以复Morlet函数作为小波母函数推导了2M路线性啁啾高斯脉冲堆积形成的整形脉冲的时间分辨能量谱密度解析表达式。通过小波变换获得了堆积啁啾脉冲功率和瞬时波长随时间的分布; 堆积啁啾高斯脉冲功率随时间呈现振荡变化, 瞬时波长在功率接近零的极小值点发生跳变; 啁啾的增大会加剧功率的时域振荡和瞬时波长的跳变; 瞬时波长的跳变仅发生在功率接近零的极小值附近, 脉冲的能量仍然主要集中在由基元脉冲啁啾决定的波长范围内。同时, 研究表明脉冲重叠因子的微小变化会极大地影响整形脉冲峰值功率与等效平均功率之比和包络平坦度, 且两者不能同时达到最佳, 需折衷选取。

We deduced the analytical expression of the time-resolved energy spectrum density for shaped pulse stacked by 2M chirped Gaussian pulse using wavelet transform and complex Morlet function. Time-resolved power and instantaneous central wavelength distribution of the stacking chirped Gaussian pulse have been obtained through wavelet transform. It’s found that the power oscillates in the time domain, and the instantaneous central wavelength jumps when the power is zero. Increasing the chirp will aggravate the power oscillation and the instantaneous central wavelength jump. The instantaneous central wavelength jump occurs only when the power is zero. Therefore, the pulse energy remains in the wavelength range determined by the chirp of fundamental pulse. Simulating results also show that a little change of the pulse overlap factor will greatly influence the packing ratio and the flatness of the shaped pulse, both of those cannot simultaneously reach optimum. Therefore, the pulse overlap factor should be selected eclectically.