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Abstract
We demonstrate a laser-diode-pumped multipass Nd:glass laser amplifier with a range of advanced characteristics. The amplifier exhibits high extraction efficiency, enables arbitrary shaping of spatial beam intensity, and effectively suppresses frequency modulation to amplitude modulation conversion. Our approach achieves excellent beam quality via thermal lensing and thermal depolarization compensation. When a 1.82 mJ/5 ns laser pulse was injected into the amplifier, the output energy reached up to 3.3 J with a repetition rate of 1 Hz at a central wavelength of 1053.3 nm. The near-field modulation of the amplified output beam was below 1.2, and the far-field focusing ability of the beam was 90% at 2.9 times the diffraction limit. This laser amplifier system holds potential for integration as a preamplifier within the SG-II upgrade high power laser facility.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-power large-scale laser facilities play a pivotal role in various domains such as high energy density physics research, laboratory astrophysics, and laser inertial confinement fusion (ICF) [1,2]. Within these contexts, the preamplifier system stands as a crucial component, particularly in laser facilities focused on ICF [3–6], for achieving the highest-gain amplification. It facilitates the amplification of nanojoule energy injected by the fiber seed source into several joules of energy output. At present, the preamplifier system in a laser facility adopts a working state with a low repetition rate. For example, the preamplifier system in National Ignition Facility (NIF) employs a laser diode (LD)-pumped regenerative amplifier (with a repetition rate of 1 Hz) and a xenon-lamp-pumped neodymium-doped glass (Nd:glass) rod four-pass amplifier to achieve an impressive 10 J output level [3,7]. After beam splitting, the laser pulses are injected into four subsequent amplification beam-lines, and the operation repetition rate of the preamplifier is one shot every ten minutes. Similarly, the pump laser at the front-end of the Omega EP laser facility incorporates a regenerative amplifier and an LD-pumped ring amplifier with a repetition rate of 5 Hz, However, the use of Nd:YLF as the gain medium results in strong gain narrowing [8,9], which induces the frequency modulation to amplitude modulation (FM-to-AM) conversion and endangers the subsequent large aperture optical elements [10]. The preamplifiers of Laser MegaJoule (LMJ) also include a high energy regenerative amplifier and a four-pass laser amplifier with a xenon-lamp-pumped Nd:glass rod laser head. The regenerative amplifier outputs a flat-top near-field modified by a diffraction mirror in the laser cavity. The preamplifier operates at a low repetition rate and they are considering improving that by changing the laser gain medium to Nd, Lu:CaF2 [11–13].
Beyond their primary role in amplification, repetition-rate laser amplifier can be used to improve the alignment efficiency of laser facilities. However, improving the repetition rate of the preamplifier is constrained by thermal effects present in the laser gain medium, which induce wavefront distortion and deteriorate the beam quality. Considerable efforts have been devoted to overcoming this limitation and increasing the repetition of joule-level Nd:glass laser for preamplifiers. Yao etc. recently reported a 1J/1 Hz amplifiers with an LD-pumped square-rod Nd:glass laser head and a deformable mirror inserted in the cavity [14]. While the output near-field beam quality was 1.4:1, details regarding the temporal modulation depth in laser amplifiers were not explicitly reported. Furthermore, The team from LMJ compared the simulation and experimental results of a four-pass LD-pumped active-mirror laser amplifier using an Nd, Lu:CaF2 gain medium [15]. Building on these efforts, we have developed a series of multipass repetition rate laser amplifiers, such as a high-gain lamp-pumped laser amplifier [16], a ring multipass laser amplifier with double laser heads [17], and an LD end-pumped square rod laser amplifier [18]. We demonstrated that a repetition rate laser can be applied in a laser facility given that the thermal effect in the laser amplifier meticulously controlled.
In this study, we present an LD-pumped, high-energy, eight-pass Nd:glass amplifier with active polarization control and high extraction efficiency. In the amplifier, the thermal lens and thermal depolarization were well compensated for. Precision control was achieved over the temporal waveform and spatial intensity. To suppress the FM-to-AM conversion, a broadband regenerative amplifier and a second spectral controller were deployed, with the temporal amplitude modulation depth remaining below 10%. Finally, the laser amplifier system realized 3.3 J/1 Hz/5 ns repetition-rate laser amplification output with a central wavelength of 1053.3 nm. The laser amplifier system would be applied to the preamplifier system of the SG-II upgrade laser facility.
