1.Key Laboratory for Laser Plasmas (Ministry of Education) and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China 2.IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 61675129, 61275136, 61138006, 11121504).
Received Date:25 February 2019
Accepted Date:22 April 2019
Available Online:01 August 2019
Published Online:05 August 2019
Abstract:The shock ignition scheme has the advantages of low ignition energy threshold, high gain, and good hydrodynamic stability, which has become one of the key schemes for the potentially successful ignition of inertial confinement fusion. The crucial element of shock ignition is how to achieve a highly efficient shock laser pulse. We propose a new scheme based on a time-lens system combining the fiber-loop phase modulation and the grating-pair compression to generate a highly controllable shock pulse. Based on the asymmetric phase modulation in time-domain followed by linear dispersion compensation in frequency domain, the shock pulse can be actively controlled with high precision in both pulse duration and pulse contrast (peak power ratio of the compression part to the shock part of the pulse). We construct a theoretical model based on the nonlinear Schr?dinger equation to simulate the evolution of the spectrum and temporal shape of the shock laser pulse. The influences of various key parameters of the proposed system on the characteristics of the generated shock pulse are analyzed in depth. The time lens system consists of three parts, i.e. the seed pulse carving part, the phase modulation loop, and the chirp-compensating grating pair. The operation principle of this system for generating shock pulse is as follows. First, a single-mode continuous wave 1053 nm distributed feedback seed laser is chopped into pulses with a Mach-Zehnder intensity modulator. Then the pulses enter into a fiber-loop for phase modulation. Owing to different modulation frequencies exerted on the left and right side of the pulse, the amount of spectral broadening of these two sides of the spectrum are also different after phase modulation. The spectrally broadened pulses are linearly chirped when the phase-modulation function has a parabolic shape. Finally, the pulse transits through a grating pair system for chirp compensating. Just like an anomalous dispersion delay line, the grating pair applies an anomalous group velocity dispersion to the passing optical pulse. When the chirp is compensated for appropriately, the pulse will be compressed. What the target pulse can be finally shaped into is dependent on the combined optimization of all the above processes.The simulation results show that by systematically designing the parameters such as chopping function, phase modulation function, modulation depth, modulation frequency, and chirp compensating, the target shock pulse can be actively controlled with high-precision in the pulse width, pulse rising edge, and peak-power contrast. In addition, we can also tune only one parameter (such as the pulse width) of the pulse, with the other parameters kept unchanged. This new design idea and the proposed system can actively and independently adjust the two key parameters (the peak power contrast and the pulse width) of the generated shock pulse, which is not only helpful in deepening our understanding of the principle of laser-pulse shaping, but also significant for the subsequent practical implement of shock ignition of inertial confinement fusion. Keywords:shock ignition/ shock pulse/ time-lens/ electro-optic modulation
3.模拟结果与分析影响时间透镜系统最终输出的冲击脉冲特性的主要因素有初始斩波脉冲的特性、相位调制函数的调制频率、调制深度、光栅对压缩量等. 本节主要阐述产生冲击脉冲的具体设计方案以及分析影响冲击脉冲特性的关键因素. 首先利用强度调制器斩波出脉宽大约1.06 ns、频谱宽度大约为0.0045 nm的超高斯脉冲(如图2所示). 图 2 强度调制器斩波出的脉冲频谱(a)与波形(b) Figure2. Spectrum (a) and pulseshape (b) of the seed laser after the intensity modulator.
图4是经过相位调制器后的频谱信号与输出脉冲波形. 图4(a)表示输出频谱信号. 随着环绕圈数的增加, 频谱宽度不断增加. 相位调制函数右侧对应的是短波信号, 即蓝移分量, 左侧对应的是长波信号, 即红移分量. 在图3所示的相位调制函数调制下(右侧调制频率大于左侧调制频率), 短波对应的频谱展宽量会大于长波对应的频谱展宽量. 由于能量守恒的原因, 所以图4(a)频谱图中左侧短波信号对应的幅值小于右侧长波对应的幅值. 当环绕圈数达到55圈时, 光谱会发生细微振荡, 这是因为脉冲宽度也在不断增加, 相位调制函数已经不能够完全调制脉冲(脉冲边缘部分没有被调制), 由于光纤的非线性效应(自相位调制)和色散相互作用导致光谱振荡. 图4(b)表示的是输出脉冲信号. 由于光纤的正常色散特性, 脉冲经过光纤环内循环多圈后, 脉冲宽度会展宽. 由于光纤的色散对称地施加于脉冲频谱两侧, 而宽频谱展宽量的脉冲部分获得的色散量更大, 使得脉宽展宽更大, 因此经过光纤色散后输出的脉冲信号的两侧脉宽都展宽, 但是右侧相对展宽更大, 从而也导致右侧的强度幅值小于左侧的强度幅值. 图 4 考虑色散与非线性效应时脉冲信号经过光纤环不同圈数相位调制之后的频谱(a)与脉冲(b) 的演化 Figure4. Evolution of the spectrum (a) and shape (b) of the pulse after different round trips of phase modulation (before compression) when the dispersion and nonlinear effects of fibers are included.
