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Abstract
Stimulated Brillouin scattering (SBS) is a non-linear process which has the capacity to improve the beam quality and pulse characteristics of laser beams. In this paper, we theoretically and experimentally study the process of SBS in fused silica. In particular, we examine the energy reflection and pulse compression of input laser pulses as functions of focus position, pump energy and beam diameter. We utilized coupled wave equations and a distributed noise model to simulate the reflected energy and time waveform under different gain parameters. An experimental system is constructed and used to qualify the numerical simulations. The results reveal that the threshold for the SBS process and the energy reflectivity significantly change with laser focus position under the same pump and focusing parameters. Ultimately, the gain characteristics of the SBS material is the primary factor that influences the SBS output. This work presented here offers insight into the operation of short-length solid-state SBS lasers and serves as a basis for the design and optimization of such systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Stimulated Brillouin scattering (SBS) [1] is a third-order non-linear process which is well known for its applications in pulse compression [2–5], phase conjugation [6–9], linewidth narrowing [10–13], and beam shaping [14,15]. It has been used in laser systems applied to biomechanical imaging, laser processing, lidar and other fields [16–18]. SBS occurs via the interaction between strong incident light waves and elastic acoustic waves within media including gases, solids, liquids and plasmas. The refractive index and speed of sound characteristics of various media influence the SBS process and hence the characteristics of SBS-laser outputs [19–22]. Gases have been extensively studied as an SBS media as increasing the pressure of gases can be a highly effective method of achieving higher steady-state SBS gain [20]. Gases also have high breakdown thresholds, making them suitable for high pulse energy SBS applications. However, the long phonon lifetime and the complexity and cost of the SBS gas cell limit its range of applications [6,23]. Liquids have also been shown to exhibit excellent SBS performance and have the advantages of low cost and simple media cell containment [24]. As a result, liquids are perhaps the most widely applied SBS media at this point in time [4,25,26]. However, in recent years there has been a push from the industry for the development of high repetition rate and on-chip lasers for which the above two SBS media types are largely incompatible [8,9,27–29].
Solid-state media have shown great potential in high repetition rate SBS systems, exhibiting characteristics such as high gain coefficient, no thermal convection, high compatibility with a range of systems, and a highly stable structure [21,28]. SBS has been observed in solid-state media including diamond, As2S3 and fused silica, and the media list is ever-expanding [21,30–32]. Among these SBS-active media, fused silica has become a preferred material owing to its high damage threshold and long length. According to scaling laws, the damage threshold of fused silica can reach up to 120 J/cm2.
Some of the first investigations exploring the SBS characteristics of fused silica were performed by H. Yoshida et. al. [33] wherein they performed a phase conjugation experiment using a laser with a pulse duration of 16 ns, a spot diameter of 25 mm, and a pump energy of 2.3 J. Following this work, H. Yoshida et. al. [34] used two right-angle prisms and fused silica to form a compact SBS-based pulse compressor. In that work, they were able to compress an incident laser pulse by order of magnitude. G. Marcus et. al. [35] used a multi-stage compression-amplification structure to compress a 2.5 ns pulse to 175 ps. These early results demonstrated that the pulse compression characteristics using SBS in solid media were similar to that in liquids. Further investigations into the application of fused silica as an SBS medium include that of Z. Zhao et. al. [36], where a large-aperture fused silica tapered fiber phase conjugate mirror with a maximum SBS reflectivity of 70% at a repetition rate of 1 kHz was demonstrated. H. Wang et. al. [28] was also able to demonstrate sub-nanosecond output with a repetition rate of 100-1000 Hz via SBS pulse compression in fused silica.
Studies on fused silica show that the solid media benefits high repetition rate SBS experiments due to its high stability, high thermal conductivity, and easy-to-manipulate structure. This provides an opportunity for its application in master oscillator power amplifier laser systems with a high repetition rate. At short to media lengths (in the range of millimeters to centimeters), the output characteristics of laser pumped SBS media can change dramatically with laser focus parameters. Previous numerical simulations and experiments on SBS systems that have attempted to examine and predict changes to the output have only examined the changes in response to a single variable [37]. Systems that can model the output characteristics as functions of multiple variables simultaneously have yet to be developed.
