1.Joint Laboratory of High Power Laser and Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China 2.Shanghai Institute of Laser Plasma, China Academy of Engineering Physics, Shanghai 201800, China 3.Changzhou Institute of Technology, School of Sciences, Changzhou 213032, China 4.Shanghai Institute of Laser Technology, Shanghai 201800, China 5.Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:Project supported by the Key Projects of Special Development Funds for Zhangjiang National Innovation Demonstration Zone (Grant No. ZJ2020-ZD-006)
Received Date:03 November 2020
Accepted Date:22 February 2021
Available Online:10 May 2021
Published Online:20 May 2021
Abstract:In order to accurately analyze the broadband pulsed amplification performances of the domestic picosecond petawatt laser system, which uses large aperture N31 or N41 neodymium glass as gain medium, the broadband pulsed amplification model is improved by introducing the actual stimulated emission cross section (SECS) of neodymium glass. Comparing with the SECS under Gaussian approximation, the amplified pulsed spectrum gain narrowing effect with different SECSs are analyzed. It is found that in the actual SECS of N31 neodymium glass laser, the gain-narrowing effect is enhanced, the output energy decreases, gain’s saturation effect weakens, system’s accumulated B integral augments, but the laser system turns insensitive to the center wavelength simultaneously. Based on the Shenguang II high energy picosecond petawatt laser system which uses N31 neodymium glass, the spectral shape, center wavelength, and energy stability of amplified output pulse are simulated by using different SECSs. It is shown that the super-Gaussian spectral shape narrows more greatly than Gaussian spectral shape, the spectrum bandwidth narrows from 10 to about 3 nm with gain larger than 107, and the accumulated B integral increases to 1.7. Additionally, the gain-narrowing effect makes the output spectrum (with 1054 nm of center wavelength) less affected by changing the inputted center wavelength from 1052 to 1056 nm, and the gain saturation effect can improve output energy stability to less than 2% (root mean square (RMS)) with about 3% (RMS) inputted energy stability, which are beneficial to the subsequent pulse compression and physical experiment. Based on the above analysis, a broadband pulsed amplified experiment is conducted by using Shenguang II petawatt laser system, the injected seed is about 10 nm (full width at half maximum (FWHM)) with 5 order super Gaussian shape at 1054-nm center wavelength, and 1.2 mJ with 3% (RMS) energy stability from optical parametric chirped pulse amplification. The amplified pulse with 1900 J at 1054.2 nm (3 nm FWHM) and stability < 2% (shot to shot) is achieved, and the spectral shapes and bandwidths after bar and disk amplifiers are measured, which are consistent with theoretical analysis results. The results can provide a necessary reference for constructing high energy broadband laser system and improving its performances in the future. Keywords:high energy broadband laser/ picosecond petawatt laser system/ neodymium glass/ stimulated emission cross section/ gain narrowing
$B\left( t \right) = \frac{{2{\rm{\pi }}}}{{{\lambda _0}}}\int_0^L {{n_2}} \left( z \right)I\left( {z,t} \right){\rm{d}}z,$
式中, ${\lambda _0}$为宽带激光中心波长; $L$为增益介质长度; ${n_2}$为增益介质的非线性折射率; $I(z, t)$为激光脉冲传输到$z$位置时对应的光强. 本文中考虑的B 积分为最大B 积分, 没有考虑不同波长权重对 B 积分的影响[24]. 国内N31 型磷酸盐钕玻璃的SECS[25,26]与高斯近似下的SECS (为描述方便, 后文简称实际SECS 和高斯SECS)如图1所示. 从图1中可以看出, 虽然两种情况具有相同的1054 nm中心波长和20 nm带宽(FWHM), 但是实际SECS(蓝实线)为非对称结构, 形状更为尖锐. 图 1 国内N31型磷酸盐钕玻璃实际SECS和高斯近似SECS对比 Figure1. The compared SECSs between real N31 glass and Gaussian approximation.
