-
在激光器的谐振腔中插入一块非线性晶体,当不同的纵模和非线性晶体相互作用时,不仅有各自的倍频过程,而且有纵模之间的和频过程。假如谐振腔中有两个相邻的纵模,这两个纵模的频率为$ {\omega }_{1} $和$ {\omega }_{2} $,对应光强分别为$ I\left({\omega }_{1}\right) $和$ I\left({\omega }_{2}\right) $,当这两个模式和倍频晶体相互作用时,产生总的倍频光功率可以表示如下:
$$ \begin{array}{c}P\propto \left[{I}^{2}\left({\omega }_{1}\right)+4I\left({\omega }_{1}\right)I\left({\omega }_{2}\right)+{I}^{2}\left({\omega }_{1}\right)\right]\end{array} $$ (1) 其中,对于$ {\omega }_{1} $和$ {\omega }_{2} $而言,各自经受的非线性损耗为:
$$\begin{split} &Loss\left({\omega }_{1}\right)=k\left[{I}^{2}\left({\omega }_{1}\right)+2I\left({\omega }_{1}\right)I\left({\omega }_{2}\right)\right]\\ &Loss\left({\omega }_{2}\right)=k\left[{I}^{2}\left({\omega }_{2}\right)+2I\left({\omega }_{1}\right)I\left({\omega }_{2}\right)\right] \end{split} $$ (2) 式中:k为非线性转化系数。则各纵模所经受的相对非线性损耗为:
$$ \begin{array}{c}l\left({\omega }_{i}\right)=\dfrac{Loss\left({\omega }_{i}\right)}{I\left({\omega }_{i}\right)}\end{array} $$ (3) 式中:$ i=\mathrm{1,2} $。 这样,频率为$ {\omega }_{1} $和$ {\omega }_{2} $的两纵模的相对损耗分别为:
$$ \begin{split} &l\left({\omega }_{1}\right)=k\left[I\left({\omega }_{1}\right)+2I\left({\omega }_{2}\right)\right]\\ &l\left({\omega }_{2}\right)=k\left[I\left({\omega }_{2}\right)+2I\left({\omega }_{1}\right)\right] \end{split}$$ (4) 假设在模式竞争的作用下,$ {\omega }_{1} $的增益远大于$ {\omega }_{2} $,即$ I\left({\omega }_{1}\right)\gg I\left({\omega }_{2}\right) $,则有:
$$ \begin{array}{c}l\left({\omega }_{2}\right)\approx 2l\left({\omega }_{1}\right)\end{array} $$ (5) 即谐振腔内主振荡模所经受的非线性损耗是次振荡模的一半,在模式竞争的作用下,次模将被自动抑制,因此激光器将以稳定的单纵模方式运转。
-
通过分析谐振腔内各个模式的运转情况可知,谐振腔中每个振荡的模式具有相等的线性损耗,当激光谐振腔内有非线性转化过程时,除了线性损耗,还存在有倍频以及和频引起的非线性损耗。要想使激光器实现单纵模稳定运转,则主振荡模式的净增益等于零,而次振荡模式的净增益则必须小于零。根据线性损耗和非线性损耗之间的关系,可以得出激光器单模运转的物理条件[20]:
$$ \begin{split} &{1}/{2}-2sinc^{2}\left({1.39}/{2\gamma }\right) < \\ &\dfrac{{a}_{0}}{\sqrt{{\left({a}_{0}-{\varepsilon }_{0}\right)}^{2}+4{\varepsilon }_{0}}-{\alpha }_{0}-{\varepsilon }_{0}} \end{split} $$ (6) 式中:$ \gamma=\Delta \lambda_{N L} / \Delta \lambda_g$表示非线性晶体非线性谱宽和增益晶体的增益带宽的比值;$ {\alpha }_{0} $和$ {\varepsilon }_{0} $分别为归一化的线性损耗和非线性损耗;谐振腔的线性损耗为$ {\alpha }_{0}=(L+t)/2{g}_{0}l $,$ L $为腔内线性损耗,$ t $为输出镜的透射率,$ {g}_{0} $为小信号增益,$ l $为激光晶体的长度;谐振腔的非线性损耗为$ \varepsilon_0=k I_0 /\left(4 g_0 l\right)$,$ k $为非线性转换系数,$ I_0$为饱和功率。
基于提出的物理条件,将一块非线性LBO晶体插入如图1所示的四镜环形谐振腔内达到引入非线性损耗的目的。LBO晶体尺寸为3 mm×3 mm×18 mm,采用I类温度匹配,被放置在工作温度为149 ℃,控制精度为0.1 ℃的控温炉中。根据公式(6)得到的图2,即表示激光器可以实现单纵模运转的物理条件。其中,左上角区域为单纵模区域,右下角为多纵模区域。从图中可以看出,通过在谐振腔内引入适当的非线性损耗以及线性损耗即可获得一个很宽的单纵模区域,实现激光器的单纵模激光输出。
图 1 单频1064 nm激光器的腔型结构示意图
Figure 1. The cavity structure diagram of the single-frequency 1064 nm laser