This paper seeks to address this knowledge base gap by providing a theoretical and experimental study of the SBS output parameters in response to changes to pump energy, beam diameter, focal length and focal position, with fused silica as the SBS medium. The results presented in this work highlight the impact different focusing parameters can have on the SBS output, notably the change in gain intensity. This characteristic is theoretically modeled and supported by our experiments. Also investigated in this work are the changes which occur to the reflected laser pulse energy and pulse compression. This far more comprehensive study of the effect of gain on the SBS process has great value for the broader development of SBS systems based on solid media.
2. Simulation and analysis
SBS is a three-wave coupling process involving a pump field (EP), an acoustic field (ρ) and a Stokes field (ES). The interaction between the three fields in the SBS process can be described using wave equations [38]
The coupled wave equations were modified and made appropriate for focusing geometries. This is achieved by solving the coupled wave equations and substituting the expression for light intensity as follows
The value of GB is primarily affected by the focal length (F) and the beam diameter (D). The strength of SBS is also closely related to the power of the pump laser. The system gain G of the SBS system is hence
where P is the peak power of the pump laser, ${P = }{{E}_\textrm{P}}{\; }{ / }{\; }{{t}_\textrm{P}}$, EP is the energy of the pump laser, and tP is the pump pulse width. In the case of a fixed pulse width, P is mainly affected by the pump energy.By numerically solving coupled wave Eqs. (4)–(6), we can model the SBS process after the laser field is injected into the SBS medium. Our algorithm uses an implicit finite differencing in time and a backward differencing scheme in space [39,40]. In order to simply the calculation, dimensionless parameters K, R and Q are introduced. Here, K = g·c·ωB·Δt2/(H·4n), R = c·Δt/(n·Δz), Q=α·R·Δz/2, P1 = AP·AS·e^(iωB-ΓB/2 + iH)·Δt), and P2 = AP·AS·e^(iωB-ΓB/2-iH)·Δt), where H=√(ωB2-ΓB2/4). The discretized form of the equations then become
In the simulation, the pump laser waveform is assumed to be Gaussian, and the pump laser has a wavelength of 1064 nm, and a pulse width of 10 ns. The SBS medium is fused silica (JGS1) with the following parameters: refractive index of 1.45, density of 2.2 g/cm3, phonon lifetime of 0.98 ns, Brillouin frequency shift of 16.3 GHz, and the steady-state SBS gain coefficient of 2.9 cm/GW [22]. The absorption coefficient of the fused silica we used in the experiment is 0.001 m-1.
The effects of pump energy, beam diameter and focal length on the output characteristics of the SBS system were analyzed by examining the energy reflectivity and pulse compression ratio at different focus positions. Since the system gain G is a function of multiple parameters, analysis over multiple variables was used to accurately analyze the impacts of changes to the system gain G which thereby impacts the SBS system outputs. From this analysis we were able to determine the dominant factors which impact the SBS process. Shown in Figs. 1(a) - (c) are contour maps of the SBS energy reflectivity; here, the energy reflectivity is plotted as a function of pump energy, beam diameter, focal length and beam focus position, respectively. In the numerical simulation, boundary conditions include pump energy EP =20 mJ, beam diameter D = 3 mm, and focal length F = 70 cm. The results show that higher pump energy, larger incident beam diameter and shorter focusing lens lead to a higher energy reflectivity. In each plot, the energy reflectivity displays a symmetric character as a function of focus position. Maximum energy reflectivities of 75% in Fig. 1(a), 46% in Fig. 1(b) and 44% in Fig. 1(c) can be obtained at the center of the gain medium, respectively. In order to understand the gain characteristics of the system, discrete positions P1, P2 and P3 on the plot of Fig. 1(c) were chosen. P1 and P2 correspond to EP =20 mJ, D = 3 mm, F = 20 cm; P3 corresponds to EP =20 mJ, D = 3 mm, F = 70 cm. These discrete positions were used to generate plots of the gain g as functions of focus position. In analyzing the plot of Fig. 1(d), it is apparent that the way in which g varies with focus position is highly dependent on the focal length. For this set of parameters, the system achieves a higher g value for shorter focal lengths, with the peak of g coinciding with the focus position. In addition, discrete lines (L1 and L2) have been chosen from the plot of Fig. 1(c). L1 and L2 reflect GB as functions of focus position and focal length, respectively. Figure 1(e) shows that for a fixed focal length, GB maintains a peak value across a broad range of focus positions. The plot of Fig. 1(f) shows that GB decreases as the focal length increases for a fixed focus position.