在利用高斯SECS分析增益窄化等物理过程时, (1)式—(4)式存在解析解, 便于研究宽频带放大过程的物理规律, 但与实际SECS相比, 会存在差异. 为此, 首先我们校核了数值程序的准确性. 对于高斯型光谱注入(图2(a))和高斯SECS的情况[20], 在小信号增益下, 输出光谱宽度可以用公式${1/ {\Delta {\lambda ^2}}} = {{\ln {G_0}}/ {{\Delta ^2}}} + {1/ {\delta {\lambda ^2}}}$ ($\Delta \lambda $, $\Delta $和$\delta \lambda $分别为输出谱宽, 高斯SECS 宽度和注入光谱带宽, ${G_0}$ 为小信号增益倍数) 来描述, 输出光谱宽度与增益的变化趋势如图2(b)中的红点线(解析解)和绿短线(数值解)所示, 而实际SECS下的光谱窄化趋势如图2(b)中的蓝实线(数值解)所示. 可以看出, 与高斯SECS相比, 实际SECS会加剧光谱的窄化. 因此, 如果采用高斯SECS分析、设计宽频带激光输出特性, 必然会带来偏差, 进而影响实际装置性能评估. 为了更加准确地分析宽频带激光的放大特性, 将针对神光II高能拍瓦宽频带激光系统, 深入对比不同SECS对宽频带放大光谱特性及装置性能分析结果的影响. 图 2 小信号增益下, 10 nm (FWHM)高斯型光谱注入时, 不同SECS下增益窄化分析结果的对比 (a) 10 nm (FWHM)高斯光谱注入; (b) 高斯SECS和实际SECS下光谱窄化分析结果对比 Figure2. In small-signal-gain regime and input of 10 nm (FWHM) Gaussian spectrum, the compared results of gain narrowing by different SECSs: (a) Input of 10 nm(FWHM) Gaussian spectrum; (b) the results of gain narrowing by Gaussian SECS and real SECS.
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3.1.小信号近似下, 不同SECS增益窄化对放大激光谱宽的影响
首先分析了不同SECS作用时, 增益窄化效应对输出光谱宽度的影响, 注入光谱如图3(a)所示, 输出结果如图3(b)所示. 由图3可以看出, 当增益为107时, 宽频带放大输出的光谱宽度分别为5 nm (对应约350 fs压缩极限脉宽)和3 nm(对应约500 fs压缩极限脉宽). 实际SECS明显地加剧了增益窄化效应. 图 3 采用不同SECS时, 增益窄化对输出光谱宽度影响的对比分析 (a) 10 nm(FWHM), 5阶超高斯注入光谱; (b)采用高斯SECS和实际SECS时, 光谱窄化分析结果对比 Figure3. The influence results of gain narrowing to spectrum bandwidth by different SECSs: (a) Input of 10 nm (FWHM), 5-order super-Gaussian spectrum; (b) the compared gain narrowing results between Gaussian SECS and real SECS.
23.2.增益饱和下, 不同SECS对放大光谱形状、中心波长、谱宽和能量的影响 -->
3.2.增益饱和下, 不同SECS对放大光谱形状、中心波长、谱宽和能量的影响
在宽频带激光放大过程中, 为了获得高的能量提取效率, 提高输出稳定性, 激光放大需要进入饱和放大区域, 伴随的增益饱和效应会导致脉冲时间前沿消耗更多的上能级粒子数, 由此对脉冲时间波形和光谱形状同时产生作用, 进而影响宽频带激光的放大特性. 下面, 对比在增益饱和情况下, 不同SECS对放大光谱形状、中心波长、谱宽、上能级粒子数变化和输出能量的影响. 当宽频带激光注入能量为1.2 mJ 时(放大链路棒放和片放全部开启, 对应系统输出约2 kJ), 分别分析了棒放输出(图4(a)和图4(b))和片放输出位置(图4(c)和图4(d))的放大光谱形状及上能级粒子数变化情况, 结果如图4所示. 从图4可以看出: 1) 棒放输出位置, 从上能级粒子数变化的趋势来看, 此时饱和效应不明显, 属于高增益放大阶段, 由此带来的光谱中心红移较小; 2) 片放输出位置, 从粒子数变化来看, 饱和效应的影响增强, 对于高斯SECS, 光谱中心红移至1055.5 nm, 而对于实际SECS, 其中心波长为1054.2 nm, 中心波长并未发生明显红移, 这主要是由实际SECS(图1所示)非对称结构和饱和效应共同决定的. 图 4 不同SECS 下, 棒放(a), (b)和片放(c), (d)输出光谱形状及上能级粒子变化分析结果的对比 Figure4. The compared numerical results of spectrum and upper state population after 70 (a), (b) and 350 (c), (d) amplifier, which influenced by different SECSs.