2. Experimental setup
As shown in Fig. 1, the system consists of four parts: an all-fiber seed source, a broadband regenerative laser amplifier, a beam near-field shaping module (BSM), and a multipass laser amplifier system (MPA). The all-fiber seed source is capable of producing a single-longitudinal-mode laser pulse, which is then phase modulated to obtain different bandwidth spectrum (∼0.1 nm and ∼0.3 nm) with the ∼3-GHz and ∼20-GHz sinusoidal phase modulation (PM) signals applied [19]. The modulation depth of the two modulation frequencies is 1.8π and 0.7π, respectively. A broadband regenerative amplifier is used to support the broadband amplifier system and suppress the FM-to-AM conversion resulting from gain narrowing in the high-gain regenerative amplifier [20]. The BSM includes a 10-times beam expander (BX10), a 13 mm × 13 mm precompensated soft edge aperture (AP), and a spatial light modulator (SLM), which can precisely control the near field of the entire system. The SLM is an optically addressed liquid crystal spatial light modulator (OASLM), that was independently developed by our team [21]. The output laser pulse from the regenerative amplifier is a fundamental mode Gaussian pulse with a FWHM (Full Width at Half Maximum) diameter of 3 mm. After the output, the beams are expanded and injected into the BSM, which is used to control near field profile and the softening factor of the beam edge, the transmission of the BSM is approximately 30%. The beam aperture satisfies the requirements for the subsequent amplification of the beamline. After beam shaping, an approximately 10 mJ/5 ns laser pulse is injected into the downstream laser amplifier. Therefore, the front-end seeder and the regenerative amplifier system can accurately control the temporal, frequency and spatial domains of the laser beam to satisfy the requirements of the high-power laser facility.
Fig. 1. Schematic diagram of the entire system: BX10, ten times beam expander; SLM, spatial light modulator; AP, soft edge aperture; PBS, polarizing beam splitter; HWP, half-wave plate; TFP, thin-film polarizer; FR, Faraday rotator; PC, Pockels cell electro-optic switch; L1-L4, flat convex lens with focal length of 1 m; AMP, laser gain module; CSF1-CSF2, M1-M11, 45° or 0° high reflectivity mirrors.
The beam output from the regenerative laser amplifier was spatial shaped and injected into the MPA. The detailed structure of the multipass amplifier is shown in Fig. 1. The amplifier is a polarization multiplexing eight-pass amplifier controlled by a Pockels cell electro-optic switch. The MPA is a relay-imaged off-axis system in which the AP is used as the initial image relay plane, and the laser head and the end mirror are set at the image plane. Two sets of image relay of vacuum spatial filters (CSF1 and CSF2) were used in the subsequent amplifier cavity to realize image-relay amplification. The focal lengths of L1∼L4 in CSF1 and CSF2 were 1 m, and lenses L5 and L6 were used to image relay the output beam to the main amplifier in the laser facility. The pinhole of CSF1 is a two-circle-overlapping hole that is used to achieve off-axis amplification. The beam #1, #3, #5, #7 pass the center of circle one, and the beam #2, #4, #6, #8 pass the center of circle two. The relay imaging system maintains the near field beam quality by decreasing the Fresnel diffraction. Thus this method avoided optical elements damage by near field modulation.
Multipass amplification of the laser pulse was realized by using the first Pockels cell electro-optic switch (PC1), with the second PC used to improve the output pulse signal to noise ratio. Upon injecting the laser pulse into the MPA, PC1 was switched off, allowing the laser pulse (S polarization) to enter the MPA through TFP4 after traversing TFP2 and being reflected by TFP3. Subsequently, the laser pulse was amplified by four times in the laser cavity terminated by M7 and M8, with FR2 facilitating the translation of S polarization to P polarization (or vice versa) after every two passes. Subsequent to the four-fold-amplification of the laser pulse (S polarization), it was reflected by TFP4 and TFP3. At this juncture, PC1 was switched; the polarization remained constant in this pass and was reflected by the end mirror M10. Following this, the laser pulse was injected into the cavity again and amplified another four times. After the laser pulse passed PC1 a third time, PC1 was switched off, enabling the eight-times-amplified laser pulse to be emitted from the laser cavity. Finally, after passing thought the isolator, the laser pulse was injected into the downstream main amplifier.