在实验中,当非线性晶体没有插入谐振腔时,通过扫描共焦F-P干涉仪,可以看到激光器同时有三个纵模起振,如图3(a)所示。而当LBO插入谐振腔内并工作在最佳相位匹配温度后,输出耦合镜的透射率分别为HR、16%、19%时,激光器都可以稳定地以单纵模方式运转,如图3(b)所示。而当输出耦合镜的透射率为22%时,由于谐振腔内基频光强度较低,使得由非线性过程引入的非线性损耗较小,导致激光器不能满足公式所示的单纵模运转的物理条件,最终,激光器不能以稳定的单纵模方式运转。将激光器的相关参数代入公式(6)中,可以从图2(实验点)中很清楚地看到,当透射率低于19%,激光器均运转在单纵模区域。而当输出耦合镜的透射率高于19%后,激光器就工作在单纵模区域以外。最后,当输出耦合镜的透射率为19%时,获得了输出功率为33.7 W的连续单频1064 nm激光器,同时有1.13 W的连续单频532 nm激光输出,总的光光转化效率高达46.5%。
-
为实现高质量的高功率单频连续波激光器,需要对激光器内的往返损耗进行精确测量。腔内往返损耗与净增益之间的关系是决定激光器运行状态的主要因素,精确测量这一损耗对于在实验上实现稳定高效运转的高功率激光器来说至关重要,因为它对泵浦阈值功率和激光器的输出功率有着深远的影响。1996年,Findlay和Clay提出了一种通过测量不同透射率的输出耦合镜下对应的阈值泵浦功率,进而推算出腔内往返损耗的方法[21]。然而这种方法操作繁琐,且误差较大。2008年,Song 等人提出一种将泵浦光功率带入速率方程并进行数值拟合的方法来得到腔内损耗的方法[22],但是此方法在高功率激光器中不适用。2012年,笔者课题组也曾提出过一种通过测量弛豫振荡频率和输出功率得出腔内损耗的方法[23],然而此方法无法被应用到高增益激光器中。针对此,笔者在利用非线性损耗实现激光器单频运转的基础上,通过操控非线性损耗的大小,提出了一种简便高效,且适用于高功率激光器的腔内(线性)损耗测量方法[24]。
当非线性损耗被引入谐振腔后,单频激光器可以实现双波长激光输出,此时激光器内的往返损耗可以进一步细分为线性损耗和非线性损耗。实验中可以通过调整非线性晶体LBO的相位匹配温度对谐振腔内的非线性损耗的大小进行调整,进而影响激光器的输出特性。通过精确测量不同情况下的基频光和倍频光的输出功率,即可反推出谐振腔内线性损耗的大小,从而得出激光器内的往返损耗。激光器中基频光和倍频光的输出功率分别可表示为[24]:
$$ \begin{array}{c}{P}_{f}=tAI\end{array} $$ (7) $$ \begin{array}{c}{P}_{sh}=\eta I{A}^{2}\end{array} $$ (8) 基频光的强度表达式为:
$$ \begin{split} I=&\left[\sqrt{ ({\left(t+L-{I}_{0}\eta \right)}^{2}+4\eta {I}_{0}{g}_{0}l)}-\right.\\& \left. (t+L+{I}_{0}\eta )\right]/2\eta \end{split} $$ (9) 式中:$ {P}_{f} $和$ {P}_{sh} $分别表示基频光和倍频光的输出功率;$ A $为增益介质处的激光横截面积;$ t $为输出耦合镜的透射率;$ \eta $为非线性转化因子;$ {I}_{0} $为饱和强度。另外,对于运转稳定的激光器而言,$ {g}_{0}l=K{P}_{in} $,其中$ {g}_{0} $为小信号增益;$ l $为增益晶体长度;K为泵浦光转化因子;Pin为泵浦光的功率。将公式(9)代入公式(7)和(8)可以得到腔内线性损耗的表达式:
$$ \begin{split} L= & \left(\left(I_0 K P_{ {in }} P_f^2-\left(P_{s h} t\right)^2-t P_f P_{s h}\left(t+I_0 \eta\right)-\right.\right. \\ & \left.\left.I_0 \eta t P_f^2\right)\right) /\left(I_0 \eta P_f^2+t P_f P_{s h}\right) \end{split} $$ (10) 在公式(10)中,除腔内线性损耗L与泵浦光转化因子K外,其余均为已知量或可测量,即公式(10)是关于谐振腔的腔内线性损耗L以及泵浦光转化因子K的二元一次方程。在激光器输出耦合镜透射率一定的条件下,只改变非线性转化效率的大小,就可以调控基频光和倍频光的输出功率。换言之,只要精确测量不同非线性转化效率下的基频光和倍频光的输出功率并代入公式(10)中,就可以得到一组关于腔内线性损耗L与泵浦光转化因子K的二元一次方程组。通过对该方程组进行求解即可得出泵浦光转化因子和腔内线性损耗的大小。
基于图1的实验装置,在输出耦合镜的透射率为20%的情况下,通过改变非线性晶体LBO的相位匹配温度可以改变谐振腔输出基频光和倍频光的功率。输出功率随温度的变化情况如图4所示。通过记录激光器在单频运转区域内6个采样点的数据,可以得到6个关于线性损耗和泵浦因子的二元一次方程;通过将每两个方程进行组合并求解,可以解出15组对应的腔内线性损耗L和泵浦因子K,对其求平均值和标准差可以得到,实验中的激光器的腔内线性损耗L为(4.84±0.26)%,泵浦因子K为(6.91±0.07)% W−1。
在精确测量激光器腔内线性损耗的基础上,结合腔内增益与损耗的数据设计并实现了一款高功率全固态单频连续波1064 nm激光器[25]。在设计过程中,除重点分析激光器的增益和损耗外,还结合了直接泵浦、复合晶体、像散自补偿以及非线性损耗等技术。在各方面优化下,通过将激光器的泵浦功率提高到113 W,输出耦合镜的透射率优化为25%,该激光器的最高输出功率高达50.3 W,激光器的输出功率曲线如图5所示。在增加泵浦功率的过程中,由于晶体的热透镜焦距在不断变化导致晶体处的模式匹配效率也在变化,因此输出功率并不随着泵浦功率的增加而线性增加。与此同时,由于非线性晶体的存在,同时产生了1.9 W的单频532 nm激光输出,总的光光转换效率为46.2%。激光器在5 h范围内的峰值功率稳定性为±0.54%。激光器的模式结构如图6所示,通过监测输出激光的横模与纵模可得,在最大输出功率处,X方向和Y方向的光束质量分别为1.08和1.10,通过一个精细度为210,自由光谱区为750 MHz的F-P干涉仪监测可得激光器处于稳定的单纵模运转状态。该激光器后续被应用于研究纵模结构与相对噪声强度之间的关系,以及作为高质量注入锁定激光器以及MOPA结构的种子源激光器。
