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Abstract
Broadband high-efficiency diffraction gratings play a crucial role in the pulse stretcher and compressor of high-energy ultrafast lasers. Nevertheless, conventional grating manufacturing techniques, including mechanical ruling and holographic recording, face challenges in creating accurate blazed groove profiles necessary for the fabrication of broadband, high-efficiency mid-infrared gratings. In this work, we utilized combined electron-beam lithography and anisotropic wet etching technology to fabricate nearly perfect blazed grooves, producing high efficiency broadband mid-infrared (IR) grating for 4.3 µm 100 femtosecond laser. Global optimization was performed to achieve a design of > 90% efficiency over spectral range of 3.6 µm – 6.6 µm. Hybrid metal-dielectric coating (Au-Al2O3) is employed and optimized to minimize absorption and to enhance diffraction efficiency and laser-induced damage threshold (LIDT). Prototype gratings undergo testing at a desired application wavelengths of 4.3 µm in a tunable range of 0.2 µm, revealing that the optimal sample achieves a diffraction efficiency of 92%, closely approaching the theoretical value of 94.2%
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mid-infrared (MIR) ultrafast lasers are important to a variety of applications, including precise material processing [1], medical diagnostics [2], high precision spectroscopy [3], and directed energy and particle acceleration using strong laser field [4]. Current technologies used in high-energy MIR ultrafast laser systems, such as optical parametric chirped-pulse amplification (OPCPA), rely heavily on MIR diffraction gratings to manipulate pulse durations by exploiting the broad spectral bandwidths inherent in ultrashort-duration pulses [5]. These MIR gratings, which can be either reflective or transmissive, play a particularly crucial role in the post-amplification pulse compression stage, especially in multi-pass configurations, enabling the generation of high-peak-power pulses with durations below 100 fs. Unfortunately, the limited diffraction efficiency (DE) in broad spectral band from commercially available MIR diffraction gratings imposes a severe challenge that is compounded in multiple-grating configurations, which causes significant losses in MIR ultrafast laser output power. For example, the Treacy compression scheme, which allows for effective pulse compression to tens of femtoseconds in a compact form factor, requires four interactions of the amplified laser pulse with diffraction gratings, as illustrated in Fig. 1. As a result, small reductions in grating efficiency, the ratio of the energy in the first-order diffracted light to that of the incident beam, can result in large reductions in compressed laser-pulse output. For example, a 15% grating efficiency reduction (e.g., from 90% to 75%) can reduce laser-output power by more than a factor of two.
Fig. 1. The basic components of optical parametric chirped pulse amplification, OPCPA [Ref. [5], Fig. 1]. Schematic showing a four-pass Treacy compression setup, implemented via the use of two gratings and a retroreflecting mirror. Four passes off 90% efficient gratings result in total throughput of ∼66%; use of gratings with 75% efficiency reduces throughput to ∼32%.
Grating development for OPCPA and chirp pulse amplification (CPA) applications have been mostly focused on the visible and near IR wavelength region [6]. Nonetheless, attaining the development of a grating with high efficiency, broad spectral bandwidth, and a robust high damage threshold has presented significant challenges. Researchers have successfully achieved one or two of these three goals through meticulous design and fabrication [7]. In MIR and long-wavelength IR (LWIR) high power ultrafast laser, gratings face additional challenges with even fewer material choices of substrate/coating in the grating fabrication. Table 1 outlines the current state-of-art gratings developed so far in the MIR range that are employed in CPA and OPCPA applications. As illustrated in the table, only a limited number of MIR gratings demonstrate an efficiency exceeding 90%. Nevertheless, all the gratings exhibit a constrained bandwidth, limiting their applicability to pulse widths greater than 150 fs and within a restricted center wavelength tuning range (i.e., the grating's high diffraction efficiency wavelength range has a bandwidth narrower than the required fs laser pulse frequency). To our knowledge, there is no adequate MIR grating for sub 100 fs pulse compression.
