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SRS是一种三阶非线性光学效应,其散射过程为非弹性散射。当高功率密度的激光和物质分子发生相互作用时(具有阈值特性),物质内部原子或分子振动会使光波产生能量交换,导致激发的散射光频率相较于泵浦光有所差异[68-69]。若散射光的频率低于泵浦光频率,且满足:
$$ \omega_{S}=\omega_{P}-\omega_{V} $$ (1) 则该散射光称为斯托克斯(Stokes)光;若散射光频率高于泵浦光频率且满足:
$$ \omega_{AS}=\omega_{P}+\omega_{V} $$ (2) 则该散射光称为反斯托克斯(anti-Stokes)光。公式(1)和(2)中的ωS、ωAS、ωP、ωV分别表示Stokes光、anti-Stokes光、泵浦光和拉曼介质中粒子振动的频率。SRS的能级跃迁过程可以通过图2进行描述。最初,拉曼介质粒子位于基态(v=0)能级,在吸收一个泵浦光光子并发射一个Stokes光子后,粒子跃迁到激发态(v=1)能级上。随后,粒子从激发态(v=1)能级退激发到基态(v=0)能级,并发射一个能量为$\hbar \omega_{{V}}$的声子。粒子从基态(v=0)能级到激发态(v=1)能级的跃迁可以通过一个中间能级过渡,该能级是非稳能级。
SRS根据泵浦光脉宽τP与粒子振动弛豫时间T2的长短,可以分为稳态SRS(τP$\gg $T)和瞬态SRS(τP$\ll $T)。稳态SRS过程产生的一阶Stokes光功率密度可以表示为:
$$ {I_S}({l_R}) = {I_S}(0)\exp ({g_S}{I_P}{I_S}) $$ (3) 式中:IS为一阶Stokes光功率密度;IP为泵浦光功率密度;lR为拉曼介质长度;gS为一阶Stokes光的拉曼增益系数,其表达式为:
$$ {g_S} = \frac{{8\pi {c^2}N}}{{\hbar \omega _P^3{n^2}\Delta {v_S}}}\frac{{{\rm{d}}\sigma }}{{{\rm{d}}\varOmega }} $$ (4) 式中:N为拉曼介质单位体积内的粒子数密度(cm−3);c为真空中的光速;dσ/dΩ为自发拉曼散射截面;$\hbar $=h/(2π)(h为普朗克常数);n为拉曼介质折射率;ΔvS为拉曼谱线宽度。稳态拉曼增益系数与自发拉曼散射截面dσ/dΩ成正比,与ΔvS成反比。因此,理论上利用窄线宽激光泵浦自发拉曼散射截面的增益介质,可以实现较高的稳态拉曼增益系数。
在满足四波混频(four-wave mixing,FWM)相位匹配条件下,SRS可以产生anti-Stokes光,即:
$$ \Delta k = 2k_{P}一k_{S 1}—k_{AS}= 0 $$ (5) 式中:kP、kS1和kAS分别为泵浦光、一阶Stokes光和一阶anti-Stokes光的波矢。在FWM过程中,拉曼介质粒子吸收两个泵浦光光子,并放出一个一阶Stokes光子和一个一阶anti-Stokes光子,在这个过程中拉曼介质内没有产生或消耗声子。图3(a)为FWM相位匹配示意图,图3(b)为反Stokes拉曼散射能级跃迁图。
图 3 (a) FWM相位匹配示意图;(b)反Stokes拉曼散射能级跃迁图
Figure 3. (a) Schematic diagram of FWM phase matching; (b) Energy level transition diagram of anti-Stokes Raman scattering
SRS辐射传输方程可以描述拉曼介质中泵浦光与Stokes光的相互作用。1965年,Shen和Bloembergen根据SRS耦合波方程推导出了SRS辐射传输方程[70]。2006年,丁双红考虑高至三阶斯托克斯光及后向SRS的情况,在稳态近似条件下建立了适用于外腔拉曼激光器的辐射传输方程[71]。2014年,王聪建立了适用于拉曼放大器的辐射传输方程,该方程描述了泵浦光参数、Stokes光参数与拉曼介质参数的变化关系,对于拉曼放大器的设计和优化具有重要的参考价值[67,72]。在泵浦光和Stokes种子光沿同一方向单程通过拉曼介质的条件下,拉曼放大器的辐射传输方程可表示为:
$$ \begin{split} \dfrac{n}{c}\dfrac{\partial {I}_{P}(z,t)}{\partial t}+\dfrac{\partial {I}_{P}(z,t)}{\partial z}= -{g}_{P}{I}_{P}(z,t){I}_{S}(z,t)-\alpha {I}_{P}(z,t) \end{split} $$ (6) $$ \begin{gathered} \frac{n}{c}\frac{{\partial {I_S}(z,t)}}{{\partial t}} + \frac{{\partial {I_S}(z,t)}}{{\partial z}} = {g_S}{I_S}(z,t){I_P}(z,t) - \alpha {I_S}(z,t) + {K_{S P}}{I_P}(z,t) \\ \end{gathered} $$ (7) 式中:IP(z,t)、IS(z,t)为泵浦光和Stokes光在不同空间和时间条件下的功率密度;α为腔内损耗系数;KSP为自发拉曼散射系数;gP为泵浦光的拉曼增益系数。在拉曼介质长度为lR时,放大后的Stokes光在t时刻的功率密度为IS(lR,t),忽略损耗和自发拉曼散射,其表达式为:
$$ \begin{split} {I_S}({l_R},t) = \dfrac{{{I_0}(t)\dfrac{{{I_S}(0,t)}}{{{I_P}(0,t)}}\exp \left[\dfrac{{{\omega _S}}}{{{\omega _P}}}{g_P}{I_0}(t){l_R}\right]}}{{1 + \dfrac{{{\omega _P}}}{{{\omega _S}}}\dfrac{{{I_S}(0,t)}}{{{I_P}(0,t)}}\exp \left[\dfrac{{{\omega _S}}}{{{\omega _P}}}{g_P}{I_0}(t){l_R}\right]}} \\ \end{split} $$ (8) $$ {I_0}(t) = {I_P}(0,t)\left[1 + \frac{{{\omega _P}}}{{{\omega _S}}}\frac{{{I_S}(0,t)}}{{{I_P}(0,t)}}\right] $$ (9) 参照上述理论模型,笔者可以对外腔拉曼放大器的输出特性进行模拟,从而为自由空间拉曼放大器的设计和参数优化提供理论依据。
目前,自由空间拉曼放大器的常用介质主要包括气体和晶体两种,因此人们通常根据拉曼介质的不同将其分为气体拉曼放大器和晶体拉曼放大器,两者均在高功率特殊波段激光技术领域有着十分重要的贡献。下面对气体拉曼放大器和晶体拉曼放大器的主要特性及研究进展进行介绍。
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气体拉曼介质具备拉曼频移大、自聚焦阈值低、光耦合波损耗低、尺寸几乎不受限制等优点,过去在高功率拉曼激光技术领域应用最为广泛。得益于气体拉曼介质的优良特性,气体拉曼放大器在高功率特殊波段激光技术领域具有重要的研究价值。
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拉曼放大器根据Stokes光与泵浦光沿着传输方向在相互作用区域是否存在夹角分为共线和非共线两种结构。共线拉曼放大器通常具备更大的相互作用长度且可以有效避免相位失配,因此能够充分提取泵浦光能量,从而实现高效率大能量的拉曼放大[73-78]。2009年,Hooper等人[79]以D2作为拉曼介质通过共线拉曼放大,得到了单脉冲能量250 mJ的1560 nm激光输出。2016年,周冬建等人[80]以H2为拉曼介质通过共线拉曼放大,得到了单脉冲44.0 mJ、波长1.9 μm的激光输出。此外,共线拉曼放大器还展现了良好的光束净化特性,可以将低光束质量的泵浦光转换为高光束质量的Stokes光,从而实现高光束质量的拉曼放大输出。1983年, Chang等人[81]以H2为拉曼介质,基于前向SRS放大将畸变的泵浦光转换为发散度略高于衍射极限1.5倍的Stokes光输出,实验装置如图4所示。
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单从拉曼增益角度来看,相同注入光参数时,放大器结构宜采用种子光与泵浦光同轴的共线拉曼放大方式以便实现高效率的拉曼转换[82-83]。对应地,非共线拉曼放大方式引起的相互作用长度变短和相位失配将导致拉曼放大的总增益相对有所下降[84-86]。此外,若种子光与泵浦光满足FWM相位匹配条件,还会产生二阶Stokes光,导致一阶Stokes光的转换效率下降。1986年,Duncan等人[87]研究了在不同输入光角度下拉曼放大倍数与泵浦光能量的变化关系。结果显示,在FWM相位匹配条件下,拉曼放大倍数随泵浦光能量增大以非指数形式增长,其拉曼放大倍数甚至小于非相位匹配条件下拉曼放大倍数的10−7。此外,非共线拉曼放大器同样可以实现光束净化。1985年,继验证了共线放大的光束净化效应后[81],Chang等人[88]通过非共线拉曼放大器将严重畸变(120×DL)泵浦光转换为近衍射极限的高光束质量拉曼激光。
当Stokes种子光能量较小、泵浦光能量较为充足的条件下,可以采用多通结构使种子光与泵浦光多次相互作用,提高拉曼放大器的转换效率[89-92]。多通拉曼放大器对共线和非共线形式均适用。1984年,Goldhar等人[90]通过CH4气体双通拉曼放大器实现了泵浦光光子提取效率约75%~85% 的拉曼放大,实验装置如图5所示。多通拉曼放大器的输出脉宽可以达到百飞秒量级,Szatmári等人[91]和Glownia等人[92]分别通过ArF双通拉曼放大器先后得到了脉宽340 fs以及脉宽 300 fs的193 nm激光输出。
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根据光束作用结构的不同,基于拉曼和布里渊放大的激光组束(两种非线性过程相似)均可以分为串行激光组束和并行激光组束[28,93-97]。串行和并行拉曼组束的区别在于,串行组束是利用一束Stokes光逐级抽取与之相互作用泵浦光的能量,各光束之间可无需进行相位锁定;并行拉曼激光组束利用一束Stokes光同时抽取与其相互作用的若干束泵浦光能量,相互作用的光束之间往往需要进行相位锁定。其中,串行拉曼激光组束具有结构设计灵活、功率拓展性强、对光同步要求相对较低等优点,且对Stokes光与泵浦光的相互作用形式是否共线没有限制。