Fig. 1. (a) - (c) plots of SBS energy reflectivity as a function of pump energy, beam diameter and focal length at different focus positions; boundary conditions: EP =20 mJ, D = 3 mm, F = 70 cm. (d) Plot showing the distribution of g in the medium when the focus is at points P1, P2 and P3 shown in Fig. 1(c). (e) (f) Plots showing variation in system gain GB when the focal point is located on the white dotted lines L1 and L2 shown in Fig. 1(c).
Whether the peak power of the pump (P) increases or total gain intensity GB increases, as the SBS process enters the gain saturation state [9], the rate of increase of the energy reflectivity gradually decreases. Suppose the SBS threshold point is set to reach 1% energy reflectivity. In the simulation, the SBS threshold is always reached when G = 175 GHz, no matter how the conditions change. Therefore, under the condition of constant optical power, the total gain intensity GB of the medium can be increased by reducing the focal length or by increasing the spot radius, thereby reducing the SBS threshold and improving the energy reflectivity.
Shown in Figs. 2(a) - (c) are contour maps of the SBS output pulse compression ratio as functions of pump energy, beam diameter and focal length at different focusing positions. Here, the same boundary conditions EP =20 mJ, D = 3 mm, and F = 70 cm are used in the numerical simulation. The highest pulse compression ratios 2.68, 3.12 and 3.14 can be obtained, respectively. Individual plots of the output Stokes field pulse shapes are shown in Figs. 2(d) - (f) for discrete positions P1, P2 and P3 as outlined in Fig. 2(c). Unlike the more “regular” trend shown by the contour plots of energy reflectivity, the contour plots of the pulse compression ratio show a high degree of irregularity. This is because the SBS output/Stokes pulse width is also affected by the interaction length. In Fig. 2(a), the compression ratio generally increases with interaction length. As seen in Figs. 2(a) - (c), when the focus is located in the front 3/4 of the medium, the pulse compression trend is similar to the energy reflectivity trend, mainly being affected by GB. When the focal point is located at the rear quarter of the medium, the output pulse widths all show the effect of being first compressed and then broadened. On the one hand, this is due to the increase in the interaction length, and on the other hand, due to the variation of GB [4]. In Figs. 2(d) and (f), it can be seen that when GB is fixed, the long interaction length amplifies the leading edge of the Stokes waveform, thereby compressing the pulse width.
Fig. 2. (a)-(c) Plots showing the change in SBS output pulse compression as a function of pump energy, beam diameter and focal length at different focus positions; boundary conditions: EP =20 mJ, D = 3 mm, F = 70 cm. (d)-(f) are plots of the pulse characteristics of the Stokes output at positions P1, P2, P3 as indicated in Fig. 2(c).
From this theoretical investigation, it is clear that the pump laser intensity and the total gain intensity in the medium must be optimized in order to achieve high energy reflectivity or pulse width compression ratio when using focusing geometries in SBS systems.
3. Experimental setup
Figure 3 shows a schematic diagram of the experimental system where the pump beam was focused into the SBS medium using a lens. The entire experimental setup comprised the pump laser, optical isolation system, beam splitter, and SBS medium. A p-polarized, Q-switched Nd: YAG laser with a pulse duration of 10 ns was used as the pump source [41]. An optical isolator was used to prevent light propagating back into the pump laser. Fused silica was the SBS medium and had a length of 20 cm. Due to damage threshold considerations, the ends of the fused silica were optically polished and uncoated. The system was characterized using a Fabry-Perot (F-P) interferometer, laser beam profilers, energy meter and photodiode.