23.1.光栅对的间距对冲击脉冲特性的影响 -->
3.1.光栅对的间距对冲击脉冲特性的影响
光栅对实际上类似于反常色散延迟线, 即对脉冲信号施加反常色散. 对于拥有正啁啾的脉冲信号经过此光栅对时, 脉冲宽度就会被压缩. 如图4(a)所示, 短波对应的频谱展宽量比长波更大, 因此脉冲在经过光栅对压缩时, 短波更容易被压缩, 所以短波部分对应的强度幅值大于长波部分对应的强度幅值, 于是在时域上便被调制出冲击脉冲形状. 对于拥有一定频谱展宽的脉冲再利用光栅对进行压缩时, 该压缩量必然有一个范围, 超过这个范围, 脉冲就会发生分裂和振荡. 脉冲压缩量逐渐增大时, 压缩脉冲与冲击脉冲的宽度都会被压缩且冲击脉冲的峰值功率的对比度也会相应地发生改变. 在本系统中, 控制光栅对角度不变, 通过改变光栅对的间距来调节了光栅对提供的压缩量. 如图5所示, 随着光栅对距离的增大, 光栅对所提供的压缩量越大, 则其压缩输出的脉冲宽度越窄, 同时冲击脉冲峰值功率的对比度越大. 当光栅对的距离为3 m时, 冲击脉冲功率与压缩脉冲的功率之比约为2︰1, 且冲击脉冲的宽度约为100 ps, 符合冲击点火对冲击脉冲宽度的要求. 当光栅对的距离为3.5 m时, 由于光栅对提供的压缩量相对较大造成了过度压缩, 因此冲击脉冲峰值处逐渐发生分裂, 脉冲波形也产生了畸变(如图5插图所示). 因此, 在采用光栅对进行脉冲压缩时, 并不是压缩量越大越好, 需要根据冲击脉冲的特性而设计出相应的压缩参数方案. 图 5 不同光栅对距离对最终输出脉冲的影响(光纤环环绕圈数设定为55圈, 光栅对角度设定为30°) Figure5. Final output pulse shape with different grating-pair distance settings (the number of fiber loops is set to 20 turns and the grating pair angle is set to 30 degrees).
式中, 参量T0为脉冲功率最大值一半处的全宽度; τ采用纳秒单位(10–9 s); m为输入函数的阶数, 主要决定了脉冲前后沿的陡度; X和m共同决定输入脉冲的宽度. m = 1, 就是高斯脉冲情形, 如果m值较大, 函数就对应为前后沿陡峭的方形脉冲. 而输入脉冲宽度越小, 相应的有效相位调制频率就越大, 因此在同等的相位调制次数下, 脉冲获得的频谱展宽量就越大, 脉冲更容易被压缩. 模拟过程中, 控制X = 1.7, 脉冲在光纤环中环绕圈数不变(55圈), 控制光栅对参数不变($ \vartheta $ = 30°, d = 3 m), 分析输入脉冲波形对最终产生的冲击脉冲特性的影响. 如图6所示, 随着初始斩波脉冲边缘陡峭度的增加(波形函数阶数增加), 脉冲光谱的展宽宽度也逐渐增大, 最终压缩输出的脉冲宽度越窄, 冲击脉冲与压缩脉冲峰值功率的对比度也越高(1.25—2.5). 图6其实也说明了调制频率对冲击脉冲性能的影响, 因为脉冲越陡峭得到的有效调制频率越高, 频谱展宽量越大, 在同等压缩量下, 脉冲更容易被压缩. 图 6 输入脉冲陡峭度对经过时间透镜系统之后的频谱展宽(a)和脉冲波形(b)的影响 Figure6. Influences of the input pulse shape (different orders of Gaussian function) on the spectrum (a) and pulse shape (b) of the output pulse after being operated by the time lens system.
