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All- and mixed-dielectric grating for Nd:glass-based high-energy pulse compression

Published online by Cambridge University Press:  18 September 2023

Yuxing Han
Affiliation:
Laboratory of Thin Film Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China Key Laboratory of Materials for High Power Laser, Chinese Academy of Sciences, Shanghai, China
Hongchao Cao
Affiliation:
Laboratory of Thin Film Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China Key Laboratory of Materials for High Power Laser, Chinese Academy of Sciences, Shanghai, China China-Russian Belt and Road Joint Laboratory on Laser Science, Shanghai, China
Fanyu Kong
Affiliation:
Laboratory of Thin Film Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China Key Laboratory of Materials for High Power Laser, Chinese Academy of Sciences, Shanghai, China China-Russian Belt and Road Joint Laboratory on Laser Science, Shanghai, China
Yunxia Jin*
Affiliation:
Laboratory of Thin Film Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China Key Laboratory of Materials for High Power Laser, Chinese Academy of Sciences, Shanghai, China CAS Center for Excellence in Ultra-Intense Laser Science, Chinese Academy of Sciences, Shanghai, China China-Russian Belt and Road Joint Laboratory on Laser Science, Shanghai, China
Jianda Shao
Affiliation:
Laboratory of Thin Film Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China Key Laboratory of Materials for High Power Laser, Chinese Academy of Sciences, Shanghai, China CAS Center for Excellence in Ultra-Intense Laser Science, Chinese Academy of Sciences, Shanghai, China Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou, China China-Russian Belt and Road Joint Laboratory on Laser Science, Shanghai, China
*
Correspondence to: Yunxia Jin, Laboratory of Thin Film Optics, Shanghai Institute of Optics and Fine Mechanics, No. 390 Qinghe Road, Jiading District, Shanghai 201800, China. Email: yxjin@siom.ac.cn

Abstract

Maximizing the energy-loading performance of gratings is a universal theme in high-energy pulse compression. However, sporadic grating designs strongly restrict the development of high-power laser engineering. This study proposes an all- and mixed-dielectric grating design paradigm for Nd:glass-based pulse compressors. The solution regions are classified according to the line density. High diffraction efficiency solutions are described in more detail based on the dispersion amount and incident angle. Moreover, an energy scaling factor of 7.09 times larger than that of the National Ignition Facility’s Advanced Radiographic Capability (NIF-ARC) is obtained by taking advantage of the low electric field intensity at transverse magnetic polarization and a small incident angle. These results make a pioneering contribution to facilitate future 20–50-petawatt-class ultrafast laser systems.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2023. Published by Cambridge University Press in association with Chinese Laser Press

1 Introduction

In the past four decades, the race to deliver petawatt (PW)-scale peak power based on the techniques of chirped pulse amplification (CPA)[ Reference Strickland and Mourou 1 ] and then optical parametric CPA (OPCPA)[ Reference Dubietis, Jonušauskas and Piskarskas 2 ] has been underway. Multi-PW laser technology opens the door to groundbreaking research in areas such as laser-driven particle acceleration[ Reference Wang, Feng, Ke, Yu, Xu, Qi, Chen, Qin, Zhang, Fang, Liu, Jiang, Wang, Wang, Yang, Wu, Leng, Liu, Li and Xu 3 ], high-energy-density physics[ Reference Hatfield, Gaffney, Anderson, Ali, Antonelli, Du Pree, Citrin, Fajardo, Knapp, Kettle, Kustowski, MacDonald, Mariscal, Martin, Nagayama, Palmer, Peterson, Rose, Ruby, Shneider, Streeter, Trickey and Williams 4 ] and astrophysics[ Reference Takabe and Kuramitsu 5 ]. In particular, laser-driven inertial confinement fusion (ICF)[ Reference Betti and Hurricane 6 ] has picked up speed to boost clean power hopes in the next decade.

