We present a detailed theoretical and numerical analysis on the temporal-spectral-spatial evolution of a high-peak-power femtosecond laser pulse in two sets of systems: a pure lithium niobate (LN) plate and a periodically poled lithium niobate (PPLN) plate. We develop a modified unidimensional pulse propagation model that considers all the prominent linear and nonlinear processes and carried out the simulation process based on an improved split-step Fourier transformation method. We theoretically analyze the synergic action of the linear dispersion effect, the second-order nonlinearity (2nd-NL) second-harmonic generation (SHG) effect, and the third-order nonlinearity (3rd-NL) self-phase modulation (SPM) effect, and clarify the physical mechanism underlying the peculiar and diverse spectral broadening patterns previously reported in LN and PPLN thin plate experiments. Such analysis and discussion provides a deeper insight into the synergetic contribution of these linear and nonlinear effects brought about by the interaction of a femtosecond laser pulse with the LN nonlinear crystal and helps to draw a picture to fully understand these fruitful optical physical processes, phenomena, and laws.

中文翻译：

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线性色散、二阶非线性和三阶非线性的协同作用对铌酸锂晶体中传输的飞秒脉冲的光谱轮廓进行整形

我们对两组系统中高峰值功率飞秒激光脉冲的时间-光谱-空间演化进行了详细的理论和数值分析：纯铌酸锂（LN）板和周期性极化铌酸锂（PPLN）板。我们开发了一种改进的一维脉冲传播模型，该模型考虑了所有突出的线性和非线性过程，并基于改进的分步傅里叶变换方法进行了仿真过程。我们从理论上分析了线性色散效应、二阶非线性（2nd-NL）二次谐波产生（SHG）效应和三阶非线性（3rd-NL）自相位调制（SPM）效应的协同作用，并阐明先前在 LN 和 PPLN 薄板实验中报道的奇特且多样的光谱展宽模式背后的物理机制。这样的分析和讨论提供了对飞秒激光脉冲与 LN 非线性晶体相互作用所带来的这些线性和非线性效应的协同贡献的更深入的了解，并有助于绘制一幅图画以充分理解这些富有成果的光学物理过程、现象、和法律。