3. Results and discussion
3.1 Laser head performance
The laser head (AMP) contains a LD-pumped circular rod gain medium (N31 Nd:glass), which is actively cooled by flowing water. To obtain uniform gain distribution, the LD is set as ring pumping around the circular rod. The Nd3+ doping concentration is 1.0 wt. %. The maximum peak pump power is 160 kW, and the pump pulse width is 500 µs, with the operation repetition rate of 1 Hz. To achieve a uniform distribution of storage energy in the laser rod, various parameters of the laser head, such as the diameter of the laser gain medium, the diameter of the pump diode, and the thickness of water flow, were systematically simulated and optimized using the ray tracing method. In high-power repetition-rate laser amplifier systems, thermal effects pose a major problem that can cause serious deterioration of the laser beam quality [22,23]. Thermal lensing, thermally induced birefringence, and thermal depolarization, are consequences of the thermal effects that occurring in the gain medium. Therefore, it’s necessary to evaluate the gain and thermal performance of the laser head.
To evaluate the gain performances of the laser heads, the gain distribution at different pump powers were measured using methods outlined in [24]. As shown in Fig. 2, the small-signal gain versus pump power of the LD-pumped laser head was tested. The inset of Fig. 2 (a) shows the two-dimensional (2D) single-pass small-signal gain distribution at a pump power of 160 kW, where the average small-signal gain G0 is 4.25, with nearly identical gain values observed at both the center and the edge. Figure 2(a) shows the small-signal gain and stored energy versus the pump power. The gain increases almost linearly with the pump power, indicating that the gain in the laser head is not constrained by the ASE effect, which typically consumes the stored energy in a large-aperture slab laser gain medium [5].
Fig. 2. (a) Small-signal gain and stored energy versus pump power, inset: two-dimensional single-pass small-signal gain distribution at a pump power of 160 kW and a repetition rate of 1 Hz, and (b) wavefront aberration of the LD-pumped laser head at a pump power of 160 kW and a repetition rate of 1 Hz.
To evaluate the thermal performance of the laser head, an SID4 wavefront sensor to measure the thermal wavefront aberration at a pump power of 160 kW and a repetition rate of 1 Hz. The probing beam was a horizontal-polarized low-energy 1053 nm laser pulse from the regenerative amplifier. This beam underwent expansion to cover the total aperture of laser rod and passed through the laser head during the pumping process. The resulting laser pulse was collected by the wavefront sensor. The equipment was synced via a digital delay generator. The wavefront aberration distribution is depicted in Fig. 2(b). Notably, the main part of the thermal wavefront in the laser rod was almost spherical thermal lens. The polarized beam would undergo different optical delay at the radial and tangential component because of the photoelastic effect at a thermal laser rod pumped by LD. This causes the wavefront aberration not to be perfectly symmetrical. The PV of the entire cross section reached approximately 4.7 λ. The thermally induced wavefront aberration was composed of three parts: temperature-dependent variation, stress-dependent variation, and end face deformation. The first two components accounted for the most of the thermal lensing, with the third component (caused due to rod face deformation) contributing less than 6% [22,25]. Thermal lensing causes the laser beam focus at unexpected location, potentially damaging the optical elements. In this amplifier, thermal lensing at the fixed pump power was compensated for by adjusting the distance between L3 and L4 in CSF2. The stress-dependent variation would cause thermal stress birefringence and thermal depolarization. The mitigation of thermal depolarization was achieved through the utilization of FR2, end mirror M7, and CSF2. This involved imaging the AMP onto itself after the second pass while rotating the polarization by 90° [23,26]. As discussed in Section 3.3, the efficacy of this method was demonstrated through the examination of the output near-field.