23.3.频谱展宽量对冲击脉冲性能的影响 -->
3.3.频谱展宽量对冲击脉冲性能的影响
上述分析表明, 当脉冲获得不同的频谱展宽量时, 必须要计算出光栅对提供的合适压缩量才能产生特定性能指标的冲击脉冲. 影响频谱展宽量的因素主要有单次相位调制的展宽量与相位调制的次数. 影响单次相位调制展宽量的主要因素是相位调制深度与调制频率. 本文研究通过控制光栅对参数不变($ \vartheta $ = 30°, d = 3 m), 将不同频谱展宽量的脉冲经过相同的光栅对压缩参数进行脉冲压缩, 从而将输出的脉冲进行对比. 本节控制初始斩波脉冲函数不变、相位调制频率不变, 通过改变相位调制深度和调制次数来改变光谱的展宽量. 图7中输入函数X = 1.7, m = 5, 左侧调制频率fl设定约为1.17 GHz、右侧调制频率fr设置约为1.31 GHz、控制光栅对参数不变($ \vartheta $ = 30°, d = 3 m), 图7(a)表示相位调制次数设定55圈时, 相位调制深度越大, 则脉冲经过相位调制之后的频谱展宽越大, 当调制深度取为40, 此时调制函数已经无法完全调制脉冲信号函数, 因此频谱产生振荡. 图7(b)表示的是脉冲频谱展宽量越大, 脉冲越容易被压缩, 但是一旦压缩过量, 脉冲就会产生畸变. 图7(c)表示相位调制深度取30时, 相位调制次数越多, 则脉冲经过相位调制之后的频谱展宽越大. 图7(d)表示经过特定压缩量下输出的冲击脉冲信号, 相位调制次数越多时(光谱展宽越大)脉冲压缩后的脉宽越窄、对比度越高. 图 7 压缩量一定时, 频谱展宽量不一样时被压缩输出后的脉冲 (a), (b) 表示调制深度不同的情况下, 频谱展宽与被压缩输出后的脉冲; (c), (d) 表示相位调制次数不同, 频谱展宽与被压缩输出后的脉冲 Figure7. Output pulse after different amount of spectrum broadening when the amount of compression is constant: (a), (b) Broadening spectrum and the output pulse after different modulation depth; (c), (d) the broadening spectrum and output pulse after different round trips.
23.4.产生特定冲击脉冲波形的参数设计方案 -->
3.4.产生特定冲击脉冲波形的参数设计方案
在具体使用冲击点火方案时, 可能会根据现场实验条件而选择不同指标的冲击脉冲. 基于以上分析, 影响冲击脉冲性能指标的因素有初始斩波函数、相位调制函数、光栅对压缩等参数, 因此通过优化组合设计上述参数达到保证冲击脉冲宽度一定时独立控制冲击脉冲峰值功率对比度、或者保证冲击脉冲峰值功率对比度一定时独立控制冲击脉冲宽度将对灵活控制最终的实验效果具有参考意义. 如果光栅对的压缩量不变, 那么经过相位调制之后的频谱展宽中, 仅有在短波(蓝移分量)的频谱展宽量也保持不变的情况下, 冲击脉冲的宽度与冲击脉冲对应的强度幅值才会保持不变, 此时仅需要调节长波(红移分量)的频谱展宽量, 即可单独控制冲击脉冲峰值功率的对比度. 如果冲击脉冲的脉宽发生变化, 则其对应的强度幅值也会发生变化. 在这种情况下, 必须综合调节短波长部分的频谱展宽量、光栅对的压缩量才能保持冲击脉冲峰值功率对比度不变. 因此通过斩波函数、相位调制函数、光栅对压缩量的综合参数设计才能保证冲击脉冲峰值功率对比度一定时独立控制冲击脉冲宽度. 图8(a)中, 斩波函数中X = 1.7, 高斯阶数m = 5, 相位调制函数中调制深度为30, 右侧调制频率fr设置约为1.31 GHz, 光纤环的环绕圈数为55, 控制光栅对参数不变($ \vartheta $ = 30°, d = 3 m), 通过调节左侧调制频率, 本时间透镜系统最终可以实现对控制冲击脉冲的脉宽不变而单独调节冲击脉冲峰值功率的对比度. 图8(b)中, 斩波函数中高斯阶数m = 5, 相位调制函数中调制深度为30, 光纤环的环绕圈数为55, 光栅对的角度保持不变($ \vartheta $ = 30°). 通过调节输入斩波函数的X变量、左侧调制频率、右侧调制频率、光栅对的间距, 最终可以实现保持冲击脉冲的峰值功率的对比度不变而单独调控冲击脉冲宽度. 图 8 不同参数设计下最终压缩输出的脉冲 (a) 控制冲击脉冲宽度不变, 改变冲击脉冲峰值功率对比度; (b) 控制冲击脉冲峰值功率之比不变, 改变冲击脉冲宽度 Figure8. Final output pulse under different combined-parameter design: (a) Tuning the ratio of the peak power of the shock pulse and the compress pulse while keeping the shock pulse width unchanged; (b) modifying the shock pulse width while keeping the ratio of the peak power of the shock pulse to the compress pulse unchanged.