基于能量守恒和三波耦合波方程, 建立了超短脉冲在参变过程中二次谐波产生时的I类和II类相位匹配条件、基波与谐波之间的群速延迟时间、以及群速失配对晶体长度限制的理论基础。以负单轴非线性光学晶体CsLiB6O10为例, 分析和数值计算了超短脉冲宽度为100 fs时, 谐波的群速匹配长度随基波波长变化的规律。研究结果表明在I类相位匹配条件下, 基波波长为642 nm时, 群速延迟最小, 相应的群速匹配晶体长度最长为19.1 mm;在II类相位匹配条件下, 基波波长为767 nm, 群速延迟最小, 群速匹配长度最长为0.89 mm。

The theoretical model of type-Ⅰ and type-Ⅱ phase matching conditions for second harmonic generation, group velocity delay of fundamental and second harmonic, and limitation of nonlinear crystal matching length by group velocity mismatch, was obtained by using energy conservation and three-wave coupled equations in optical parametric process of ultra-short pulses. The relation of the group velocity matching length of the harmonic and fundamental wavelength is analyzed by numerical simulation for a negative uniaxial crystal CsLiB6O10 with an 100 fs pulse. The maximum group velocity matching length of nonlinear crystal is 19.1 mm for fundamental wavelength 642 nm in type-Ⅰ and 0.89 mm for wavelength 767 nm in type-Ⅱ, which correspond to the minimum group velocity delay time, respectively.