基于外部谐振腔可以实现两基频激光的高效和频转换,通常可以采用泵浦不消耗近似(PUA)或小信号近似(SSA)来理论模拟实验结果。然而当基频光功率相近且转换效率较高时,此两种近似的误差就会变得不可接受,然而三波耦合波方程(TWCE)解析解通常需要进行椭圆积分,直接数值求解就变得简单易行。本文首先基于龙格-库塔方法求解准相位匹配下的TWEC,并与PUA和SSA下的解析解进行比较分析,确定了两种近似的适用条件;最后基于该精确数值解结合腔模理论对外腔高效和频对腔模线型的影响进行了研究。

Sum frequency generation (SFG) with high efficiency can be obtained via an external resonator. Two theoretical dealing methods of pump undepletion approximation (PUA) and small signal approximation (SSA) can be used to simulate the experimental results. However,when the two fundamental lights have similar order of intensities and high conversion efficiency, the two approximations can introduce larger errors. Solving the three wave coupling equations (TWCE) by numerical way becomes more acceptable because the analytical solution for the equations requires the elliptical integration. In this paper,the TWCE with quasi-phase match was numerically calculated based on the Runge-Kutta method. The analytical solutions based on PUA and SAA were then compared with the numerical accurate solution and the applicable conditions were determined. Finally the influence of high sum frequency conversion efficiency on the external cavity modes was analyzed based on this numerical exact solution to TWCE.