3.2 Laser amplifier ability
To evaluate the laser amplifier ability, the output energy and stability were measured at the pump power of 160 kW. Figure 3(a) shows the output energy versus input energy for different passes with each marked accordingly. The amplified output energies for two-passes, four-passes and eight-passes are presented. The Frantz–Nodvik equation was employed to simulate and optimize the pulse amplification process, with the simulation results depicted as a solid curve in Fig. 3(a). At an input energy of 1.82 mJ and a pulse width of 5 ns, the output energy reached 3.3 J at the eighth pass and 0.125 J at the fourth pass. The static single pass transmittance of the laser cavity is approximately 81%. At the maximum output energy of 3.3 J during the eight passes, the total net gain was 1800 times. At an output energy of 0.125 J on the fourth pass, the gain factor was 68.8 times. For a high-energy laser amplifier, the energy extraction efficiency $\eta $ is defined as $\eta = {{({E_{\textrm{out}}} - {E_{\textrm{in}}})} / {{E_{\textrm{st}}}}}$, where ${E_{\textrm{out}}}$ and ${E_{\textrm{in}}}$ are the output energy and input energy, respectively. In addition, the overall stored energy in the laser head is ${E_{\textrm{st}}} = \ln ({G_0}){E_s}{A_{\textrm{beam}}}$, where ${G_0}$ is the single-pass small-signal gain, ${A_{\textrm{beam}}}$ is the laser beam cross section.${E_s}$ is the saturated energy density. Moreover, ${E_\textrm{s}} = h\nu /\gamma \sigma \textrm{ = }{4.967^{}}\textrm{J/c}{\textrm{m}^\textrm{2}}$, where $\gamma = 1$ and $\sigma = 3.8 \times {10^{ - 20}}\textrm{ c}{\textrm{m}^\textrm{2}}$ for N31 Nd:glass. The stored energy of the laser head was 20.5 J. The full aperture extraction efficiency of the stored energy was 16%.
Fig. 3. (a) Output energy versus input energy at different passes with a pump power of 160 kW, where the line is the simulation result. (b) The amplified output energy stability at maximum output energy and a repetition rate of 1 Hz.
The energy stability of a preamplifier affects the operational success rate and power balance in ICF facilities. To increasing the energy stability, a high-rigidity and high-strength laser optical box were deployed and the laser amplifier was approximately operated in the saturated regime which reduced the sensitivity to fluctuations in the injected energy. Figure 3(b) shows the amplified output energy stability at a maximum output energy of 3.3 J and a repetition rate of 1 Hz. Based on the highly stable regenerative laser amplifier, where the output energy stability is <0.5%RMS, the output energy stability of the MPA is excellent, with 1.08%RMS at 4 h.
3.3 Programmable spatial-shaping capability and beam quality
Considerable efforts have been dedicated to maintain good beam quality, including all image-relay laser cavity, compensation for thermal depolarization caused by the thermal effect of the laser head, and the arbitrary shaping ability based on the OASLM. The first two methods have been presented above. The arbitrary programmable spatial-shaping capability is based on the OASLM and programmable shaping algorithm. The OASLM can be used as precision beam-shaping device in ICF laser facilities, such as those used in the NIF and Omega laser facilities [27,28]. Using this technique, arbitrarily-defined masks with smooth edges and the desired blocker shape can be realized.
The amplified output near field at the eight pass was measured with CCD (pixel size 13 µm × 13 µm, number of active pixels 1024 × 1024, imaging area 13.3 mm × 13.3 mm), as shown in Fig. 4. Figures 4(a) and (b) display the output amplified near-field profiles without and with spatial shaping, respectively. Prior to spatial shaping, the near field was severely affected by the 2D gain distribution of the rod laser head, and the beam intensity was higher at the center and the four corners. This is attributed to the amplification of a square beam in the circular rod laser head, which has a radially dependent gain distribution. This non-uniformity of the near field would damage the optical element and limit the maximum output energy. Thus, near-field spatial shaping with the OASLM was deployed, and the beam quality of the near field was improved significantly, as shown in Fig. 4(b). The near field intensity modulation (FM), defined as the ratio of maximal to average optical intensities inside the beam aperture, was FM = 1.19 after eight passes from the laser amplifier. After the amplified laser pulse was output from the MPA, the laser beam was expanded by a vacuum spatial filter and shaped by a second soft-edge aperture to meet the beam aperture of the main amplifier. The resultant output near-field spatial profile after shaped is illustrated in Fig. 4(c), wherein the beam edge becomes steeper, which is helpful in improving the energy extraction efficiencies in subsequent laser amplifiers in laser facilities.
Fig. 4. Amplified output near-field spatial profile without (a) and with (b) spatial shaping, and (c) the output near-field spatial profile after shaping by the second soft-edge aperture at the output of MPA after beam expanding.
At the output of the laser amplifier, a thin lens with a focal length of 1 m was employed for measuring the far-field profile. The far-field profile and cumulative energy are shown in Fig. 5. The figure shows that the output amplified laser beam delivers nearly diffraction-limited performance without the need for complex wavefront aberration correction equipment. Over 86.1% of the energy was in the range of two times the diffraction limit (TDL) while 95.2% was in the range of 3TDL.