The challenges of low diffraction efficiency and limited spectral bandwidth result from imperfect MIR grating groove fabrication and grating structure design. The manufacturing method used to achieve precise groove facets is a key aspect of realizing high-efficiency gratings [16]. There are two traditional grating manufacturing methods widely used for commercial gratings –mechanical ruling using a diamond-turned tip and holographic recording with Ion-beam etching. Two manufacturing-induced errors are inherent in the mechanical ruling method: groove surface roughness, causing light scattering, and groove period error, resulting in ghost diffraction. While holographic recording reduces scattering and ghost diffraction significantly, ion-beam etching can reintroduce substantial scattering. Additionally, holographically recorded groove shapes have limitations in enhancing grating diffraction efficiency, particularly for low line-density gratings commonly employed in infrared applications [19].
Lately, electron-beam lithography (EBL) coupled with a subsequent etching process has been used for manufacturing high-efficiency X-ray gratings [20–25]. The key advantage of this fabrication approach is its precision in producing groove facets for blazed gratings. This is made possible by combining EBL with anisotropic etching in monocrystalline silicon. This results in atomically smooth facets and a blaze angle defined by exposed {111} crystallographic planes [22]. Scattering and ghost diffraction in gratings developed by EBL can be reduced to less than 10−4 [21]. This manufacturing technology provides the required manufacturing parameters and the high precision required for MIR grating. To overcome the current MIR grating efficiency problems, our team design a high efficiency ultrabroadband MIR grating based on lithography manufacture process and demonstrate MIR grating manufacturing as proof-of-concept lithography. A conformal coating process is also employed to the MIR grating grooves to boost laser induced damage threshold (LIDT). Conformal coating ensures uniformity, maximizing LIDT for gratings. Non-uniform coatings induce stress concentrations, weakening the material and increasing susceptibility to damage. Such coatings are prone to defects like pinholes, cracks, or delamination, acting as initiation sites for damage. Reference [8] reports a 30% increase in LIDT for near-IR (NIR) gratings.
Grating design is a complicated process, especially for high efficiency gratings, as the parameter space for grating design is large. In general, a grating is usually optimized for specific applications through multi-dimensional optimization. Theoretically, vector electromagnetic analysis [16,17] has been used for grating design and optimization. This rigorous theoretical analysis has also been developed into commercial software packages such as PC-Grate and G-solver [18]. Some design principles used to achieve high efficiency have been summarized in Ref. [16]. A key principle for high efficiency grating design is to utilize blazing to maximize the diffraction efficiency at specific wavelengths or wavelength range. Detailed design process of the MIR grating is described in section 2. In Section 3 the grating fabrication and testing of the grating are described. A summary is presented in Sect. 4.
2. Design of gratings for MIR broadband high efficiency
The grating design process consists of three phases: initial design, design optimization for efficiency within a broad spectral band, and the final design to accommodate manufacturing conditions.
2.1 Initial design of the MIR grating
In recent years, significant advancements have been made in the development of MIR ultrafast lasers [4,26,27]. In this study, our focus centers on the design of gratings tailored for utilization in ultrafast lasers operating for a specific application in a 4.3 µm ultrafast laser. Achieving a first-order diffraction efficiency exceeding 90% is crucial for our objectives.
During the ultrafast laser pulse compression stage, laser damage is a major concern. In a grating compressor, a high-angle incidence (AOI) design enhances damage threshold by enlarging beam size, reducing intensity, and improving overall pulse energy tolerance on the grating surface. Therefore, the selected AOI, θ, is greater than 55°.
The selection of blaze angles adhered to the principles outlined in Ref. [16]. In Fig. 3, efficiency curves are presented for the “high blaze angle” grating family, characterized by a blaze angle falling within the range of 22° < γ < 38°. For the ultrafast laser application, only the S-plane curve (TM polarization mode in PC-grate) requires consideration, given the polarized nature of the laser.
Fig. 2. Ref [16, Fig. 9.9], diffraction efficiency curve for the “high blaze angle” grating family. θB is the blaze angle. The solid curve is for S-plane (TM) and the dashed curve is for P-plane (TE).
Fig. 3. Comparing the natural silicon crystallographic blaze angle γ = 29.5°, 35.26°, 19.47°, and 38.9° to determine the best blaze angle for the MIR grating. Other design parameters in the simulation: AOI = 60°, grating groove period = 3.333 um, and gold coating applied to enhance reflective diffraction.
