1.Key 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.Innovation Research and Development Center, Shanghai Institute of Laser Technology, Shanghai 201800, China 4.Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:Project supported by the Major Program of the Zhangjiang National Innovation Demonstration Zone Special Development Fund, China (Grant No. ZJ2020-ZD-006)
Received Date:16 October 2020
Accepted Date:20 November 2020
Available Online:05 April 2021
Published Online:20 April 2021
Abstract:In recent years, chirped pulse amplification (CPA) technology injects vitality into the development of ultra-strong and ultra-short lasers. However, in the CPA based gain media, the gain narrowing effect limits the higher output of ultrashort pulse in energy, power, signal-to-noise ratio. In order to compensate for the gain narrowing caused by the broadband amplification of Nb:glass in picosecond pewter laser system, a method of high-energy spectral shaping is proposed based on LiNbO3 birefringent crystal, and the spectral phase introduced by the crystal is analysed for the first time. Based on the strict Jones matrix, the transmittance function of birefringent crystal and the spectral phase introduced by the crystal are obtained. Further, three kinds of birefringent crystals are compared among each other, and the results show that the higher birefringence and the smaller thickness are required to achieve the same intensity modulation. For the laser pulse at 1053 nm, LiNbO3 is selected as the spectral shaping crystal due to its high birefringence, large diameter, and non-deliquescent. The influences of crystal thickness, tilt angle, and in-plane rotation angle on the spectral intensity modulation are simulated theoretically, and the results show the above parameters affect the modulation bandwidth, center wavelength, and modulation depth of the shaping. By analyzing the spectral phase introduced by the crystal, it is found that the dispersion of each order changes with the thickness of the crystal, the tilt angle, and the in-plane rotation angle, and it is the most sensitive to the change of thickness. In addition, by controlling the dispersion of each order, the influence on the pulse signal-to-noise ratio can be weakened during spectrum shaping. On the basis of theoretical analysis, the shaping experiment with a center wavelength of 1053 nm, modulation bandwidth of 10 nm, and modulation depth of 80% is carried out. And the phase introduced by the LiNbO3 is measured. The experimental results are consistent with the theoretical analysis. For the Shenguang Ⅱ high-energy petawatt laser system, by the above-mentioned shaping scheme, a high-energy broadband laser output of 1700 J and 6 nm (FWHM) is realized for the first time in China, which is 2 times that at 3.2 nm when it is not shaped. The research effectively compensates for the Nb:glass gain narrowing effect, and will provide references for the parameter design, material selection and spectral phase compensation in the birefringent spectral shaping. Keywords:high-energy spectral shaping/ birefringent crystal/ spectral phase/ high-energy petawatt laser system
双折射晶体通过在放大介质增益中心波长处增加损耗来抑制增益窄化效应, 即双折射晶体透过率函数在放大介质增益线型的中心波长处透过率低, 在中心波长两侧, 增益相对较小处透过率高, 以此来补偿放大过程中的增益窄化. 从(6)式可以看出, 透过率函数除了与晶体厚度t、倾斜角θ、面内旋转角?有关外, 还与晶体主折射no和ne有关, 因此, 本文对BBO、铌酸锂(LiNbO3)和石英(quartz) 3种不同双折射晶体进行了对比. 三者的双折射率如图2(a)所示, 双折射率由大到小依次为BBO、铌酸锂、石英. 在实现如图2(b)的强度调制时, BBO、铌酸锂、石英的厚度t依次为1.0, 1.5, 13.5 mm. 由此可见, 当强度调制相同时, 晶体双折射率越高, 所需厚度越小. 图 2 BBO、铌酸锂(LiNbO3)和石英(quartz) 3种晶体的对比图 (a) 3种晶体的双折射率曲线; (b) 3种晶体实现相同强度调制的透过率曲线 Figure2. Comparison graph of three crystals of BBO, LiNbO3, and quartz: (a) The birefringence curves of three crystals; (b) the transmittance curves of the three kinds of crystals achieve the same intensity modulation.