表1注入1.2 mJ, 5 ns, 10 nm宽带种子, 不同SECS下, 棒放和片放输出位置主要参数分析结果对比. Table1.Input a 1.2 mJ, 5 ns, 10 nm broadband seed, and the main simulation parameters after bar and disk amplifier, which influenced by different SECSs.
23.3.不同SECS下, 注入中心波长偏移和能量抖动对装置性能的影响 -->
3.3.不同SECS下, 注入中心波长偏移和能量抖动对装置性能的影响
首先, 分析了注入宽带种子中心波长分别为1052 nm (黑实线), 1054 nm (红点线)和1056 nm (绿短线), 如图5(a)所示, 采用高斯SECS和实际SECS分析时, 片放位置输出光谱特性的对比结果, 分别如图5(b)和图5(c)所示, 其他参数与图4(c)相同. 从图5(a)可以看出: 在SECS的有效区域内, 注入种子中心波长的变化并不会严重影响输出光谱特性, 只会导致光谱前后沿略有起伏. 而且, 由于实际SECS下的光谱窄化更严重, 使得有效放大的光谱范围更小, 这进一步地降低了对注入光谱中心波长的要求. 图 5 不同SECS下, 注入种子中心波长变化对放大光谱特性的影响, 其他参数与图4(c)相同 (a) 不同中心波长的注入光谱; (b) 高斯SECS下的放大光谱; (c) 实际SECS下的放大光谱 Figure5. The influences of different inputted center wavelength spectrums to amplified spectrum by different SECSs: (a) Input spectrums of different center wavelength; the amplified spectrums by Gaussian SECS (b) and real SECS (c).
其次, 分析了不同SECS下, 宽频带放大输出能量抖动与输入能量抖动性的关系. 选取注入能量抖动(相对1.2 mJ, ± 10%)与输出能量抖动的关系如图6所示, 其他参数与图4(c)相同. 从图6可以看出: 当输入能量抖动在 ± 10%变化时, 输出抖动在 ± 6%以内, 而且高斯SECS分析结果稳定性优于实际SECS情况, 这主要是由于增益饱和效应带来的好处, 饱和程度越大(如图4(d)), 输出稳定性越好; 进一步地, 由于皮秒拍瓦宽频带激光系统要求累积B积分小于2, 直接限制了2 kJ输出能量和进入饱和放大区域的程度, 此时输出的能量稳定性只能依靠注入宽带种子源的稳定性来保障, 对于目前预放注入为3% (RMS)的稳定性来说, 理论上输出能量稳定性可以控制在2% (RMS)以内. 图 6 不同SECS 下, 宽频带激光放大输出和输入能量抖动性的分析曲线对比 Figure6. The simulation relationship between input and output energy jitter by different SECSs.
图 8 10 nm(FWHM), 5阶超高斯光谱注入, 输出1866 J时, 棒放和片放位置的实验数据与图4理论分析结果的对比 (a) 输入光谱实验及拟合数据; 棒放(b)和片放(c)位置光谱对比 Figure8. The compared results between experiment and simulation results after bar and disk amplifiers: (a) The compared input spectrums of experiment and simulation; the compared spectrum results after rob amplifier (b) and disk amplifier (c).
参数
发次1
发次2
发次3
发次4
实际输出/J
1482
1642
1711
1866
光谱宽度/nm
3.1
3.2
3.0
3.0
中心波长/nm
1054
1054
1054.1
1054.2
预估能量/J
1500
1650
1700
1900
偏差/%
1.2
0.5
0.6
1.8
表2利用神光II高能拍瓦宽频带激光系统得到的实验数据. Table2.The experiment results of amplified broadband laser by using SG II PW laser amplification chain.