As depicted in Fig. 2, the grating groove period (d) is governed by the condition λ/d < 2. In our application, where λmax > 5 µm, it is imperative that d exceeds 2.5 µm. However, excessively increasing d compromises diffraction resolution and is consequently constrained to less than 4 µm. Table 2 provides a summary of the starting conditions for the grating design, tailored to our specific application.
Table 2. The grating initial design for our specific application.
2.2 Grating design optimization
In anisotropic wet etching, the etching speed is contingent upon the density of silicon atoms. Opting for etching against the Si crystallographic plane {111} proves advantageous due to its high atomic density, resulting in heightened etching resistance and, consequently, a slower etching rate. Consequently, the angle formed by {111} and another selected plane can be effectively employed as the blazing angle for the triangular groove structure of the grating [22]. Based on the “high blaze angle” design constraints of 22° < γ < 38°, there are 2 choices of blaze angle for Si: 29.5° (between {111} and {311}) and 35.26° (between {111} and {411}) [22]. Modeling with PC-Grate is employed to ascertain the superior efficiency between these two blaze angles.
As depicted in Fig. 3, a blaze angle of γ = 29.5° outperforms γ = 35.26° in generating a relatively higher and flatter efficiency curve for diffraction order M = -1 and TM polarization. Introducing a blaze angle of γ = 38.9° (between {111} and {511}) serves to illustrate the decline in efficiency associated with larger blaze angles. Similarly, blaze angle γ = 19.47° (between {111} and {211}) is included for comparative purposes, highlighting that the “high blaze angle” grating family (22° < γ < 38°) stands as a sound principle for achieving high efficiency across a broad wavelength range. Angle of incidence (AOI) θ = 60° is selected due to its notable high diffraction efficiency, as illustrated in Fig. 5.
Fig. 5. AOI optimization: θ=64° is chosen as a good compromise between efficiency and beam size expansion.
Subsequently, we proceed to optimize the groove density (f) to align the wavelength range with the desired interval of 3.6 µm – 6.6 µm. Figure 4 illustrates the diffraction efficiency as the groove density varies from f = 230 lines/mm to f = 310 lines/mm. Evidently, a lower groove density results in a shift of the wavelength range towards longer wavelengths. We identify the groove density f = 270 lines/mm as the optimized parameter, corresponding to a groove period of d = 3.704 µm
Next, we proceed to scan the AOI, commencing from 45° and progressing to higher angles. The outcomes are presented in Fig. 5. As θ increases, the diffraction efficiency demonstrates an increase, reaching its zenith at θ = 60°. Subsequently, the efficiency diminishes as θ continues to increase. Although θ = 60° has the overall highest diffraction efficiency, we select θ = 64° for grating manufacturing to achieve the highest diffraction efficiency at 3.6 µm –3.7 µm while maintain efficiency to be >94% in the wavelength regime of 3.8 µm –6.8 µm. The expansion of beam size resulting from AOI, characterized by a factor of 1/cos(θ), is approximated at ∼2.28 for θ=64°. This estimation serves to mitigate the potential for laser damage and predict the required grating size for the compressor. Another consideration for a higher AOI is to better separate diffracted beam from incident beam spatially to ease the design of compressor/stretcher since the compressor/stretcher design needs to accommodate large range of wavelength.
2.3 Design optimization for e-beam manufacturing
Given that silicon does not reflect MIR light as effectively as gold (Au), an Au coating was applied to the silicon groove. The impact of coating thickness on diffraction efficiency was simulated to identify an optimal thickness that maximizes efficiency without overly smoothing out the sharp profile features of the groove. In Fig. 6, the diffraction efficiency at λ = 3.7 µm (simulations at 5 µm and 6 µm demonstrate similar performance) for Au coating is presented, with thickness varying from 10 nm to 400 nm. Notably, for the gold coating, the diffraction efficiency reaches its peak and remains consistent from 170 nm and beyond. Taking into account potential errors during the Au layer coating process (± 10 nm), we opt for a 200 nm Au coating in the fabrication of the grating. To prevent Au deterioration from handling damage, we follow a standard practice to coat a thin protective layer. Al2O3, HfO2, and SiO2 are among commonly used materials for the high damage threshold protective layer. Al2O3 is chosen as the protective coating material due to its high MIR transmission and bandgap, reducing ionization and heating probability and maximizing the LIDT for MIR gratings. The thickness of the Al2O3 overcoat was also simulated. A 70 nm thick Al2O3 overcoat is chosen based on the simulation results in Fig. 6.