1980年,Jacobs等人[98]以CH4为拉曼介质,通过共线拉曼激光组束得到了脉宽7 ns、波长268 nm的后向脉冲输出,实验装置如图6所示。1989年,Mandl等人[99]以H2为拉曼介质,利用高度畸变的光束作为泵浦光与近衍射极限的种子光进行共线拉曼激光组束,得到了单脉冲能量约0.8 J的414 nm近衍射极限的组束激光。1979年,Basov等人[100]以H2为拉曼介质,通过非共线拉曼激光组束实现了单脉冲能量360 mJ、脉宽3 ns的1.13 μm激光输出,实验装置见图7(图中,1 atm=1.013×105 Pa)。1986年,Shaw等人[101-102]分别以CH4和H2为拉曼介质进行了非共线拉曼激光组束:用CH4为拉曼介质时,实现了单脉冲能量为8.4 J的268 nm激光组束输出;采用H2为拉曼介质时,实现了单脉冲能量为5.0 J的277 nm激光组束输出。
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气体拉曼放大器具有输出能量高、介质尺寸可拓展性高等优点,表1总结了近年来自由空间结构的气体拉曼放大器的参数。目前,自由空间结构的气体拉曼放大器主要应用于短脉宽、高峰值功率、大能量的激光的放大和光束合成,其输出的激光峰值功率已达到兆瓦量级、单脉冲能量达到焦耳量级。但是,气体拉曼放大器也存在气体介质难以保存、增益介质容器体积大、系统集成化较难的问题,且实验中需要对气体的压强等参数进行控制。近年来,基于气体填充空心光纤的拉曼放大器得到广泛的关注,尤其在实现低阈值特定波长转换中具有较为明显的优势[103-104]。
表 1 气体拉曼放大器研究进展
Table 1. Research progress of Raman amplifier in gas
Year Raman
mediumStructure Pump
wavelength/μmStokes
wavelength/μmOutput
energy/mJPulse
duration/nsPeak
power/MWRef. 1979 H2 Beam combination 1.06 1.13 360 3 120 [100] 1980 CH4 Beam combination 0.248 0.268 - 7 - [98] 1983 H2 Collinear amplifier 0.308 0.353 20 50 4 [81] 1986 CH4/H2 Beam combination 0.249 0.268/0.277 8400/5000 - - [101] 1989 H2 Beam combination 0.353 0.414 800 - - [99] 1996 H2 Collinear amplifier 0.390 0.465 0.02 0.00035 57.1 [73] 2001 CH4 Collinear amplifier 0.248 0.268 - 5 - [83] 2009 D2 Collinear amplifier 1.064 1.560 250 4 62.5 [79] 2016 H2 Collinear amplifier 1.06 1.9 44 - - [80] -
相较于气体拉曼介质,晶体拉曼介质具有拉曼增益系数高、热导性能好、性能稳定和易于实现小型化等优点。随着晶体制备技术的发展,晶体拉曼介质的品质日益提高,极大推动了晶体拉曼放大器在高功率激光技术领域的应用。
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2007年,Raghunathan等人[105]实现了首台中红外硅晶体拉曼放大器,输出光波长为3.39 μm,拉曼增益高达12 dB。随后,科研人员们采用Ba(NO3)2、YVO4、KGW、BaWO4、PbWO4、金刚石等晶体拉曼介质陆续进行了实验研究[106-111],所得输出光脉冲能量主要集中在毫焦量级,单脉冲能量最高为71.5 mJ,由王聪等人[109]在2014年通过BaWO4拉曼放大器实现,实验装置如图8所示。晶体共线拉曼放大器的输出光脉宽集中在纳秒、皮秒等量级,最小输出光脉宽约6 ps,由Yakovlev等人[107]在2009年通过YVO4拉曼放大器实现。2019年,刘兆军等人[112]成功将晶体拉曼放大技术应用于钠信标光源领域,结合CaWO4晶体拉曼放大器和倍频技术实现了单脉冲能量8.2 mJ、线宽1.3 GHz的589.159 nm 钠黄光,光束质量因子小于1.5。
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在非共线拉曼放大条件下,拉曼增益因子会随输入光夹角的增加而下降。在2017年, McKay等人[66]推导了非FWM相位匹配条件下有效增益gnc与波束偏移b的关系,通过公式gnc=g0 exp(−b2/2)I0(b2/2)来表示该变化关系。其中,g0是拉曼增益系数,I0(x)是第一类零阶修正贝塞耳函数。随着泵浦光与种子光夹角的增大,波束偏移b增大,有效增益gnc迅速下降。若拉曼放大器中种子光与泵浦光通过FWM相互作用,仅在种子光与泵浦光满足相位匹配条件下,拉曼光增益效果最佳。徐洋等人[113]在2013年以YVO4晶体为拉曼介质研究了通过四波混频实现的拉曼放大与输入光夹角的变化关系,实验装置如图9所示。他们发现无论是正三阶Stokes光,还是反三阶Stokes光,只要偏离相位匹配角超过0.5°,输出光功率密度都会大幅度下降。此外,晶体非共线拉曼放大器的输出脉宽目前主要集中在纳秒、皮秒、百飞秒量级,最小脉宽约100 fs,由Grigsby等人[114]在2008年通过双通结构下的Ba(NO3)2非共线拉曼放大器实现。