When the power density of the pump beam reached the threshold for the SBS process, a backward-propagating Stokes light was generated due to the electrostriction effect. Due to the phase-conjugation property of SBS, the Stokes light was circularly polarized. This polarization state became s-polarized after being transmitted through the quarter-wave plate and was then reflected out of the beam path towards the measurement system by the polarizer. In the experiment, a 30 cm focal length lens was used and the pump energy was kept at 20 mJ. The fused silica was mounted on a translation stage and this enabled its position to be varied and hence the position of the laser focal point within the bulk of the medium.
4. Experimental results and discussion
A homemade F-P interferometer (an F-P etalon in combination with a CMOS beam profiler) with a free spectral range (FSR) of 34.47 ± 0.24 GHz was used to measure the SBS frequency shift. The F-P interferometer has a spectral resolution of 1 MHz, which is limited by the size of the CMOS pixel size [42,43]. The SBS frequency shift obtained by the formula ${{\omega }_\textrm{S}} = 2n{\nu }{{\omega }_{{P}\; }}{ / }\; {c}$ was 16.335 GHz, and the average SBS frequency shift obtained by collecting 30 interferograms from the experimental system was 16.490 ± 0.018 GHz. The experimentally determined value was hence within the error range of the theoretical value. Plotted in Fig. 4 (b1) is the experimentally obtained pulse energy and pulse widths as functions of focus position within the fused silica (data points with error bars). Also shown in the plot are the theoretically determined values. It can be seen that the experimental results correlate well with the theoretical predictions, and the energy and pulse width trends are consistent with the previous analysis. The lower gain intensity at both ends of the medium will result in a concomitant decrease in the output energy [44]. Overall, the compression ratio of pulse width is proportional to the interaction length. However, when the focus position is close to the two ends of the fused silica, the decrease of the energy reflectivity leads to an anomalous change in the pulse width. Even at the focus position of 0 cm, there is still a small gain intensity. The plots of Figs. 4(b2) and (b3) show the pulse waveforms of both the incident pump pulse and the resultant Stokes pulse. The slight artifact of the waveform shown in Fig. 4(b2) is the inherent output characteristic of the self-made passively Q-switched pump source [41]. Here, the resultant Stokes pulse was shorter than that of the pump pulse (3.2 ns c.f. 9.7 ns), thus highlighting the pulse compression characteristics of the SBS process.
Fig. 4. Plots showing (a) the SBS frequency shift (inset: the interferogram of the pump and SBS fields, the calculation interval is the position of the red line in the inset); and (b1) plots of the output Stokes pulse energy and pulse widths at different focus positions. (b2) and (b3) show plots of the pulse characteristics of the incident pump pulse and the output Stokes pulse respectively at a focus position of 19 cm.
The spatial profile of the output Stokes light at different focus positions is shown in Fig. 5. The uniformity of the Stokes light was better than that of the pump laser, thus demonstrating the excellent beam clean-up properties of the SBS process. It was observed that the divergence angle of the pump laser after passing through the focal point within the fused silica was greater than the convergence angle when being focused. The implication of this was that for short interaction lengths, the position at which the SBS process occurred was further into the medium than the actual laser focal point. This manifested in changes to the spot size of the generated Stokes field as a function of the laser beam focus position and this is shown in Fig. 5(b).
Fig. 5. Plots of (a) the spatial profile of the pump field; and (b) the beam diameters of the generated Stokes field in the x and y directions, as a function of focal position (representative spatial profiles are shown inset).
5. Conclusions
In summary, this work examines the effect of gain characteristics on SBS generation and output. A theoretical model describing the SBS process under focused pumping was developed as applied to solid media. Using this model, we determined that the system gain G was the dominant factor influencing the energy reflectivity characteristics of the SBS process. The value of G is determined by pump energy, beam diameter, focal length and focal position. The experimental results show that the system gain G decreased when the focal point was close to the end face of the media, which led to an increased SBS threshold and a decrease in energy reflectivity. Furthermore, the interaction length was found to influence the pulse compression characteristics of the SBS process greatly. The results highlight that there is an optimal reflectivity that must be achieved in order to also achieve a high pulse width compression ratio and this value is dependent on the overall length of the SBS media. The experimental results in this work were found to be consistent with the theoretical simulations. We anticipate that the work presented here can be used effectively for the design and optimization of future SBS systems which utilize solid media and focusing geometries.