Fig. 5. (a) Amplified output far-field profile and (b) cumulative energy of far-field profile versus diffraction limit.
3.4 Temporal waveform and the FM-to-AM conversion control
In high-power laser facilities, the temporal waveform is crucial to the control of damage to optical elements and time-power curve. In addition, the symmetry in target compression would be affected by the temporal waveform profile. For the preamplifier in laser facilities, the constraint regulation minimizes the square pulse distortion, maintains the waveform stability, and controls the FM-to-AM conversion [10,29]. The first two constraints were guaranteed by optimizing reasonable parameters in the design process. The main reason the preamplifier causes the FM-to-AM conversion is the gain narrowing in the regenerative amplifier and MPA, which features the largest gain in the entire laser facility. In addition, experimental results have demonstrated that the wavelength-detuning of the laser source (±0.23 nm UV) mitigated cross-beam energy transfer (CBET) in inertial confinement implosions [30]. Wavelength-detuning would further enhance the temporal amplitude modulation [31]. Thus, a broadband preamplifier was used to support wavelength-detuning and the FM-to-AM control. In this study, two stages spectral controllers were designed to compensate for this gain narrowing effect. The first spectral controller was inserted into the regenerative amplifier cavity and the temporal modulation was greatly reduced [20,32]. The second spectral controller was inserted into the BSM module after amplification by the regenerative amplifier. The second spectral controller was composed of a birefringent quartz crystal (BRF) between two polarizing beam splitters. The spectral transmittance of the BRF can be adjusted using the pitch angle $\theta $, and rotation angle $\phi $. The FM-to-AM conversion in this laser facility was significantly reduced using this method, the experimental results are shown in Fig. 6 and Fig. 7.
Fig. 6. (a) Output amplified temporal waveform of MPA without shaping, (b) the temporal waveform shaped by arbitrary waveform generator (AWG) at output of MPA measured with 30 GHz high-speed oscillator.
Fig. 7. Temporal waveform at the output of main amplifier with different central wavelengths of 1052.8 nm (a), 1053.3 nm (b), and 1053.9 nm (c).
When a square pulse waveform from the frond-end seeder was injected to preamplifier, the temporal pulse waveforms at the output were measured using the Tektronix DPO7064B oscilloscope with a bandwidth of 6 GHz and a high-speed photodetector with a bandwidth of 5 GHz (Thorlab, DET08CFC). Figure 6(a) shows the output amplified temporal waveform before compensation. The square pulse distortion (SPD) was defined to evaluate temporal distortion induced by the MPA as the ratio of the amplitude of leading edge to the trailing edge of the output temporal waveform, when a square pulse was injected into the laser amplifier. The square pulse distortion of the output amplified temporal waveform of MPA was 2.7:1. The temporal waveform was precisely shaped based on the arbitrary shaping ability of the front-end seeder. When the phase modulators (∼3-GHz and ∼20-GHz, spectral bandwidth of ∼0.3 nm) in the seeder were operated, the output temporal waveform after shaped is shown in Fig. 6(b), with a perfect square waveform. In addition, to evaluate the temporal waveform amplitude modulation depth induced by FM-to-AM conversion of the preamplifier, the output temporal waveform was measured using a high speed oscilloscope (Agilent DSO93004 L, 30 GHz) and a high-speed pin tube (Newport, 1014, 45 GHz), as shown in the Fig. 6(b). The temporal waveform modulation depth $\alpha $ is defined to describe the temporal waveform distortion as [31]
Currently, the advanced preamplifier was assembled into the laser prototype beamline of the SG-II upgrade facility [33]. The temporal modulation depth at the output of the main amplifier, whose output energy was more than 6 kJ, was measured using a high-speed oscilloscope (Agilent DSO93004 L, 30 GHz) and a high-speed pin tube (Newport, ET3600, 22 GHz). The results are shown in Fig. 8. Three different injection center wavelengths were used and measured. Figure 7(a)-(c) show the results at center wavelengths of 1052.8 nm, 1053.3 nm, and 1053.9 nm with a bandwidth of ∼0.3 nm (∼3-GHz and ∼20-GHz), which indicate a 1.1 nm detuning of center wavelength. The temporal waveform modulation depths were 6.0%, 9.1%, and 7.3% respectively. The experimental results indicate that the FM-to-AM conversion of the temporal waveform was effectively suppressed, preventing potential damage to the large-aperture optical elements in the main amplifier.