Fig. 6. Diffraction efficiency at λ=3.7 um with thickness of Au coating change from 10 nm to 400 nm. The thickness of a protective overcoat Al2O3 is simulated on top of 200 nm of Au coating on the groove structure.
Figure 7(a) depicts the triangular groove geometry following the aforementioned optimizations. Another critical factor in manufacturing is the e-beam linewidth, representing the developed line width from Electron Beam Lithography (EBL) to form a ridge on the grating groove, as illustrated in Fig. 7(b). The E-beam linewidth influences the topography of the grating groove by consuming the apex, creating a flat platform that may impact diffraction efficiency.
Fig. 7. (a) The designed triangular groove geometry after optimizations. (b) E-beam linewidth effect on the manufactured grating groove geometry. (c) Linewidth effect on grating efficiency. Linewidth changes from 0 to 600 nm.
The minimum linewidth achievable through EBL is as small as ∼70 nm. In Fig. 7(c), the change in grating efficiency with linewidth is presented. The grating efficiency at 4.3 µm remains relatively consistent within the linewidth range of 100 nm to 300 nm. To mitigate manufacturing challenges, we opt for a linewidth of 200 nm for EBL. Further exploration of the linewidth effect and its physical mechanism will be discussed elsewhere. As a practical choice for the EBL manufacturing process, a 200 nm linewidth is selected. Following the grating optimization and considering practical aspects in fabrication, Table 3 enumerates the final design parameters.
Table 3. Final grating design after optimization and practical consideration of fabrication.
3. Grating fabrication and testing
3.1 Grating groove fabrication
The MIR grating groove structure of the blazed grating was fabricated through a process that exploits the crystal structure of Si to produce triangular structures. The EBL + anisotropic wet etching process, developed by the co-authors from Penn State University [28,29], has been used to fabricate extremely high-precision X-ray gratings for astronomy applications. The fabrication was initiated with the procurement of a {311}-orientated 4-inch Si wafer substrates (0.5 mm-thick) coated with Si3N4. Then 6 steps followed in the fabrication process. Details of these 6 steps are described in Ref. [28] and outlined in Fig. 8. First, a wafer coated with silicon nitride (Si3N4) is spin-coated with an electron-beam resist, where a groove layout is defined by EBL. The details of the electron-beam resist and etching information are described in Appendix. This pattern is transferred into the silicon nitride, where the resist is removed through reactive ion etching (RIE). Native oxide (SiO2) on the wafer is removed with a buffered oxide etch (BOE), before a timed crystallographic etch using potassium hydroxide (KOH) is carried out to expose {111} planes. Finally, the Si3N4 is removed using hydrofluoric acid (HF), leaving only the groove structure with a depth h and flat-top width w that both depend on d and the degree of KOH-etch undercut. The details are described in Ref. [28]. It is worth pointing out that the use of a negative resist (HSQ) enables narrow line widths to be achieved.
Fig. 8. Step 1: Coat silicon wafer with Si3N4 and e-beam resist. Step 2: Undergo e-beam exposure and post e-beam development, retaining Si3N4 layer between grooves and silicon substrate. Steps 3a and 3b: Remove Si3N4 from exposed areas and residual e-beam resist. Step 4: Remove native oxide layer without altering groove pattern. Step 5a: Employ anisotropic KOH etch to transfer groove pattern into silicon, setting grating's blaze angle. Step 5b: Continue KOH etch, causing undercutting of residual Si3N4 layer and enhancing features at groove tops. Step 6: Present the final state of the grating after completion. This figure was modified from [Ref. [28], Fig. 2].