Funding
National Natural Science Foundation of China (61927815); Natural Science Foundation of Tianjin City (20JCZDJC00430); Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices (KF202201); Funds for Basic Scientific Research of Hebei University of Technology (JBKYTD2201).
Acknowledgments
Bin Chen acknowledges support from the Postgraduate Training Program for the Cross-discipline of Hebei University of Technology (HEBUT-Y-XKJC-2021101).
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. O. Mangir and R. Jones, “Time-resolved measurements of stimulated-Brillouin-scattering phase jumps,” Phys. Rev. Lett. 68(11), 1702–1705 (1992). [CrossRef]
2. D. T. Hon, “Pulse compression by stimulated Brillouin scattering,” Opt. Lett. 5(12), 516–518 (1980). [CrossRef]
3. C. Feng, X. Xu, and J.-C. Diels, “High-energy sub-phonon lifetime pulse compression by stimulated Brillouin scattering in liquids,” Opt. Express 25(11), 12421–12434 (2017). [CrossRef]
4. Z. Liu, R. Fan, D. Jin, T. Luo, S. Li, N. Li, S. Li, Y. Wang, and Z. Lu, “Quarter acoustic period pulse compression using stimulated Brillouin scattering in PF-5060,” Opt. Express 30(8), 12586–12595 (2022). [CrossRef]
5. C. Shi, Q. Sheng, S. Fu, S. Sun, J. Zhang, W. Shi, and J. Yao, “Power scaling and spectral linewidth suppression of hybrid Brillouin/thulium fiber laser,” Opt. Express 28(3), 2948–2955 (2020). [CrossRef]
6. A. Brignon and J.-P. Huignard, “Phase conjugate laser optics,” (2004).
7. K. Tsubakimoto, H. Yoshida, and N. Miyanaga, “High-average-power green laser using Nd: YAG amplifier with stimulated Brillouin scattering phase-conjugate pulse-cleaning mirror,” Opt. Express 24(12), 12557–12564 (2016). [CrossRef]
8. Z. Kang, Z. Fan, Y. Huang, H. Zhang, W. Ge, M. Li, X. Yan, and G. Zhang, “High-repetition-rate, high-pulse-energy, and high-beam-quality laser system using an ultraclean closed-type SBS-PCM,” Opt. Express 26(6), 6560–6571 (2018). [CrossRef]
9. H. Wang, S. Cha, H. J. Kong, Y. Wang, and Z. Lu, “Rotating off-centered lens in SBS phase conjugation mirror for high-repetition-rate operation,” Opt. Express 27(7), 9895–9905 (2019). [CrossRef]
10. S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, N. Chauhan, and J. Nohava, “Sub-hertz fundamental linewidth photonic integrated Brillouin laser,” Nat. Photonics 13(1), 60–67 (2019). [CrossRef]
11. D. Jin, Z. Bai, Z. Lu, R. Fan, Z. Zhao, X. Yang, Y. Wang, and R. P. Mildren, “22.5-W narrow-linewidth diamond Brillouin laser at 1064 nm,” Opt. Lett. 47(20), 5360–5363 (2022). [CrossRef]
12. C. Shi, H. Tian, S. Fu, Q. Sheng, Z. Shi, P. Jiang, W. Shi, and J. Yao, “High-energy single-frequency pulsed fiber MOPA at 1064 nm based on a hybrid active-fiber,” Opt. Express 30(9), 15575–15582 (2022). [CrossRef]
13. D. Jin, Z. Bai, M. Li, X. Yang, Y. Wang, R. P. Mildren, and Z. Lu, “Modeling and characterization of high-power single frequency free-space Brillouin lasers,” Opt. Express 31(2), 2942–2955 (2023). [CrossRef]
14. L. Lombard, A. Brignon, J.-P. Huignard, E. Lallier, and P. Georges, “Beam cleanup in a self-aligned gradient-index Brillouin cavity for high-power multimode fiber amplifiers,” Opt. Lett. 31(2), 158–160 (2006). [CrossRef]
