在超短脉冲的谐波转换过程中, 由于不同波包之间的群速度失配的存在, 非线性晶体的有效厚度、转换效率及带宽等将相互制约, 不能获得理想结果。基于耦合波方程, 在平面波和小信号近似条件下推导出了关于基频、倍频光群速度关系的解析表达式。通过对200 fs超短脉冲在II类KDP晶体中的混频过程的模拟分析, 发现在满足相位匹配的前提下, 三次谐波转换效率随着基频、倍频光群速度倒数的差值的平方呈现出指数衰减的关系, 与理论结果吻合。得出的关于基频光、倍频光群速度的表达式, 作为三倍频群速度匹配关系式的必要补充, 对寻找合适的色散晶体和选择有效的匹配措施, 实现宽带三次谐波转换具有理论指导意义。

In the frequency conversion process of ultrashort pulses, due to group-velocity mismatch (GVM), conversion efficiency, crystal length and pulse bandwidth will affect each other and result in low efficiency or small bandwidth. Based on the nonlinear coupling equations, the analytical expressions about group-velocities of fundamental (FH) and second-harmonic (SH) pulses are derived under the plane-wave and pump un-depletion approximations. THG mixing process with ultrashort pulses (FWHM ≈200 fs) input is numerically simulated in type-Ⅱ KDP crystals. The results show that conversion efficiency of 3ω exponentially decrease along with the square of difference between reciprocal of group-velocities of FH and SH pulses, which agree with our theoretical results. Conclusions of this paper are the necessary supplement to the group-velocity-matching relationship of THG, which will be useful for finding proper nonlinear crystals and choosing effective GVM methods in the THG process of ultrashort pulses.