Figure 9 displays grating groove structures imaged using a Zeiss Merlin field-emission scanning microscope (FESEM) at three zoom levels. Across a 4-inch wafer, four parameters are measured, with results summarized in Table 4. Each parameter undergoes 13 measurements, contributing to the error in Table 3. Linear parameters, like groove period and depth, exhibit errors in the range of a few nanometers. The groove top platform width, affected by undercut during fabrication, deviates from the design width based on itching time (Eq. (2) in Ref. [28]). Apex angle error solely stems from measurement inaccuracies, aiming for the exact value (70.53°) determined by the angle between two Si {111} and {311} planes.
Fig. 9. FESEM images at three zoom levels capture grating groove details for parameter measurement. Please note that the images provided depict the bare grating groove prior to coating
Table 4. Groove parameters measured across the wafer.
3.2 Grating surface coating
The wafer is diced into multiple 1-inch by 1-inch grating pieces. A 200 nm thick conformal Au coating layer is applied to these gratings using a sputtering coating process. In the final step, a protective layer of 70 nm thick Al2O3 is coated onto the wafer through sputtering. Figure 10 presents images of the grating after both Au and Al2O3 coating. The measured Au thickness is 190 nm, slightly below the intended value of 200 nm. Similarly, the Al2O3 layer is measured to be 70.8 nm, slightly deviating from the design value of 70 nm. The roughness of the finished grating is measured using an atomic force microscope (AFM). The root-mean-square roughness Rq measures at 2.1 nm, suggesting a smooth coating.
Fig. 10. (a) top view SEM image after Au is coated. (b) side view SEM image after both Au and Al2O3 are coated. (c). AFM image of the optically active surface of the groove after coating is completed. Roughness of the surface is measured to be Rq = 2.1 nm.
3.3 Grating diffraction efficiency testing
Grating diffraction efficiency testing employs a 4.3 µm mid-IR diode laser. Laser polarization is purified through a Wollaston Prism with an extinction ratio of 100,000:1. Figure 11 illustrates the testing setup and settings. At an AOI of 64°, M = -1, the diffraction yields an exit angle ϕ = -7.4° for the 4.3 µm laser. An Ophir Vega power meter measures both incident and diffracted beam power. Four 1” x 1” grating samples underwent testing with a 3 mm radius laser beam at five evenly spaced points from the center to the edge. Each test point received a 30 mW laser for 60 seconds to minimize thermal fluctuations, resulting in a measurement error of approximately ±1%. The diffraction efficiency for TM diffraction at M = -1 was observed to be approximately 92%, with uniformity within 2%, slightly below the expected 94.2% efficiency. Additionally, wavelength tuning tests conducted between 4.3 µm ± 0.1 µm indicated no significant efficiency change within the ±1% measurement error. The test results demonstrate promising potential for utilizing this grating in constructing low-loss grating compressors for 4.3 µm, 100 fs lasers.
The approximate 2% loss in diffraction efficiency may stem from various origins. A significant contributor is the measurement uncertainty associated with the power meter, estimated to be within the range of 1%. The examination of alternative sources is elaborated upon in the following analyses.
Errors in the groove structure are anticipated to contribute only a modest fraction, with a projected loss of less than 0.5% at most. This projection is based on simulations utilizing the maximum structural errors outlined in Table 3. Scattering from surface roughness is usually a key root cause for grating diffraction efficiency loss. The surface roughness is measured to be Rq = 2.1 nm. At paraxial smooth surface approximation for normal incidence, total integrated scatter (TIS) can be simplified to following equation:
where σ here is surface roughness and $\lambda $ is the laser wavelength [30,31]. Using Eq. (1), scattering loss is calculated to be 0.004%. This scattering level of 4 × 10−5 is consistent with scattering testing results for gratings fabricated by EBL [19,21]. Another possible fabrication error could come from coating non-uniformity. To investigate the coating uniformity, a cross sectional view of sputtered Au coated grating was prepared by Focused Ion Beam (FIB) as shown in Fig. 12. Thickness variation was observed at the bottom of the grating surface, leading to a small angle change which can possibly explain the 2% efficiency loss. The reduced deposition was introduced by apex shadowing during sputtering process.Fig. 12. FESEM cross-sectional view of sputtered Au coated grating. The sample was prepared by FIB milling. The grating surface covered by 169 nm of Au. However, Au thickness started to drop at the lower 1/3 of the surface about 30% due to apex shadowing during the sputtering process.