15. Q. Gao, Z. Lu, C. Zhu, and J. Zhang, “High efficient beam cleanup based on stimulated Brillouin scattering with a large core fiber,” Laser Part. Beams 32(4), 517–521 (2014). [CrossRef]
16. I. Remer, R. Shaashoua, N. Shemesh, A. Ben-Zvi, and A. Bilenca, “High-sensitivity and high-specificity biomechanical imaging by stimulated Brillouin scattering microscopy,” Nat. Methods 17(9), 913–916 (2020). [CrossRef]
17. Y. Wang, C. Cui, Z. Lu, Z. Bai, Y. Wang, and H. Yuan, “Beam spatial intensity modification based on stimulated Brillouin amplification,” Opt. Express 30(20), 35792–35806 (2022). [CrossRef]
18. J. Shi, J. Xu, Y. Guo, N. Luo, S. Li, and X. He, “Dependence of stimulated Brillouin scattering in water on temperature, pressure, and attenuation coefficient,” Phys. Rev. Appl. 15(5), 054024 (2021). [CrossRef]
19. R. G. Brewer and K. E. Rieckhoff, “Stimulated Brillouin scattering in liquids,” Phys. Rev. Lett. 13(11), 334–336 (1964). [CrossRef]
20. E. Hagenlocker and W. Rado, “Stimulated Brillouin and Raman scattering in gases,” Appl. Phys. Lett. 7(9), 236–238 (1965). [CrossRef]
21. G. W. Faris, L. E. Jusinski, and A. P. Hickman, “High-resolution stimulated Brillouin gain spectroscopy in glasses and crystals,” J. Opt. Soc. Am. B 10(4), 587–599 (1993). [CrossRef]
22. Z. Bai, H. Yuan, Z. Liu, P. Xu, Q. Gao, R. J. Williams, O. Kitzler, R. P. Mildren, Y. Wang, and Z. Lu, “Stimulated Brillouin scattering materials, experimental design and applications: A review,” Opt. Mater. 75, 626–645 (2018). [CrossRef]
23. M. Damzen, V. Vlad, A. Mocofanescu, and V. Babin, Stimulated Brillouin scattering: fundamentals and applications (CRC press, 2003).
24. H. Yoshida, V. Kmetik, H. Fujita, M. Nakatsuka, T. Yamanaka, and K. Yoshida, “Heavy fluorocarbon liquids for a phase-conjugated stimulated Brillouin scattering mirror,” Appl. Opt. 36(16), 3739–3744 (1997). [CrossRef]
25. H. Yuan, Y. Wang, C. Zhu, Z. Zheng, and Z. Lu, “Investigation of sub-phonon lifetime pulse amplification in active frequency matching stimulated Brillouin scattering,” Opt. Express 27(12), 16661–16670 (2019). [CrossRef]
26. J. Wang, Z. Bai, X. Hun, B. Chen, C. Cui, Y. Qi, J. Ding, B. Yan, Y. Wang, and Z. Lu, “Stokes linewidth narrowing by stimulated Brillouin scattering in liquid media,” Appl. Phys. Express 16(1), 012014 (2023). [CrossRef]
27. C. Cao, Y. Wang, J. Yue, Z. Meng, K. Li, Y. Yu, Z. Bai, and Z. Lu, “High-repetition-rate, quarter acoustic wave oscillation period pulse compression using transient stimulated Brillouin scattering,” Opt. Express 30(19), 33721–33732 (2022). [CrossRef]
28. H. Wang, S. Cha, Y. Wang, H. J. Kong, and Z. Lu, “SBS pulse compression using bulk fused silica by diode-pumped solid-state lasers at 1 kHz repetition rate,” Opt. Laser Technol. 128, 106258 (2020). [CrossRef]
29. X. Tang, J. Qiu, Z. Fan, H. Wang, H. Liu, Y. Liu, and Z. Kang, “Experimental study on SBS-PCM at 200 Hz repetition rate pumped with joule-level energy,” Opt. Mater. 67, 64–69 (2017). [CrossRef]