Research progress on enhancing the output power of all-solid-state single-frequency continuous-wave lasers by using intracavity nonlinear loss mode-selecting technology (invited)
-
摘要: 全固态单频连续波激光器因其噪声低、线宽窄、光束质量好、功率稳定性高等优点已经被广泛应用于产生非经典光场、冷原子物理研究、引力波探测等诸多领域。随着科学技术的不断发展,传统的全固态激光器的输出功率已经不能满足前沿领域的需求,因此亟需在保持全固态激光器整体性能的同时进一步提升激光器的输出功率。为此首先需要更高的泵浦功率,而这将使激光器内部增益提高,在腔内损耗不变的情况下,原非振荡模式也将满足起振条件,从而使激光器在跳模或多模状态下运转。此外,激光晶体的热效应和损伤阈值也限制了输出功率的提高。本文介绍了一种利用非线性损耗大幅度提升全固态单频连续波激光器的输出功率的技术和方法。通过在谐振腔中引入非线性损耗,使主模经受的非线性损耗是次模的一半。在模式竞争的作用下,谐振腔内的模式被更进一步的选择,从而允许全固态单频激光器在更高的增益下保持单纵模运转。通过在谐振腔内插入多块增益晶体可以有效缓解由于激光增益晶体热效应的限制,从而实现更高功率的单频激光输出。目前高功率全固态连续波激光器的输出功率已经达到了一百瓦的量级,且还在进一步提高。通过在谐振腔内引入非线性损耗,全固态单频连续波激光器的整体性能在得以保障和提高的同时,其应用范围也得到了进一步的推广。Abstract:
Significance: All-solid-state single-frequency continuous-wave (CW) laser have found extensive applications in diverse domains such as the generation of non-classical light fields, cold atom physics, detection of gravitational waves, and so on, which primarily attributed to their merits of low noise, narrow bandwidth, excellent beam quality, and high power stability. In line with the advancement in science and technology, the output power of the traditional all-solid-state laser (ASSL) cannot satisfy the application requirements of many frontier research fields, so it is necessary to further scale the ASSL power and simultaneously maintain other excellent performance. For the purpose of improving the output power of the ASSL, its pump power has to be primarily elevated. However, with the increasement of the pump power, the laser gain is enhanced, and the non-oscillating laser modes of the ASSL start to oscillate, which results in the mode-hopping or the multi-mode oscillating operation of the ASSL. Moreover, the severe thermal effect of the laser gain medium and its relatively lower damage threshold also further restrict the improvement of the ASSL power. In this paper, an effective method of improving the all-solid-state single-frequency CW laser power via deliberately introducing a nonlinear loss into the resonator was presented. When the nonlinear loss was introduced, the nonlinear loss of the lasing mode was half of that of non-lasing mode, and the non-lasing mode was effectively inhibited, under the mode competition of the laser. As a consequence, the stable single-longitudinal mode operation of the laser can be guaranteed at higher laser gain. In addition, the design of multi-laser-crystal resonator can be adapted to efficiently mitigate the negative impact of the thermal effects of the laser