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与气体拉曼激光组束相比,晶体拉曼激光组束减轻了线宽和热负载的约束以及相干光束组合的相位约束。晶体拉曼激光组束目前主要采用串行组束结构和并行组束结构,其中串行组束结构使系统的负载能力得到了大幅提高,实际操作性较强,且可以通过结构优化对系统进行升级。2013年,Kulagin等人[115]实现了以Ba(NO3)2为拉曼介质的串行拉曼激光组束,通过布里渊和拉曼脉冲压缩产生了脉宽约30 ps、单脉冲能量50 mJ的1530 nm脉冲输出,光束质量接近衍射极限(M2≤1.2)。在2015年,Men等人[116]采用CaWO4晶体进行了串行激光组束实验,实现了单脉冲能量26.7 mJ、峰值功率5.2 MW的1178 nm单频激光脉冲输出。在2019年,Liu等人[117]以BaWO4为拉曼介质实现了串行组束,获得了脉宽44.1 ns、单脉冲能量41.0 mJ的1178 nm单频激光脉冲输出,实验装置如图10所示。
采用拉曼晶体进行并行激光组束的实验目前较少,但同样是获得高功率特殊波段激光输出的有效方法。在2017年,McKay等人[66]采用金刚石晶体进行了并行拉曼激光组束实验,得益于金刚石晶体的优良特性[118-121],实现了峰值功率8.78 kW的拉曼激光输出,实验装置如图11所示。
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表2总结了部分晶体拉曼放大器的实验参数,晶体拉曼放大器的脉宽已经覆盖纳秒、皮秒至飞秒量级,峰值功率已达到GW量级、单脉冲能量达到毫焦耳量级。相较于气体拉曼放大器,晶体拉曼放大器的体积小,在实际应用中更具有优势,但是受限于拉曼晶体尺寸等因素其输出能量较低。晶体拉曼放大器的最大单脉冲能量为71.5 mJ,小于气体拉曼放大器的最大单脉冲能量。未来晶体拉曼放大器发展方向主要在于开发新型拉曼晶体、优化大尺寸晶体制备技术以及优化放大器结构。
表 2 晶体拉曼放大器研究进展
Table 2. Research progress of crystalline Raman amplifier
Year Raman medium Structure Pump wavelength/
μmStokes wavelength/
μmOutput energy/
mJPulse
duration/nsPeak
power/MWRef. 2008 Ba(NO3)2 Collinear amplifier 1.064 1.197 63 - - [106] 2008 Ba(NO3)2 Non-collinear amplifier 0.800 0.873 3 10−4 30000 [114] 2009 YVO4 Collinear amplifier 1.064 1.174 3×10−3 6×10−3 0.5 [107] 2013 Ba(NO3)2 Serial laser beam combination 1.319 1.530 50 3×10−2 1667 [115] 2014 BaWO4 Collinear amplifier 1.064 1.180 71.5 17 4.2 [109] 2014 PbWO4 Collinear amplifier 1.064 1.178 11 - - [110] 2015 CaWO4 Serial laser beam combination 1.064 1.178 26.7 2.9 9.2 [116] 2015 Diamond Collinear amplifier 1.064 1.240 - - 0.00696 [111] 2015 Diamond Parallel laser beam combination 1.064 1.240 - - 0.00878 [66] 2018 BaWO4 Collinear amplifier 1.062 1.178 3.5 - - [89] 2019 BaWO4 Serial laser beam combination 1.062 1.178 41.0 44.1 0.93 [117]
Research progress of high-power free-space Raman amplification technology (invited)
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摘要: 高功率特殊波段激光在钠信标、激光测距、激光雷达、自由空间通信等领域具有重要的应用价值。目前,基于受激拉曼散射(stimulated Raman scattering, SRS)的拉曼激光器及放大器已经被证实为拓展激光波段和功率的有效途径。不同于基于粒子数反转激光器在产生和放大过程中需匹配激光增益介质固有的吸收和发射谱,SRS过程理论上能够在其拉曼增益介质透过光谱的全范围内工作,故只需要相互作用光束的频率差满足拉曼增益介质的固有频移,便可实现光束之间的能量直接转移。因此,拉曼放大技术能够利用常规波段的泵浦光对特殊波段的种子光进行放大,从而实现高功率、大能量、高光束质量的特殊波段激光输出。该方法具备波长选择灵活、结构简单、功率拓展性强等优点,近年来已经在钠信标光源等领域得到了应用。文中综述了高功率自由空间拉曼放大技术的主要原理、特性和研究进展,并对其发展趋势和应用前景进行了展望。Abstract:
