along the length of the HC-PCF where the pump radiation is spectrally broadened by a nonlinear optical process dominated by modulation instability; disposing the first structural change portion downstream of the determined position; A method for providing 57. The method according to Item 56, wherein the arranging step optimizes the position of the starting point of the first structural change portion. 58. A method according to item 56 or 57, wherein the determining step is performed by simulating the process of generating the broadband output radiation within the HC-PCF. 59. The determining step: a) measuring the output spectrum and power output from a length of hollow-core optical fiber without a structural variation; b) cutting a length of the hollow-core optical fiber at a point proximal to the input end to obtain a shortened length; c) repeating steps a) and b) for each shortened length until the measured output spectrum confirms that the modulation instability-dominated nonlinear optical process has occurred; and 59. The method according to any of items 56 to 58, carried out by 60. The method of any of items 56 to 59, wherein the disposing step results in the broadband output radiation having a wavelength of at least 300 nm. 61. The method of any of items 56 to 59, wherein the disposing step results in the broadband output radiation having a wavelength of at least 200 nm. 62. The method of any of items 56 to 61, wherein the disposing step results in the broadband output radiation having a wavelength of at most 2000 nm. 63. The method of any of items 56 to 61, wherein the disposing step results in the broadband output radiation having a wavelength of at most 3000 nm. 64. A method according to any of items 56 to 63, wherein in the arranging step, the point spread power spectral density of the spectrum of the broadband output radiation does not vary by more than 50% from the average over the wavelength range of interest. 65. The method according to item 64, wherein the wavelength range of interest includes wavelengths between at least 400 nm and 1000 nm. 66. The method according to item 64, wherein the wavelength range of interest includes wavelengths between at least 400 nm and 2000 nm. 67. The method according to item 64, wherein the wavelength range of interest includes wavelengths between at least 200 nm and 2000 nm. 68. A method according to any of items 56 to 67, wherein at least in the arranging step, the point spread power spectral density of the spectrum of the broadband output radiation does not include a peak whose point spread power spectral density is greater than twice the average of the point spread power spectral density of the spectrum. 69. A method according to any of items 56 to 68, wherein the optimization comprises co-optimizing the position and energy of the input radiation. 70. A method according to any one of items 56 to 69, wherein the arranging step optimizes the first structural change portion to control a second nonlinear optical process. 71. A method according to any of items 56 to 70, wherein the optimizing step comprises optimizing the position of a second structural change along the length of the HC-PCF. 72. The method of item 71, wherein optimizing the second position comprises optimizing the position of the second structural change portion to control the MI-dominated nonlinear optical process. 73. The method described in Item 72, wherein the optimization step comprises optimizing the position of the first structural change portion and the position of the second structural change portion so that the second nonlinear optical process does not begin in the first structural change portion. 74. The method of claim 73, comprising optimizing a position of the second structural variation such that the dispersive wave generation further extends the short wavelength limit of the broadband output radiation. 75. The method of any of items 70 to 74, wherein the second nonlinear optical process comprises dispersive wave generation. 76. The optimization further comprises applying at least one group velocity control mechanism to minimize the time separation between at least one soliton and at least one dispersive wave, both generated by the MI-dominated nonlinear optical process; the short wavelength limit of the broadband output radiation is further extended via soliton trapping processes; 76. The method according to any one of items 56 to 75. 77. The method of claim 76, wherein the at least one group velocity control mechanism comprises at least one diameter reducer having an inner core diameter that decreases with a taper slope configured to slow down the at least one soliton relative to the at least one dispersive wave and minimize their time separation. 78. The method of claim 77, wherein the at least one diameter reduction is provided within the first structural change. 79. The method according to item 77 or 78, wherein the taper gradient is in the range between 0.01 μm / cm and 10 μm / cm. 80. The method of any of items 76 to 79, wherein the at least one group velocity control mechanism comprises a Raman-active gas or gas mixture configured to fill a hollow core of the HC-PCF in which the broadband output radiation is generated and configured to decelerate the at least one soliton relative to the at least one dispersive wave and minimize their time separation.

[0169] Although specific reference may be made in the present description 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, including 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.

[0170] Although specific reference may be made in this description to embodiments of the invention in the context of a lithography 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.