crystal. By combining the nonlinear loss technique and the multi-laser-crystal resonator scheme, the output power of the all-solid-state single-frequency CW laser had been scaled up to 100-watt level and continuously increased. Progress: First, the fundamental principle of mode selection implemented by intra-cavity nonlinear loss is presented. When the nonlinear loss is introduced into the resonator, the nonlinear loss of the lasing mode is half of that of the non-lasing mode, and the non-lasing modes are suppressed effectively under the mechanics of mode competition. Based on the principle above, the physical condition of stable SLM operation for ASSL is proposed. The condition depends on the intra-cavity linear and nonlinear losses, which is experimentally validated by changing the transmission of the output coupler. In the experiment, when the output coupler transmission is 19%, and the temperature of the type-I phase matched nonlinear crystal LBO is 149 ℃, the maximal output power of 33.7 W for the stable single-frequency 1064 nm laser is realized. On this basis, the intra-cavity round-trip loss of an ASSL is measured precisely by simply changing the temperature of the nonlinear LBO crystal to manipulate the nonlinear loss within the SLM region of the laser. According to the measured results and the oscillating condition of the ASSL, the output coupler transmission of the designed laser as well as its pump power is further optimized and the maximal output power of 50.3 W for the single-frequency 1064 nm laser is obtained. To further increase the output power of the single-frequency laser, the pump power of the laser has to be raised. However, the sever thermal effect of the laser gain medium and its lower damage threshold restrict the continuously increasing of the single-frequency laser power. For the purpose of breaking aforementioned restriction and attaining higher power single-frequency laser, a laser resonator with two identical laser crystals was designed, where the precise mode-reproduction of the two crystals was implemented by a pair of lenses with identical focal length of 100 mm. When the total pump power was 240 W, a single frequency 1064 nm laser with maximal output power of 101 W was realized. In this laser, the focal lengths of the two lenses were fixed, so the laser only would be operated at a given incident pump power, and simultaneously the optical length between the imaging lenses had to be precisely adjusted. To this end, a self-mode-matching laser with four laser crystals in a single resonator was further designed. The total four laser crystals were used for both laser gain media and