中文摘要：

基于非线性耦合波理论分析了三倍频过程中群速度之间的关系,推导出三波混频条件下的群速匹配关系式.对超短脉冲在Ⅱ类KDP晶体中的混频过程进行了模拟分析,结果表明：当三波（基波ω,谐波2ω和3ω）的群速度满足该匹配关系式时,三倍频（3ω）的带宽和转换效率均可达最大值;而随着三波群速度对该关系式的偏离逐渐增大,带宽变窄、转换效率下降.导出的三波群速匹配关系式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指导意义.

英文摘要：

　Based on the nonlinear coupling equations,the relation between group-velocities of 1ω,2ω and 3ω waves in the mixing process of broadband third-harmonic generation（THG）is investigated theoretically.The formula of three-wave group-velocity-matching（GVM）is derived.The THG mixing process of ultrashort pulses in Type-Ⅱ KDP crystals is simulated.Obtained results show that both the THG conversion efficiency and the bandwidth reach maximum when the formula is satisfied（i.e.,at zero group-velocity mismatch）,and drop down rapidly when it＇s not satisfied.The three-wave GVM formula presented is useful for finding proper nonlinear crystals and choosing effective GVM methods.