4. Conclusion
A high-efficiency mid-infrared (MIR) grating with broadband capabilities has been meticulously designed through global optimization, demonstrating efficacy exceeding 90% within the wavelength range of 3.6 µm to 6.6 µm. Utilizing an Electron Beam Lithography (EBL) coupled with an anisotropic wet etching process, we have successfully fabricated the optimized MIR gratings. Experimental verification indicates a minimal diffraction efficiency loss, approximately 2% at 4.3 µm, compared to the theoretical prediction of 94.2%. Our investigation demonstrates the reliability of the EBL + anisotropic wet etching method for making MIR gratings with high efficiency across a broad bandwidth, suitable for sub-10 fs ultrafast lasers.
Appendix: e-beam lithography and etching processes for MIR grating fabrication
The E-beam resist process commenced with spinning a 3% HSQ solution at 4000 rpm for 45 seconds, resulting in a 120 nm film thickness. Subsequently, a soft bake at 100°C for 60 seconds was performed. The sample underwent exposure to a 100 keV, 40 nA electron beam with a dose of 900 µC. Following development in 25% TMAH for 60 seconds and a DI water rinse, a CHF3 + O2 plasma dry etch was utilized for 30 seconds to define the silicon nitride wet etch mask. Wet etching with 45% KOH at room temperature for 90 minutes ensued, followed by HF treatment (49% concentration) to remove the HSQ and 30nm silicon nitride hard-mask. The process concluded with a final DI water rinse.
Funding
Air Force Research Laboratory (FA945122PA012).
Acknowledgements
Distribution Statement: A-Approved for Public Release. Release # AFRL-2024-0217
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. A.H. Nejadmalayeri, P.R. Herman, J. Burghoff, et al., “Inscription of optical waveguides in crystalline silicon by mid-infrared femtosecond laser pulses,” Opt. Lett. 30(9), 964–966 (2005). [CrossRef]
2. R. Steiner, “Medical applications of mid-IR solid-state lasers,” in M. Ebrahimzadeh and I. T. Sorokina (Eds.), “Mid-Infrared Coherent Sources and Applications (Springer, 2008), pp. 575–588 .
3. F.K. Tittel, D. Richter, A. Fried, et al., (Eds.), “Mid-infrared laser applications in spectroscopy,” in Solid State Mid-Infrared Laser Sources (Springer, 2003), pp. 458–592.
4. A. Pushkin, E. Migal, F Suleimanova, et al., “High-power solid-state near-and mid-IR ultrafast laser sources for strong-field science,” Photonics 9(2), 90 (2022). [CrossRef]
5. Marco Arrigoni and Jean-Luc Tapié, “Chirped pulse amplification,” Photonics Views 16(3), 78–82 (2019). [CrossRef]
6. S. Zhang, M. Tripepi, A. AlShafey, et al., “Femtosecond damage experiments and modeling of broadband mid-infrared dielectric diffraction gratings,” Opt. Express 29(24), 39983–39999 (2021). [CrossRef]
7. W. Zhang, W. Kong, G. Wang, et al., “Review of pulse compression gratings for chirped pulse amplification system,” Opt. Eng. 60(02), 1 (2021). [CrossRef]
8. P. Poole, S. Trendafilov, G. Shvets, et al., “Femtosecond laser damage threshold of pulse compression gratings for petawatt scale laser systems,” Opt. Express 21(22), 26341–26351 (2013). [CrossRef]
9. F. Potemkin, “Mid-infrared (3–5 um) ultrafast Fe:ZnSe laser sources for driving extreme nonlinear optics, IEEE Photonics Conference (IPC), Vancouver, BC, Canada (2021). [CrossRef]
10. L. Yuxin, The HPLSE-2018 Invited Talk, CEP stable near-single-cycle MIR laser (2018).
11. E. Migal, A. Pushkin, B. Bravy, et al., “3.5-mJ 150-fs Fe:ZnSe hybrid mid-IR femtosecond laser at 4.4 µm for driving extreme nonlinear optics,” Opt. Lett. 44(10), 2550 (2019). [CrossRef]
12. Y. Wang, X. Fu, Y. Chen, et al., “Design of 4.7 µm High-Efficiency Hybrid Dielectric Reflection Gratings. Micromachines,” Micromachines 13(4), 632 (2022). [CrossRef]
13. P. Krogen, H. Suchowski, G. Stein, et al., “Tunable and Near-Fourier-limited Few-Cycle Mid-IR Pulses via an Adiabatically Chirped Difference Frequency Grating,” CLEO, OSA Technical Digest paper SM3I.5 (2014).