In the journey to a multi-PW laser, increasing the pulse energy beyond 1 kilojoule (kJ) is an internationally recognized technical solution[ Reference Danson, Haefner, Bromage, Butcher, Chanteloup, Chowdhury, Galvanauskas, Gizzi, Hein, Hillier, Hopps, Kato, Khazanov, Kodama, Korn, Li, Li, Limpert, Ma, Nam, Neely, Papadopoulos, Penman, Qian, Rocca, Shaykin, Siders, Spindloe, Szatmári, Trines, Zhu, Zhu and Zuegel 7 Reference Li, Leng and Li 9 ]. Up to 2022, ELI-beamlines L4-Aton in Czechia[ 10 Reference Rus, Bakule, Kramer, Naylon, Thoma, Fibrich, Green, Lagron, Antipenkov, Bartoníček, Batysta, Baše, Boge, Buck, Cupal, Drouin, Ďurák, Himmel, Havlíček, Homer, Honsa, Horáček, Hríbek, Hubáček, Hubka, Kalinchenko, Kasl, Indra, Korous, Košelja, Koubíková, Laub, Mazanec, Meadows, Novák, Peceli, Polan, Snopek, Šobr, Trojek, Tykalewicz, Velpula, Verhagen, Vyhlídka, Weiss, Haefner, Bayramian, Betts, Erlandson, Jarboe, Johnson, Horner, Kim, Koh, Marshall, Mason, Sistrunk, Smith, Spinka, Stanley, Stolz, Suratwala, Telford, Ditmire, Gaul, Donovan, Frederickson, Friedman, Hammond, Hidinger, Chériaux, Jochmann, Kepler, Malato, Martinez, Metzger, Schultze, Mason, Ertel, Lintern, Edwards, Hernandez-Gomez, Collier, Korn and Silva 11 ], NIF-ARC[ Reference Barty, Key, Britten, Beach, Beer, Brown, Bryan, Caird, Carlson, Crane, Dawson, Erlandson, Fittinghoff, Hermann, Hoaglan, Iyer, Jones, Jovanovic, Komashko, Landen, Liao, Molander, Mitchell, Moses, Nielsen, Nguyen, Nissen, Payne, Pennington, Risinger, Rushford, Skulina, Spaeth, Stuart, Tietbohl and Wattellier 12 ] and OMEGA EP[ Reference Kelly, Waxer, Bagnoud, Begishev, Bromage, Kruschwitz, Kessler, Loucks, Maywar, McCrory, Meyerhofer, Morse, Oliver, Rigatti, Schmid, Stoeckl, Dalton, Folnsbee, Guardalben, Jungquist, Puth, Shoup, Weiner and Zuegel 13 ] in the USA, LFEX[ Reference Miyanaga, Azechi, Tanaka, Kanabe, Jitsuno, Kawanaka, Fujimoto, Kodama, Shiraga, Knodo, Tsubakimoto, Habara, Lu, Xu, Morio, Matsuo, Miyaji, Kawakami, Izawa and Mima 14 ] in Japan and SG-II[ Reference Zhu, Xie, Sun, Kang, Yang, Guo, Zhu, Zhu, Gao, Liang, Cui, Yang, Zhang and Lin 15 ] in China facilitated by the large-aperture Nd:glass[ Reference Hou, Li and Zhang 16 ] CPA/OPCPA technique have been operational at more than 1 PW. Furthermore, more than 20 laser facilities[ 17 ] worldwide will be scaled to 10–50 PW in the future, followed by high-energy amplification and compression at the central wavelength of 1053 nm. In engineering, the bandwidth metric of the output spectrum in the Nd:glass-based PW laser system is ±3 nm at a center wavelength of 1053 nm. In contrast, the higher pulse energy is significantly limited by the laser-induced damage threshold (LIDT)[ Reference Stuart, Feit, Rubenchik, Shore and Perry 18 ] and the aperture of the advanced pulse compression gratings.