4. Conclusion
In this work, an LD-pumped eight-pass Nd: glass laser amplifier with high-gain and 1 Hz repetition rate was proposed and experimentally demonstrated. The amplifier was designed as a relay-imaged off-axis system to achieve excellent beam quality, incorporating thermal lens and depolarization compensation. The performance of the LD-pumped laser head was detailed and the laser amplifier system demonstrated an output energy of up to 3.3 J/1 Hz/5 ns at the central wavelength of 1053.3 nm with 1.82 mJ injected. The total gain reached 1800 times. The near-field modulation of the amplified output beam below 1.2, the far-field focusing ability of the beam was 90% at 2.9 TDL, and the temporal modulation depth of the entire system remained under 10%, fulfilling preamplifier system requirements for large-scale laser facilities. The system would be applied to the preamplifier system of the SG-II upgrade laser facility, contributing to improved operational efficiency of the laser facility. Additionally, this amplifier can also be extended to other high-energy amplification systems to support high-energy picosecond petawatt laser facilities.
Funding
Strategic Priority Research Program of the Chinese Academy of Sciences (XDA25020307); Program of Shanghai Academic Research Leader (19XD1404000).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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. R. Betti and O. A. Hurricane, “Inertial-confinement fusion with lasers,” Nat. Phys. 12(5), 435–448 (2016). [CrossRef]
2. T. Tao, G. Zheng, Q. Jia, et al., “Laser pulse shape designer for direct-drive inertial confinement fusion implosions,” High Power Laser Sci. Eng. 11, e41 (2023). [CrossRef]
3. M. L. Spaeth, K. Manes, D. Kalantar, et al., “Description of the NIF Laser,” Fusion Sci. Technol. 69(1), 25–145 (2016). [CrossRef]
4. C. N. Danson, C. Haefner, J. Bromage, et al., “Petawatt and exawatt class lasers worldwide,” High Power Laser Sci. Eng. 7, e54 (2019). [CrossRef]
5. P. Mason, M. Divoký, K. Ertel, et al., “Kilowatt average power 100J-level diode pumped solid state laser,” Optica 4(4), 438–439 (2017). [CrossRef]
6. F. Lureau, G. Matras, O. Chalus, et al., “High-energy hybrid femtosecond laser system demonstrating 2 × 10 PW capability,” High Power Laser Sci. Eng. 8, e43 (2020). [CrossRef]
7. J. E. Heebner, R. L. A. Jr, D. A. Alessi, et al., “Injection laser system for Advanced Radiographic Capability using chirped pulse amplification on the National Ignition Facility,” Appl. Opt. 58(31), 8501–8510 (2019). [CrossRef]
8. V. Bagnoud, M. J. Guardalben, J. Puth, et al., “High-energy, high-average-power laser with Nd: YLF rods corrected by magnetorheological finishing,” Appl. Opt. 44(2), 282–288 (2005). [CrossRef]
9. B. N. Hoffman, N. Savidis, and S. G. Demos, “Monitoring and characterization of particle contamination in the pulse compression chamber of the OMEGA EP laser system,” High Power Laser Sci. Eng. 11, e39 (2023). [CrossRef]
10. C. Bouyer, R. Parreault, N. Roquin, et al., “Impact of temporal modulations on laser-induced damage of fused silica at 351 nm,” High Power Laser Sci. Eng. 11, e15 (2023). [CrossRef]
11. C. Bernerd, B. Da Costa Fernandes, E. Boursier, et al., “Thermal lens in diode-pumped square-section rods of Nd-doped phosphate glass and 0.5%Nd:5%Lu:CaF2 crystal: simulations and experiments,” Appl. Opt. 59(31), 9905–9911 (2020). [CrossRef]
12. X. Ribeyre, L. Videau, A. Migus, et al., “Nd: glass diode-pumped regenerative amplifier, multimillijoule short-pulse chirped-pulse-amplifier laser,” Opt. Lett. 28(15), 1374–1376 (2003). [CrossRef]