30. D.-G. Kim, S. Han, J. Hwang, I. H. Do, D. Jeong, J.-H. Lim, Y.-H. Lee, M. Choi, Y.-H. Lee, and D.-Y. Choi, “Universal light-guiding geometry for on-chip resonators having extremely high Q-factor,” Nat. Commun. 11(1), 5933–5937 (2020). [CrossRef]
31. H. Chen, Z. Bai, X. Yang, J. Ding, Y. Qi, B. Yan, Y. Wang, Z. Lu, and R. P. Mildren, “Enhanced stimulated Brillouin scattering utilizing Raman conversion in diamond,” Appl. Phys. Lett. 120(18), 181103 (2022). [CrossRef]
32. R. Botter, K. Ye, Y. Klaver, R. Suryadharma, O. Daulay, G. Liu, J. van den Hoogen, L. Kanger, P. van der Slot, and E. Klein, “Guided-acoustic stimulated Brillouin scattering in silicon nitride photonic circuits,” Sci. Adv. 8(40), eabq2196 (2022). [CrossRef]
33. H. Yoshida, H. Fujita, M. Nakatsuka, A. Fujinoki, and K. Yoshida, “Fused-quartz glass with low optical quality as a high damage-resistant stimulated Brillouin-scattering phase-conjugation mirror,” Opt. Commun. 222(1-6), 257–267 (2003). [CrossRef]
34. H. Yoshida, H. Fujita, M. Nakatsuka, T. Ueda, and A. Fujinoki, “Compact temporal-pulse-compressor used in fused-silica glass at 1064 nm wavelength,” Jpn. J. Appl. Phys. 46(3), L80–L82 (2007). [CrossRef]
35. G. Marcus, S. Pearl, and G. Pasmanik, “Stimulated Brillouin scattering pulse compression to 175 ps in a fused quartz at 1064 nm,” J. Appl. Phys. 103(10), 103105 (2008). [CrossRef]
36. Z. Zhao, Y. Dong, S. Pan, C. Liu, J. Chen, L. Tong, Q. Gao, and C. Tang, “Performance of large aperture tapered fiber phase conjugate mirror with high pulse energy and 1-kHz repetition rate,” Opt. Express 20(2), 1896–1902 (2012). [CrossRef]
37. L. Zhu, Z. Bai, Y. Chen, D. Jin, R. Fan, Y. Qi, J. Ding, B. Yan, Y. Wang, and Z. Lu, “The effect of pump beam focusing characteristics on stimulated Brillouin scattering,” Opt. Commun. 515, 128205 (2022). [CrossRef]
38. R. W. Boyd, Nonlinear optics (Academic press, 2020).
39. R. Chu, M. Kanefsky, and J. Falk, “Numerical study of transient stimulated Brillouin scattering,” J. Appl. Phys. 71(10), 4653–4658 (1992). [CrossRef]
40. X. Zhu, Y. Wang, Z. Lu, and H. Zhang, “Generation of 360 ps laser pulse with 3 J energy by stimulated Brillouin scattering with a nonfocusing scheme,” Opt. Express 23(18), 23318–23328 (2015). [CrossRef]
41. B. Chen, Z. Bai, G. Zhao, Y. Zhang, B. Yan, Y. Qi, J. Ding, K. Wang, Y. Wang, and Z. Lu, “Compound cavity passively Q-switched single-longitudinal-mode diode-pumped laser,” Front. Phys. 10, 820177 (2022). [CrossRef]
42. X. Hun, Z. Bai, B. Chen, J. Wang, C. Cui, Y. Qi, J. Ding, Y. Wang, and Z. Lu, “Fabry–Pérot based short pulsed laser linewidth measurement with enhanced spectral resolution,” Results Phys. 37, 105510 (2022). [CrossRef]
43. X. Hun, Z. Bai, J. Wang, B. Chen, C. Cui, Y. Wang, and Z. Lu, “Convolution error reduction for a Fabry–Pérot–based linewidth measurement: a theoretical and experimental study,” Photonics 9(12), 1004 (2022). [CrossRef]
44. M. Jaberi, A. Farahbod, and H. Rahimpour Soleimani, “Effect of pump mode structure on reflectance of SBS mirrors,” Opt. Quantum Electron. 49(2), 53 (2017). [CrossRef]