[0171] Although specific reference may have been made to the use of embodiments of the invention in the context of optical lithography, it will be understood that, where the context permits, the invention is not limited to optical lithography and may be used in other applications, such as, for example, imprint lithography.

[0172] While specific embodiments of the invention have been described above, it will be understood that the invention may be practiced otherwise than as described. The foregoing description is intended to be illustrative and not limiting. Thus, it will be apparent to those 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. 1. A broadband light source device configured to generate broadband output radiation upon receiving pump radiation, comprising: a hollow-core photonic crystal fiber (HC-PCF) having at least a first structural change portion and a second structural change portion; each of the first structural variation section and the second structural variation section has at least one structural parameter of the HC-PCF that varies with respect to one or more main sections of the HC-PCF; At least one of the one or more main portions of the HC-PCF separates the first structural change portion and the second structural change portion. Broadband light source device.

2. 2. The broadband light source device of claim 1, wherein the first structural change portion and the second structural change portion are constructed and arranged to control first and second nonlinear optical processes, respectively, responsible for generating the broadband output radiation.

3. 3. The broadband light source device according to claim 2, wherein the first structural change portion is constructed and arranged so that the second nonlinear optical process does not begin in the first structural change portion.

4. the first nonlinear optical process comprises modulation instability, and the second nonlinear optical process comprises dispersive wave generation; Optionally, the first structural variation is configured and arranged such that the modulation instability broadens the spectrum of the pump radiation, and the second structural variation is configured and arranged such that the dispersive-wave generation further extends a short wavelength edge of the spectrally broadened pump radiation.

4. The broadband light source device according to claim 3.

5. the first structural change and the second structural change are further configured to support propagation of a substantially fundamental mode of the pump radiation; Optionally, the wavelength in the ultraviolet region comprises a wavelength of at least 300 nm, or the broadband output radiation comprises a wavelength of at most 2000 nm.

5. The broadband light source device according to claim 1.

6. 6. The broadband light source device of claim 1, wherein at least the first structural variation portion is constructed and arranged such that the point spread power spectral density of the spectrum of the broadband output radiation does not vary by more than 50% from an average over the wavelength range of interest.

7. 7. The broadband light source device of claim 1, wherein at least the first structural change portion is constructed and arranged such that a point-spread power spectral density of the spectrum of the broadband output radiation does not include a peak whose point-spread power spectral density is greater than twice the average of the point-spread power spectral density of the spectrum.

8. 8. A broadband light source device according to claim 1, further comprising a pump radiation source for generating said pump radiation.

9. 9. The broadband light source device of claim 8, wherein the pump radiation source is configured such that the pump radiation has a pulse energy in the range between 1 μJ and 10 μJ.

10. 10. The broadband light source device according to claim 1, wherein the HC-PCF is a single ring HC-PCF.

11. 11. The broadband light source device according to claim 1, wherein the starting point of the first structural change portion is located between 5 cm and 30 cm from the input end of the HC-PCF.

12. 12. The broadband light source device according to claim 1, wherein the starting point of the second structural change section is located between 15 cm and 35 cm from the input end of the HC-PCF.

13. 1. A broadband light source device configured to generate broadband output radiation upon receiving pump radiation, comprising: a hollow-core photonic crystal fiber (HC-PCF) having one or more main sections and at least one structural change section having at least one structural parameter that changes with respect to the one or more main sections; the at least one structural change is located downstream of a position along the length of the HC-PCF and comprises at least a first structural change where the pump radiation is spectrally broadened by a nonlinear optical process dominated by modulation instability; the at least one structural change constructed and arranged such that the broadband output radiation has wavelengths in the ultraviolet region of the spectrum; Optionally, one or more of the at least one structural change comprises at least one diameter reduction, each having an inner core diameter reduced relative to a main inner core diameter of the HC-PCF. Broadband light source device.

14. A broadband light source device according to any one of claims 1 to 13, Optionally equipped with a scatterometry device, a level sensor or an alignment sensor; Measuring devices.

15. 1. A method of optimizing a position of at least a first structural change along a length of a hollow-core photonic crystal fiber (HC-PCF) such that broadband output radiation is generated from the HC-PCF following excitation with input radiation having a wavelength in the ultraviolet region, comprising: determining a position along the length of the HC-PCF where pump radiation is spectrally broadened by a nonlinear optical process dominated by modulation instability; disposing the first structural change portion downstream of the determined position; A method for providing

Images