13. J. Luce, S. Montant, J. M. Sajer, et al., “Nonlinear FM-AM conversion due to stimulated Brillouin scattering,” Opt. Express 27(5), 7354–7364 (2019). [CrossRef]
14. K. Yao, X. Xie, J. Tang, et al., “Diode-side-pumped joule-level square-rod Nd:glass amplifier with 1 Hz repetition rate and ultrahigh gain,” Opt. Express 27(23), 32912–32923 (2019). [CrossRef]
15. T. Hamoudi, H. Chesneau, T. Dubé, et al., “Comparison of simulation and experimental characterization of a 4-pass diode-pumped 4-active-mirrors 1053 nm laser amplifier,” EPJ Web Conf. 266, 13015 (2022). [CrossRef]
16. C. Wang, H. Wei, J. Wang, et al., “1 J, 1 Hz lamp-pumped high-gain Nd: phosphate glass laser amplifier,” Chin. Opt. Lett. 15, 011401 (2017). [CrossRef]
17. J. Guo, J. Wang, H. Wei, et al., “High-power, Joule-class, temporally shaped multi-pass ring laser amplifier with two Nd:glass laser heads,” High Power Laser Sci. Eng. 7, e8 (2019). [CrossRef]
18. S. Ji, W. Huang, J. Wang, et al., “LD end-pumped joule-level square-rod Nd:glass laser amplifier with high efficiency,” Opt. Laser Technol. 135, 106634 (2021). [CrossRef]
19. Z. Qiao, X. Wang, W. Fan, et al., “Demonstration of a high-energy, narrow-bandwidth, and temporally shaped fiber regenerative amplifier,” Opt. Lett. 40(18), 4214–4217 (2015). [CrossRef]
20. J. Guo, J. Wang, X. Wang, et al., “High-energy broadband Nd: Glass regenerative amplifier with coated birefringent filter for the high-power laser facilities,” Opt. Commun. 509, 127874 (2022). [CrossRef]
21. D. Huang, W. Fan, X. Li, et al., “Performance of an optically addressed liquid crystal light valve and its application in optics damage protection,” Chin. Opt. Lett. 11, 072301 (2013). [CrossRef]
22. W. Koechner, Solid-state Laser Engineering (Springer, 1999), Chap. 7.
23. A. A. Kuzmin, E. A. Khazanov, O. V. Kulagin, et al., “Neodymium glass laser with a phase conjugate mirror producing 220 J pulses at 0.02 Hz repetition rate,” Opt. Express 22(17), 20842–20855 (2014). [CrossRef]
24. A. A. Shaykin, A. P. Fokin, A. A. Soloviev, et al., “Laser amplifier based on a neodymium glass rod 150 mm in diameter,” Quantum Electron. 44(5), 426–430 (2014). [CrossRef]
25. J. Foster and L. Osterink, “Thermal effects in a Nd: YAG laser,” J Appl. Phys. 41(9), 3656–3663 (1970). [CrossRef]
26. Q. Lü, N. Kugler, H. Weber, et al., “A novel approach for compensation of birefringence in cylindrical Nd: YAG rods,” Opt. Quantum Electron. 28(1), 57–69 (1996). [CrossRef]
27. H. John, B. Michael, M. Phil, et al., “A programmable beam shaping system for tailoring the profile of high fluence laser beams,” Proc. SPIE 7842, 78421C (2010). [CrossRef]
28. M. Barczys, S. W. Bahk, M. Spilatro, et al., “Deployment of a spatial light modulator-based beam-shaping system on the OMEGA EP laser,” Proc. SPIE 8602, 86020F (2013). [CrossRef]
29. W. Fan, Y. Jiang, J. Wang, et al., “Progress of the injection laser system of SG-II,” High Power Laser Sci. Eng. 6, 27 (2018). [CrossRef]
30. J. A. Marozas, M. Hohenberger, M. J. Rosenberg, et al., “Wavelength-detuning cross-beam energy transfer mitigation scheme for direct drive: Modeling and evidence from National Ignition Facility implosions,” Phys. Plasmas 25(5), 056314 (2018). [CrossRef]
31. S. Hocquet, D. Penninckx, E. Bordenave, et al., “FM-to-AM conversion in high-power lasers,” Appl. Opt. 47(18), 3338–3349 (2008). [CrossRef]
32. J. Guo, J. Wang, X. Pan, et al., “Suppression of FM-to-AM conversion in a broadband Nd: glass regenerative amplifier with an intracavity birefringent filter,” Appl. Opt. 58(5), 1261–1270 (2019). [CrossRef]
33. J. Zhu, J. Zhu, X. Li, et al., “Status and development of high-power laser facilities at the NLHPLP,” High Power Laser Sci. Eng. 6, e55 (2018). [CrossRef]