All- and mixed-dielectric gratings (MDGs and MMDGs)[ Reference Bonod and Neauport 19 ] are preferred in narrow-bandwidth high-energy laser systems owing to their large aperture (meter scale)[ Reference Barty, Key, Britten, Beach, Beer, Brown, Bryan, Caird, Carlson, Crane, Dawson, Erlandson, Fittinghoff, Hermann, Hoaglan, Iyer, Jones, Jovanovic, Komashko, Landen, Liao, Molander, Mitchell, Moses, Nielsen, Nguyen, Nissen, Payne, Pennington, Risinger, Rushford, Skulina, Spaeth, Stuart, Tietbohl and Wattellier 12 ], high efficiency (>95%)[ Reference Perry, Boyd, Britten, Decker, Shore, Shannon and Shults 20 ] and robustness (LIDT > 3 J/cm2 at 0.5 ps)[ Reference Kong, Jin, Li, Chen, Zhu, Wang, Li, He, Xu, Shao, Exarhos, Gruzdev, Menapace, Ristau and Soileau 21 Reference Kozlov, Demos, Canning, Hoffman, Kruschwitz, Rigatti, Savidis and Waxer 23 ]. Since the 21st century, 1D reflective MDGs have been categorized into three categories according to the materials of the etched layers: high-refractive-index materials (All-H)[ Reference Shore, Perry, Britten, Boyd, Feit, Nguyen, Chow, Loomis and Li 24 Reference Wang, Jin, Ma, Sun and Jing 25 ], low-refractive-index materials (All-L)[ Reference Neauport, Bonod, Hocquet, Palmier and Dupuy 26 Reference Jerald, William, Aleksey and Christopher 27 ] and high–low-refractive-index materials (Hybrid)[ Reference Han, Jin, Kong, Wang, Zhang, Cao, Cui and Shao 28 ]. A fundamental challenge occurs through the design of the grating structure and laser architecture, that is, how to maximize the energy load capacity of the grating surface.

One design concept of the MDG is to minimize the electric field intensity (EFI) enhancement[ Reference Liu, Shen, Kong, Shen, Deng, Zhao, Shao and Fan 29 , Reference Bonod and Néauport 30 ] in the MDG pillars while meeting the spectral metrics. From 1991 to 2019, all designs were reported with high line densities between 1480–1800 l/mm at 56°–77.2°, which generated an EFI from 4.41 to 1.80. Two classic All-L MDG designs have been extensively deployed. For example, NIF-ARC loaded the high fluence of PW-class lasers by installing 1780 l/mm MDGs at a 76.5° incident angle (AOI)[ Reference Barty, Key, Britten, Beach, Beer, Brown, Bryan, Caird, Carlson, Crane, Dawson, Erlandson, Fittinghoff, Hermann, Hoaglan, Iyer, Jones, Jovanovic, Komashko, Landen, Liao, Molander, Mitchell, Moses, Nielsen, Nguyen, Nissen, Payne, Pennington, Risinger, Rushford, Skulina, Spaeth, Stuart, Tietbohl and Wattellier 12 ]. SIOM configured a 1740 l/mm MDG at 70° to maximize the energy-loading capacity of SG-II[ Reference Zhu, Xie, Sun, Kang, Yang, Guo, Zhu, Zhu, Gao, Liang, Cui, Yang, Zhang and Lin 15 ]. From a design perspective, both designs are with high dispersion at large AOIs.

A large projection ratio (>2) of high-dispersion gratings drives the expansion of the maximum grating aperture. However, the achievable aperture is restricted by the diagonal size of less than 1.1 m based on the current manufacturing processes[ 31 ]. Consequently, the biaxial meter-scale grating is a pull towards developing another design concept, that is, the low-dispersion Littrow-angle grating. From 2019 to 2022, SIOM presented a low-dispersion grating design and LIDT performance at 8.6 ps pulse compression[ Reference Han, Jin, Kong, Wang, Zhang, Cao, Cui and Shao 28 ], and LLNL received the 2022 R&D 100 Awards for 85-cm-by-70-cm high-energy low-dispersion gratings[ 32 ]. In contrast, very few studies have evaluated the design schemes and tolerances.