mode-matching elements. Under an appropriate combination of pump powers on four crystals, a stable CW single-frequency 1064 nm laser with 140 W power was obtained. Conclusions and Prospects: Introducing nonlinear losses within the resonator is a robust way to realize SLM laser output, which has been experimentally proved. With multiple gaining crystals inserted in one cavity, the heat load on each crystal is effectively shared, so more total power is tolerable. With suitable mode matching and mode reproducing in the resonant, a high-power single-frequency CW ASSL has been designed and built which can deliver 140 W single-frequency CW laser, this is to our knowledge the highest SLM ASSL power. The progress in high-power single-frequency ASSL has significantly broadened its potential applications and made substantial contributions to the advancement of related disciplines. -
Key words:
- all-solid-state laser /
- nonlinear loss /
- single frequency /
- high power
-
图 12 理论预测四块激光晶体处,腔模大小随注入四块晶体的泵浦功率( P 1, P 2, P 3, P 4)的变化情况。(a)与(b)为注入四块晶体的泵浦功率同步增加的情况;(c)与(d)为P1与P2的功率分别固定在70 W,83 W,90 W,103 W以及110 W时,增加P3和P4 功率的情况;(e)与(f)为P3和P4的功率分别固定在70 W、83 W、90 W、103 W以及110 W时,增加P1与P2功率的情况
Figure 12. Theoretical predictions of the mode size variations at the positions of the four laser crystals dependence on incident pump powers (P1, P2, P3, P4). (a) and (b) Incident pump powers of four laser crystals are synchronously increased; (c) and (d) Increasing the incident power of P3 and P4 when P1 and P2 are fixed at 70 W, 83 W, 90 W, 103 W and 110 W; (e) and (f) Increasing the incident power of P1 and P2 when P3 and P4 are fixed at 70 W, 83 W, 90 W, 103 W and 110 W
图 14 输出1064 nm激光的数据测量结果。(a) 5 h内的输出功率稳定性(插图为纵模结构); (b)横模结构; (c)线宽; (d)相对强度噪声谱
Figure 14. Measured output performances of 1064 nm laser. (a) The stability of output power over 5 h (Insert: Longitudinal-mode structure); (b) Transverse mode structure characteristic; (c) Linewidth; (d) Relative intensity noise spectrum
-
[1] Ligo Scientific Collaboration, Virgo Collaboration. Observation of gravitational waves from a binary black hole merger [J]. Phys Rev Lett, 2016, 116(6): 061102. doi: 10.1103/PhysRevLett.116.061102 [2] Pfeifer H J, vom Stein H D. Application of the laser velocimeter in supersonic wind tunnel [J]. Opto-electronics, 1973, 5(1): 53-58. doi: 10.1007/BF01421901 [3] Eismann U, Bergschneider A, Sievers F, et al. 2.1-watts intracavity-frequency-doubled all-solid-state light source at 671 nm for laser cooling of lithium [J]. Opt Express, 2013, 21(7): 9091-9102. doi: 10.1364/OE.21.009091 [4] Meyer-Scott E, Prasannan N, Eigner C, et al. High-performance source of