针对1053 nm激光脉冲, 本文选用了双折射率大于石英的铌酸锂作为分析和实验材料, 相对BBO晶体, 铌酸锂易大口径生长且不易潮解. 本文数值模拟了晶体透过率函数随厚度t、倾斜角θ、面内旋转角?的变化情况, 并同时分析了各参数对晶体引入的光谱相位的影响. 透过率函数和晶体引入的光谱总相位随厚度t变化的曲线如图3(a)所示, 可见, 晶体厚度对透过率函数的调制中心位置及调制带宽均影响明显, 但对调制深度无明显影响. 同时, 随着t的增大, 晶体引入的光谱总相位变大. 为进一步分析总相位中各阶相位的变化规律, 运用(8)式进一步计算了GVD, GDD, TOD, FOD随t变化的曲线. 如图3(b)所示, GVD随厚度在104 fs量级变化, 其余各阶色散随厚度t高频率振荡, 且振荡幅值随厚度t增大. 在厚度为1.5 mm附近时, GDD, TOD, FOD分别在 ± 105 fs2, ± 108 fs3, ± 1011 fs4区间内振荡. 图 3 当θ = 85°, ? = 30°, t = 1.0, 1.5, 2.0 mm时, 透过率函数、晶体引入的光谱总相位及各阶色散的变化曲线 (a) t = 1.0, 1.5, 2.0 mm时, 透过率函数、光谱总相位随波长的变化曲线; (b) GVD, GDD, TOD, FOD随厚度t的变化 Figure3. The curve of transmittance function, total phase of the spectrum, and each order dispersion introduced by the crystal with θ = 85°, ? = 30°, t = 1.0, 1.5, 2.0 mm: (a) The transmittance function and total phase of spectrum changes with wavelength; (b) GVD, GDD, TOD, FOD changes with thickness t.
类似地, 倾斜角θ对透过率函数和晶体引入光谱总相位的影响如图4(a)所示, 可见, 透过率函数的衰减中心位置随θ变化明显, 但调制深度及带宽无明显变化. 此外, 晶体引入的光谱总相位随倾斜角θ变化不明显, 这主要是由于GVD的影响. 为了进一步研究θ对高阶相位的影响, 对光谱总相位进行泰勒展开, 得到高阶色散随θ变化情况, 如图4(b)所示, 各级色散随θ周期振荡, GDD, TOD, FOD的振荡范围分别为 ± 105, ± 107, ± 1011 fs4. 图 4 当? = 30°, t = 1.5 mm, θ = 80°, 85°, 90°时, 透过率函数、晶体引入的光谱总相位及各阶色散的变化曲线 (a) 透过率函数、光谱总相位随波长的变化曲线; (b) GVD, GDD, TOD, FOD随厚度θ的变化 Figure4. The curve of transmittance function, total phase of the spectrum and each order dispersion introduced by the crystal with ? = 30°, t = 1.5 mm, θ = 80°, 85°, 90°: (a) The transmittance function and total phase of spectrum changes with wavelength; (b) GVD, GDD, TOD, FOD changes with thickness θ.
同样地, 透过率函数与晶体引入的光谱总相位随参数?的变化曲线如图5(a)所示, 可以看出, 随着?的变化透过率函数的调制深度发生明显变化, 衰减中心、调制带宽变化不明显, 由?取不同值时引入光谱总相位的对比可以看出, 光谱总相位随?变化不明显, 这同样是由于GVD的影响. 如图5(b)所示, 各阶色散量随?的变化, 起伏较为平缓, 如在?从25°变化到35°的过程中, FOD变化了3 × 1011 fs4. 图 5 当θ = 85°, t = 1.5 mm, ? = 25°, 30°, 35°时, 透过率函数、晶体引入的光谱总相位及各阶色散的变化曲线 (a) 透过率函数、光谱总相位随波长的变化曲线; (b) GVD, GDD, TOD, FOD随厚度?的变化 Figure5. The curve of transmittance function, total phase of the spectrum, and each order dispersion introduced by the crystal with θ = 85°, t = 1.5 mm, ? = 25°, 30°, 35°: (a) The transmittance function and total phase of spectrum changes with wavelength; (b) GVD, GDD, TOD, FOD changes with thickness ?.
考虑到一阶相位产生的延时, 以及二阶相位对脉宽的调制在光束延迟和压缩调节中可以补偿, 而更高阶相位影响较小, 本文主要对三、四阶相位进行了分析. 根据2.1节中各阶色散随晶体各参数的变化情况, 在晶体厚度为1.5 mm附近调节晶体各参数, 控制晶体引入的四阶色散分别取正最大1.4 × 1011 fs4、负最大–1.4 × 1011 fs4及0 fs4, 3种情况下, 晶体引入的三、四阶相位如图6所示. 图 6 双折射晶体引入的三、四阶相位 (a) 三阶相位; (b) 四阶相位 Figure6. Third and fourth order phase introduced by birefringent crystal: (a) Third order phase; (b) fourth order phase.
运用(9)式分别将图6中的三阶、四阶相位之和加入到中心波长为1053 nm、脉宽为230 fs、光谱宽度为6.5 nm (FWHM)的高斯信号中, 对时域脉冲的影响结果如图7所示. 图 7 在高斯信号中加入三、四阶相位后的时域脉冲图 (a) 线性坐标时域图; (b)对数坐标时域图 Figure7. Time-domain pulse diagram of third and fourth order phase added to Gaussian signal: (a) Linear coordinate time domain diagram; (b) logarithmic coordinate time domain diagram.