In the past three decades, the possible parameters of gratings operating in high-energy laser facilities have been sporadically reported. The solution region with a high diffraction efficiency (DE) in the parameter space has not been thoroughly explored. Devising the right grating for a given Nd:glass CPA/OPCPA laser system architecture can be confusing for grating designers and laser builders.

In this study, a design paradigm is introduced for all- and mixed-dielectric pulse compression gratings at a center wavelength of 1053 nm. The properties of four solution regions, namely the incompatible Region I, stable Region II, anomalous Region IIII and turbulent Region IV, are defined. High-efficiency solutions are classified into three configurations: high dispersion at a large AOI, moderate dispersion at a large deviation angle and low dispersion at the Littrow angle. Accordingly, three representative designs are presented: a 1810 l/mm ultra-low EFI design, a 1250 l/mm ultra-broad deviation-angle design and a 1150 l/mm polarization-independent design. Moreover, an energy scaling factor defined to evaluate the energy-loading performance of the grating quantitatively demonstrates the potential advantages of the AOI and transverse magnetic (TM) polarization.

2 Design scheme of the dielectric pulse compression grating

The dielectric pulse compression grating is a combination of a high-reflectivity (HR) mirror, buffer and grating structure in the traditional ‘reflectivity bottom + buffer + diffraction top’ design strategy, as shown in Figure 1. Alternating refractive-index (n) films with/without a metal film are deposited on a base substrate to obtain interference-dependent HR. In an HR mirror, d H, d L and d M denote the physical thickness of the high-n, low-n and metal films, respectively. In general, the MMDG replaces the dielectric mirror with a metal one to reduce the number of pairs, which enables the same performance level as the MDG. Therefore, the MMDG model is used for all the numerical calculations below.

Figure 1 Schematic diagram of the all- and mixed-dielectric gratings in the traditional ‘reflectivity bottom + buffer + diffraction top’ combination design strategy.

In addition, a buffer is stacked with high-n and low-n films in a structure similar to an HR mirror. However, there are no specific restrictions on the number of films, structures and materials in a buffer as long as it moderately compensates for the high-efficiency in-phase condition[ Reference Wei and Li 33 ]. The correct accumulation of the relative phase upon diffraction, propagation and reflection is required to achieve all light in the -1st order of reflection. Here, d H-Bi and d L-Bi indicate the physical thickness of the high-n and low-n films in the buffer, where the number of films is labeled with i.

Meanwhile, a top fine-tuned grating structure enables the redistribution of energy flow among the diffraction orders. The grating structure consists of partially etched or etch-through periodic pillars, where d G denotes the pillar depth, d R is the residual thickness of the etched films, f symbolizes the duty cycle in the base (the base width is the product of the grating period Λ and f) and β is the base angle of the pillar. Note that the All-L type is considered in the following design owing to the higher LIDT performance of SiO2.

All grating parameters were optimized by rigorous coupled-wave analysis (RCWA), which generates reliable calculation results of EFI distribution and DE (see more details in Refs. [Reference Han, Jin, Kong, Wang, Zhang, Cao, Cui and Shao28,Reference Liu, Shen, Kong, Shen, Deng, Zhao, Shao and Fan29,Reference Guan, Chen, Wu, Jin, Kong, Liu, Yi and Shao34,Reference Chen, Zhang, Wang, Kong, Huang, Wang, Jin, Chen, Xu and Shao35]). Here, the n values of HfO2 and SiO2 as high-n and low-n materials are 1.9 and 1.45 at 1053 nm, respectively. In order to obtain a constant complex refractive index $\tilde{n}$ , the thickness of the gold (Au) film is universally set to 200 nm and $\tilde{n}$ is derived from a database[ Reference Werner, Glantschnig and Ambrosch-Draxl 36 ].