14. H. Butcher, D. MacLachlan, D. Lee, et al., “Mid-infrared volume diffraction gratings in IG2 chalcogenide glass: fabrication, characterization, and theoretical verification,” Proc. SPIE 10528, 105280R (2018). [CrossRef]
15. F. Potemkin, E. Migal, A. Pushkin, et al., “Gigawatt mid-IR (4-5 µm) femtosecond hybrid Fe2+:ZnSe laser system,” Proc. SPIE 10238, High-Power, High-Energy, and High-Intensity Laser Technology III, 102380L, (2017).
16. C. Palmer, Richardson Gratings Handbook, 8th edition, (Richardson Grating, MKS Instruments, Inc.).
17. Q Liu and J. Wu, “Analysis and comparison of the scalar diffraction theory and coupled-wave theory about grating,” Laser J.25, 31 (2004).
18. T. Tamulevičius, I. Gražulevičiūtė, A. Jurkevičiūtė, et al., “The calculation, fabrication and verification of diffraction grating based on laser beam splitters employing a white light scatterometry technique,” Optics and Lasers in Engineering. 51(10), 1185–1191 (2013). [CrossRef]
19. L. Huang, X. Peng, C. Guan, et al., “Progress in the preparation and characterization of convex blazed gratings for hyper-spectral imaging spectrometer: a review,” Micromachines 13(10), 1689 (2022). [CrossRef]
20. D. W. Wilson, P. D. Maker, R. E. Muller, et al., “Recent advances in blazed grating fabrication by electron-beam lithography,” Proc. SPIE 5173, 115–126 (2003). [CrossRef]
21. T. Lu, J. Lowney, T. Mercier, et al., “Blazed and slanted grating mastering using crystallography-based silicon etching,” Technical Disclosure Commons (2022).
22. D. L. Voronov, S. Park, E. M. Gullikson, et al., “Highly efficient ultra-low blaze angle multilayer grating,” Opt. Express 29(11), 16676–16685 (2021). [CrossRef]
23. C. T. DeRoo, J. Termini, F. Grisé, et al., “Limiting spectral resolution of a reflection grating made via electron-beam lithography,” The Astrophysical Journal 904(2), 142 (2020). [CrossRef]
24. M. Heusinger, M. Banasch, U. D. Zeitner, et al., “High precision electron-beam-lithography for optical high-performance applications,” 59th ILMENAU scientific colloquium, Technische Universität Ilmenau, 11–15 (2017).
25. Y. Wang, F. Fleming, R. A. McCracken, et al., “Hot-isostatic-pressed Cr:ZnSe ultrafast laser at 2.4 µm,” Opt. Laser Technol. 154, 108300 (2022). [CrossRef]
26. M. Seide, X. Xiao, S. A. Hussain, et al., “Multi-watt, multi-octave, mid-infrared femtosecond source,” Sci. Adv. 4(4), 1526 (2018). [CrossRef]
27. D. Miles, J. McCoy, R. McEntaffer, et al., “Fabrication and diffraction efficiency of a large-format, replicated X-ray reflection grating,” The Astrophysical Journal 869(2), 95 (2018). [CrossRef]
28. J. A. McCOy, “Applied nanofabrication for X-ray Grating spectroscopy,” Ph.D. thesis in Astronomy & Astrophysics, Pennsylvania State University (2021).
29. H. Wu, S. Huang, C. Shih, et al., “Highly reflective silver-enhanced coating with high adhesion and sulfurization resistance for telescopes,” Nanomaterials 12(7), 1054 (2022). [CrossRef]
30. J. Harvey, S. Schröder, N. Choi, et al., “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng 51(1), 013402 (2012). [CrossRef]