Significance Lasers with special wavelengths, high power, and high beam quality have significant applications in the fields such as sodium guide star, laser ranging, and free-space communication. One of the effective approaches to extend the spectral range of lasers is based on stimulated Raman scattering (SRS), which can amplify Stokes beam with a desired wavelength using conventional pump sources. This method can produce high-power and high-quality lasers with special wavelengths, and has advantages such as flexible wavelength selection, simple structure, and strong power scalability. In recent years, SRS-based amplifiers have been applied to generate sodium guide star laser sources, and have potential for further development in other areas. This article reviews the main principles, characteristics, and research progress of high-power free-space Raman amplification technology, and discusses its future trends and application prospects. Progress Currently, the commonly used gain media for Raman amplifiers include gases and crystals. Gas Raman media have advantages such as a large Raman frequency shift, low self-focusing threshold, low optical coupling wave loss, and almost unlimited size. However, they also have disadvantages such as low gain, large volume, and susceptibility to optical breakdown. Compared to gas Raman media, crystal Raman media have advantages such as high Raman gain coefficient, good thermal conductivity, stable performance, and easy miniaturization. However, there are still bottlenecks in the output power and energy of crystalline Raman amplifiers due to factors such as crystal size and damage threshold. Beam combination based on Raman amplification is also an important way to break through the power bottleneck of a single beam and achieve power scaling. This method has advantages such as simple structure, flexible design, and high expandability, and is expected to be further developed and applied in the field of high-power special wavelength lasers. The parameters of gas Raman amplifiers with free-space structures are summarized (Tab.1). At present, the peak laser power output has reached the megawatt level, and the single pulse energy has reached the joule level. The experimental parameters of some crystal Raman amplifiers are summarized (Tab.2). The pulse width of crystal Raman amplifiers is mainly in the nanosecond, picosecond, and femtosecond levels, with peak power reaching the gigawatt level and single pulse energy reaching the millijoule level. Conclusions and Prospects In recent decades, Raman amplifiers in free space have made many outstanding achievements in the field of high-power