In this paper, a high-DE solution with a moderate line density was chosen to introduce the design paradigm. The 1300 l/mm MMDG was designed at a central wavelength of 1053 nm in transverse electric (TE) polarization with a 67.5° AOI. The design consisted of substrate/Au/(LH)5/LB1HB2/T/air. The regular film subsystem (LH)5 is a traditional HR structure, where H and L represent the HfO2 and SiO2 quarter-wavelength optical thickness layers, respectively. The SiO2 (LB1) and HfO2 (HB2) buffer combines the SiO2 top layer (T) to achieve a high DE and lay the foundation for a high LIDT. The physical parameters are d H = 152 nm, d L = 198 nm, d L-B1 = 466 nm, d H-B2 = 349 nm, d R = 308 nm, d G = 573 nm, f = 0.4 and $\beta$ is 90°.

Figure 2 shows the DE map for the above design. Four regions are defined based on the line density. Incompatible Region I is above 1900 l/mm; accordingly, the grating period is less than 526 nm. As expected, the grating law is not satisfied for the 1053 nm laser. The stable Region II is between 1600 and 1900 l/mm, where the grating exhibits high dispersion and a large AOI. The effective solutions are concentrated and regularly extended with the increased line density. Anomalous Region III occupies a large range from 1000 to 1600 l/mm. In this region, the high-efficiency solutions deviate from the Littrow configuration. Obviously, small-deviation-angle solutions are connected into a narrow strip, illustrating the narrow AOI spectrum and high requirements for engineering layouts[ Reference Webb, Guardalben, Dorrer, Bucht and Bromage 37 ]. Conversely, large-deviation-angle solutions aggregate relatively large areas, implicating greater engineering feasibility. Turbulent Region IV is in the range of 600–1000 l/mm, containing a number of sharp dips generated by the guided-mode resonances (GMRs)[ Reference Wang, Jin, Ma, Shao and Fan 38 , Reference Alessi, Nguyen, Britten, Rosso and Haefner 39 ]. These dips not only move relative to the line density but also have transverse pulsations along the AOI. Accordingly, the high-efficiency solutions generally appear at the Littrow angle, and numerous singular dissolutions appear chaotically.

Figure 2 The –1st order diffraction efficiency versus the incident angle and line density. The dashed line represents the Littrow angle at 1053 nm with the line density.

Figure 3 depicts the spectral bandwidth characteristics of these four regions. The spectrum in the 1000–1100 nm range was considered in this study; however, this could be broader. Notably, Region II had highly efficient solutions over a wide range. In comparison, the spectral bandwidth of Region III was narrower. However, the spectral performance significantly exceeded the bandwidth requirement of the Nd:glass-based laser system. Region IV is a split band in which effective solutions densely scratch the efficiency map.

Figure 3 The –1st order diffraction efficiency versus wavelength and line density.

3 High-dispersion large-incident-angle dielectric grating

In stable Region II, the effective grating structure is straightforward to construct and quickly converges to a solution with high dispersion and a large AOI. In this configuration, realizing a smaller EFI is the ultimate goal of design campaigns.

From a forward-looking perspective, two MMDG designs for the TE and TM polarizations are presented in Figure 4. One design is a 1740 l/mm MMDG, designed at 1053 nm for TE polarization with a 70° AOI. The design is as follows: substrate/Au/(LH)3/T/air. The physical parameters are d H = 167.2 nm, d L = 203.7 nm, d R = 28 nm, d G = 670 nm, f = 0.26 and $\beta$ = 90°. The fundamental challenge is to achieve HR and low EFI simultaneously. Figures 4(a)4(c) present the restrictive relationship between the 99% efficiency and maximal EFI in grating pillars, where the intersection of the fabrication and LIDT tolerances is the structure optimization region for the high-dispersion gratings. Notably, deep-etched narrow pillars with high perpendicularity are key to achieving high-yield gratings. Figure 4(d) shows a flat spectrum over 1050–1056 nm with an average DE of 99.41%. The angular spectrum at 1053 nm shows a broad tolerance range of 61°–73° for diffraction efficiencies above 99%. This behavior is related to the role of interference in the dielectric grating. A more detailed theoretical explanation needs to be developed in the future.