spectrally pure, polarization entangled photon pairs based on hybrid integrated-bulk optics [J]. Opt Express, 2018, 26(25): 32475-32490. doi: 10.1364/OE.26.032475 [5] Kimble H. The quantum internet [J]. Nature, 2008, 453(7198): 1023-1030. doi: 10.1038/nature07127 [6] Song Jiaqi, Qin Jiliang, Jin Pixian, et al. Realization of CW single-frequency tunable Ti: sapphire laser with immunity to the noise of the pump source [J]. Opt Express, 2023, 31: 745-754. doi: 10.1364/OE.479558 [7] Zhao Jian, Zhao Yong, Peng Yun, et al. Review of femtosecond laser direct writing fiber-optic structures based on refractive index modification and their applications [J]. Optics and Laser Technology, 2022, 146: 107473. doi: 10.1016/j.optlastec.2021.107473 [8] 王海龙, 杨慧琦, 苏静, 等. 基于单共振光学参量振荡器实现近红外到中红外激光输出的实验研究[J]. 中国激光, 2022, 49(18): 1801005. doi: 10.3788/CJL202249.1801005 Wang Hailong, Yang Huiqi, Su Jing, et al. Experimental study of near-infrared to mid-infrared laser output based on single resonant optical parametric oscillator [J]. Chinese Journal of Lasers, 2022, 49(18): 1801005. (in Chinese) doi: 10.3788/CJL202249.1801005 [9] 聂鸿坤, 宁建, 张百涛, 等. 光学超晶格中红外光参量振荡器研究进展[J]. 中国激光, 2021, 48(5): 0501008. doi: 10.3788/CJL202148.0501008 Nie Hongkun, Ning Jian, Zhang Baitao, et al. Recent progress of optical-superlattice-based mid-infrared optical parametric oscillators [J]. Chinese Journal of Lasers, 2021, 48(5): 0501008. (in Chinese) doi: 10.3788/CJL202148.0501008 [10] 牛昌东, 戴瑞峰, 刘瑞科, 等. 固体激光器单纵模选择技术及应用[J]. 光电技术应用, 2020, 35(5): 38. doi: 10.3969/j.issn.1673-1255.2020.05.007 Niu Changdong, Dai Ruifeng, Liu Ruike, et al. Single-longitudinal-mode selection technology and application of solid-state laser [J]. Electro-Optic Technology Application, 2020, 35(5): 38. (in Chinese) doi: 10.3969/j.issn.1673-1255.2020.05.007 [11] Wang Ran, Gao Chunqing, Zheng Yan, et al. A resonantly pumped 1 645 nm Er:YAG nonplanar ring oscillator with 10.5 W single frequency output [J]. IEEE Photonics Technology Letters, 2013, 25(10): 955-957. doi: 10.1109/LPT.2013.2255100 [12] 赵齐来. 低噪声单频光纤激光技术及其应用研究[D]. 广东: 华南理工大学, 2020. Zhao Qilai. Low-noise single-frequency fiber laser technique and its application research[D]. Guangzhou: South China University of Technology, 2020. (in Chinese) [13] Peng Weina, Jin Pixian, Li Fengqin, et al. A review of the high-power all-solid-state single-frequency continuous-wave laser [J]. Micromachines, 2021, 12(11): 1426. doi: 10.3390/mi12111426 [14] Takeno Kohei, Ozeki Takafumi, Moriwaki Shigenori, et al. 100 W, single-frequency operation of an injection-locked Nd: YAG laser [J]. Opt Lett, 2005, 30: 2110-2112. doi: 10.1364/OL.30.002110 [15] Willke