special wavelength lasers. However, the output power of Raman amplifiers is still limited by factors such as the Raman medium and amplifier structure. To overcome these limitations, future developments in Raman amplification technology will focus on developing new Raman media, optimizing the preparation technology of large-size Raman crystals, improving the conversion efficiency of Raman amplifiers, and expanding the beam combination structure of high-power Raman lasers. In the future, Raman amplification technology is expected to achieve even greater results in the field of high-power special wavelength lasers. -
Key words:
- stimulated Raman scattering /
- laser /
- amplifier /
- pulse /
- beam combination
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表 1 气体拉曼放大器研究进展
Table 1. Research progress of Raman amplifier in gas
Year Raman
mediumStructure Pump
wavelength/μmStokes
wavelength/μmOutput
energy/mJPulse
duration/nsPeak
power/MWRef. 1979 H2 Beam combination 1.06 1.13 360 3 120 [100] 1980 CH4 Beam combination 0.248 0.268 - 7 - [98] 1983 H2 Collinear amplifier 0.308 0.353 20 50 4 [81] 1986 CH4/H2 Beam combination 0.249 0.268/0.277 8400/5000 - - [101] 1989 H2 Beam combination 0.353 0.414 800 - - [99] 1996 H2 Collinear amplifier 0.390 0.465 0.02 0.00035 57.1 [73] 2001 CH4 Collinear amplifier 0.248 0.268 - 5 - [83] 2009 D2 Collinear amplifier 1.064 1.560 250 4 62.5 [79] 2016 H2 Collinear amplifier 1.06 1.9 44 - - [80] 表 2 晶体拉曼放大器研究进展
Table 2. Research progress of crystalline Raman amplifier
Year Raman medium Structure Pump wavelength/
μmStokes wavelength/
μmOutput energy/
mJPulse
duration/nsPeak
power/MWRef. 2008 Ba(NO3)2 Collinear amplifier 1.064 1.197 63 - - [106] 2008 Ba(NO3)2 Non-collinear amplifier 0.800 0.873 3 10−4 30000 [114] 2009 YVO4 Collinear amplifier 1.064 1.174 3×10−3 6×10−3 0.5 [107] 2013 Ba(NO3)2 Serial laser beam combination 1.319 1.530 50 3×10−2 1667 [115] 2014 BaWO4 Collinear amplifier 1.064 1.180 71.5 17 4.2 [109] 2014 PbWO4 Collinear amplifier 1.064 1.178 11 - - [110] 2015 CaWO4 Serial laser beam combination 1.064 1.178 26.7 2.9 9.2 [116] 2015 Diamond Collinear amplifier 1.064 1.240 - - 0.00696 [111] 2015 Diamond Parallel laser beam combination 1.064 1.240 - - 0.00878 [66] 2018 BaWO4 Collinear amplifier 1.062 1.178 3.5 - - [89] 2019 BaWO4 Serial laser beam combination 1.062 1.178 41.0 44.1 0.93 [117] -
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