Figure 4 High-dispersion large-incident-angle dielectric grating with (a)–(d) 1740 l/mm in TE polarization and (e), (f) 1810 l/mm in TM polarization. The fabrication tolerance and EFI tolerance of the (a) duty cycle f versus pillar depth d G, (b) residual layer thickness d R versus d G and (c) base angle β versus f. (d), (e) Diffraction efficiency versus wavelength and incident angle. (f) Normalized EFI distribution.

The other is the 1810 l/mm MMDG, designed at 1053 nm in TM polarization with an AOI of 82.4°. The design is as follows: substrate/Au/HB1/T/air. The physical parameters are d H-B1 = 286 nm, d R = 286 nm, d G = 688 nm, f = 0.2 and $\beta$ = 90°. As shown in Figure 4(e), the average DE is 97.71% from 1050 to 1056 nm. In the hump-like angular spectrum at 1053 nm, the two global maxima reached 97.73% at 66.2° and 82.4°, respectively. As shown in Figure 4(f), the maximum EFI has a value of 0.722, which is an unprecedented result in the history of grating design.

4 Moderate-dispersion large-deviation-angle dielectric grating

Anomalous Region III is a boon for an ultrabroad angular-deviation compressor. Considering a one-for-one replacement for the original compressor configuration of SG-II, a 1250 l/mm MMDG was designed for TE polarization in the Littrow configuration with a 29° deviation angle. The design consists of substrate/Au/(HL)15/HB1LB2HB3/T/air. The physical thicknesses are d H = 193 nm, d L = 171 nm, d H-B1 = 114 nm, d L-B2 = 453 nm, d H-B3 = 183 nm, d R = 200 nm, d G = 644 nm, f = 0.3 and $\beta$ = 85°. As shown in Figure 5(a), the angular spectrum exhibits three peaks at 22.2°, 41.3° and 70°. Accordingly, the average diffraction efficiencies were greater than 99% at 1053 ± 3 nm. It should be noted that a narrow angular tolerance results in higher engineering requirements for the grating gestures.

Figure 5 Low-dispersion large-deviation-angle dielectric grating. (a) Diffraction efficiency versus incident angle and wavelength in TE polarization. (b) Grating compressor architecture at an incident angle lower than (I), equal to (II) and higher than (III) the Littrow angle. (c) Normalized EFI distribution.

Figure 5(b) illustrates the multi-layout compatibility of this grating. The low-AOI design (I) exhibits higher dispersion for a given separation between the gratings and can have compressor geometry advantages for some systems. The Littrow angle design (II) requires out-of-plane operation for a total angular deviation greater than a few degrees. The high AOI design (III) exhibits a lower overall temporal dispersion for a given line density and separation and has the advantage that the intensity of the final grating is lower because of the larger projected angle of the beam on the grating, resulting in potentially higher pulse energy before laser damage occurs. As shown in Figure 5(c), the EFI values in the three cases spanned over a wide range from 2.2 to 6.56.

5 Low-dispersion dielectric grating at the Littrow angle

Turbulent Region IV presents problematic spectral features caused by GMRs. The careful design of the MDG can mitigate GMR dips to avoid substantial EFI and appreciable degradation of the LIDT. However, in some cases, GMRs cannot be eliminated completely. Although it is possible to eliminate the GMRs in the demand wavelength band, this leads to extremely poor preparation tolerances. Fortunately, the MDG tends to provide a high DE very close to the Littrow angle for most cases at TE and TM polarizations.