B, Danzmann K, Frede M, et al. Stabilized lasers for advanced gravitational wave detectors [J]. Class Quantum Grav, 2008, 25(11): 114040. doi: 10.1088/0264-9381/25/11/114040 [16] Frede Maik, Schulz Bastian, Wilhelm Ralf, et al. Fundamental mode, single-frequency laser amplifier for gravitational wave detectors [J]. Opt Express, 2007, 15(2): 459. doi: 10.1364/OE.15.000459 [17] Martin K I, Clarkson W A, Hanna D C. Self-suppression of axial mode hopping by intracavity second-harmonic generation [J]. Opt Lett, 1997, 22(6): 375. doi: 10.1364/OL.22.000375 [18] Lu Huadong, Sun Xuejun, Wang Meihong, et al. Single frequency Ti: sapphire laser with continuous frequency-tuning and low intensity noise by means of the additional intracavity nonlinear loss [J]. Opt Express, 2014, 22(20): 24551. doi: 10.1364/OE.22.024551 [19] Yang Xuezong, Kitzler Ondrej, Spence D J, et al. Single-frequency 620 nm diamond laser at high power, stabilized via harmonic self-suppression and spatial-hole-burning-free gain [J]. Opt Lett, 2019, 44(4): 839. doi: 10.1364/OL.44.000839 [20] Lu Huadong, Su Jing, Zheng Yaohui, et al. Physical conditions of single-longitudinal-mode operation for high-power all-solid-state lasers [J]. Opt Lett, 2014, 39: 1117-1120. doi: 10.1364/OL.39.001117 [21] Findlay D, Clay R A. The measurement of internal losses in 4-level lasers [J]. Physics Letters, 1996, 20(3): 277. doi: 10.1016/0031-9163(66)90363-5 [22] Song F, Cai H, Liu S J, et al. A method to measure the intracavity losses of LD-pumped solid-state laser: Chinese Patent, 200710058008[P]. 2008.02.27. [23] Lu H D, Su J, Peng K C. A method to measure the intracavity losses of all-solid-state laser: Chinese Patent, 201210094396.1[P]. 2012.04.01. [24] Guo Yongrui, Lu Huadong, Yin Qiwei, et al. Intra-cavity round-trip loss measurement of all-solid-state single-frequency laser by introducing extra nonlinear loss [J]. Chin Opt Lett, 2017, 15(2): 021402. doi: 10.3788/COL201715.021402 [25] Guo Yongrui, Lu Huadong, Xu Minzhi, et al. Investigation about the influence of longitudinal-mode structure of the laser on the relative intensity noise properties [J]. Opt Express, 2018, 26(16): 21108-21118. doi: 10.1364/oe.26.021108 [26] Guo Yongrui, Xu Minzhi, Peng Weina, et al. Realization of a 101 W single-frequency continuous wave all-solid-state 1064 nm laser by means of mode self-reproduction [J]. Opt Lett, 2018, 43(24): 6017-6020. doi: 10.1364/OL.43.006017 [27] Wei Yixiao, Peng Weina, Li Jiawei, et al. Self-mode-matching compact low-noise all-solid-state continuous wave single-frequency laser with output power of 140 W [J]. Opt Lett, 2023, 48(3): 676-679. doi: 10.1364/OL.478137