An ideal solution requires compromises in the DE and maximal EFI. As shown in Figure 6, each dot represents a 1150 l/mm MDG design at a 37° Littrow angle[ Reference Vyhlídka, Trojek, Kramer, Peceli, Batysta, Bartoníček, Hubáček, Borger, Antipenkov, Gaul, Ditmire, Rus, Bakule and Haefner 40 ]. A sub/(2LH)15L/air design is used as the input structure, as shown in Figure 6(a). It can be observed that with such a design, the low EFI limits of the TM-polarized and TE-polarized MDGs are approximately 2.92 and 4.66, respectively. The EFI gain factor, defined as $\mathrm{EFI}_\mathrm{TM}/\mathrm{EFI}_\mathrm{TE}$ , is 0.63, which indicates the LIDT superiority of the TM-polarized MDG[ Reference Han, Jin, Kong, Wang, Zhang, Cao, Cui and Shao 28 ]. The design of a single polarization was omitted because excellent designs can be easily iterated.

Figure 6 Trade-off between maximal EFI in the grating pillar and average diffraction efficiency in the working wavelength band for a 1150 l/mm MDG. MDG selection for (a) single TE or TM polarization, and (b) polarization independence.

This section highlights a polarization-independent MMDG design that achieves high DE at both TE and TM polarizations. We select a non-regular structure: sub/Au/(LH)5/L/air. Figure 6(b) shows the dataset of the EFI and average DE from a large number of polarization-independent designs. From the above dataset, a design is picked to obtain a high DE and a high LIDT, in which the physical thicknesses are d L = 200 nm, d H = 150 nm, d R = 66 nm, d G = 1283 nm, f = 0.633 and $\beta$ = 90°. As indicated by the black arrow in Figure 6(b), the selected design has a minimum EFI value of 2.99 at TM polarization and DE of 99.25%. Correspondingly, the EFI value for the TE polarization was 6.9, and the DE was up to 99.7%. In the All-L design solution, the EFI gain factor was as high as 2.31. This high factor value indicates that the optimal TE solution makes concessions to the TM solution to achieve polarization independence.

6 Discussion

The energy-loading capacity is determined by the grating aperture and LIDT on the grating surface. Therefore, it can be expressed using the following simple formula:

(1) $$ \begin{align}E=\frac{\cos^2\theta }{\mathrm{EFI}}\cdot {L}_{\mathrm{MAX}}^2\cdot \mathrm{LIDT}_{\mathrm{int}},\end{align}$$

where ${L}_{\mathrm{MAX}}$ denotes the largest achievable aperture of the current grating manufacturing technology, $\mathrm{LIDT}_{\mathrm{int}}$ is the intrinsic LIDT[ Reference Lamaignère, Ollé, Chorel, Roquin, Kozlov, Hoffman, Oliver, Demos, Gallais, Negres and Melninkaitis 41 ], $\theta$ is the AOI and $\kappa ={\cos}^2\theta / \mathrm{EFI}$ is defined as the energy scaling factor. Here, ${L}_{\mathrm{MAX}}$ and $\mathrm{LIDT}_{\mathrm{int}}$ are typically constant with the selected material and manufacturing conditions.

Figure 7 depicts the $\kappa$ distribution, including the grating schemes of SG-II, PETAL[ Reference Néauport and Bonod 42 ], the NIF-ARC and the above designs in this paper. The dashed line is obtained by fitting the data of SG-II, the NIF-ARC and PETAL with the expression of $\kappa$ . Two types of information can be interpreted from the picture. On the one hand, the area above the dashed line represents a lower EFI value and larger achievable energy for the same AOI. On the other hand, the $\kappa$ distribution along the dashed line causes the advantage of energy utilization owing to the angle variation. As shown in Figure 7, the $\kappa$ of the NIF-ARC is 0.03, similar to PETAL and half that of SG-II. Except for Design 1, the $\kappa$ values of Designs 2–4 are much better than those of the NIF-ARC. In particular, the $\kappa$ value of Design 4 at TM polarization is 7.09 times higher than that of the NIF-ARC. This result indicates that compressors are bound to take full advantage of the benefits from the angle and TM polarization in the future.

Figure 7 Energy scaling factor distribution. The circle represents the design in this paper. The purple circle represents the 1810 l/mm ultra-low EFI design in Section 3. The blue circles denote the 1250 l/mm ultra-broad deviation-angle design in Section 4. The red and orange circles indicate the 1150 l/mm polarization-independent and TE-polarized designs in Section 5, respectively.

7 Conclusion

In conclusion, a design paradigm was proposed for all- and mixed-dielectric pulse compression gratings. The grating solution was classified into four regions according to the line density: incompatible Region I, stable Region II, anomalous Region III and turbulent Region IV. At 1600–1900 l/mm, Region II concentrated solutions with a high dispersion and large AOI, generating an ultra-low EFI and large projection ratios. The solution in Region III, from 1200 to 1600 l/mm, had an ultra-broad deviation angle and was compatible with a wide range of compressor architectures. In Region IV, perturbed by GMRs, effective solutions with a low dispersion below 1200 l/mm appeared at the Littrow mounting. Although the partition of the line density in Regions I–IV varied for a given design, the properties of each region were unique. In addition, the potential of the angle and TM polarization to maximize the grating energy-loading capacity was elucidated by analyzing the energy scaling factor. Our research paves the way for designing and matching the best high-energy gratings for Nd:glass PW laser compressors.

Acknowledgements

This work was supported by the National Key R&D Program of China (No. 2020YFA0714500), the National Natural Science Foundation of China (Nos. 61875212 and U1831211), the Shanghai Strategic Emerging Industry Development Special Fund (No. 31011442501217020191D3101001), the International Partnership Program of Chinese Academy of Sciences (No. 181231KYSB20200040) and the Strategic Priority Research Program of Chinese Academy of Sciences (No. XDA25020314).

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Figure 0

Figure 1 Schematic diagram of the all- and mixed-dielectric gratings in the traditional ‘reflectivity bottom + buffer + diffraction top’ combination design strategy.

Figure 1

Figure 2 The –1st order diffraction efficiency versus the incident angle and line density. The dashed line represents the Littrow angle at 1053 nm with the line density.

Figure 2

Figure 3 The –1st order diffraction efficiency versus wavelength and line density.

Figure 3

Figure 4 High-dispersion large-incident-angle dielectric grating with (a)–(d) 1740 l/mm in TE polarization and (e), (f) 1810 l/mm in TM polarization. The fabrication tolerance and EFI tolerance of the (a) duty cycle f versus pillar depth dG, (b) residual layer thickness dR versus dG and (c) base angle β versus f. (d), (e) Diffraction efficiency versus wavelength and incident angle. (f) Normalized EFI distribution.

Figure 4

Figure 5 Low-dispersion large-deviation-angle dielectric grating. (a) Diffraction efficiency versus incident angle and wavelength in TE polarization. (b) Grating compressor architecture at an incident angle lower than (I), equal to (II) and higher than (III) the Littrow angle. (c) Normalized EFI distribution.

Figure 5

Figure 6 Trade-off between maximal EFI in the grating pillar and average diffraction efficiency in the working wavelength band for a 1150 l/mm MDG. MDG selection for (a) single TE or TM polarization, and (b) polarization independence.

Figure 6

Figure 7 Energy scaling factor distribution. The circle represents the design in this paper. The purple circle represents the 1810 l/mm ultra-low EFI design in Section 3. The blue circles denote the 1250 l/mm ultra-broad deviation-angle design in Section 4. The red and orange circles indicate the 1150 l/mm polarization-independent and TE-polarized designs in Section 5, respectively.