为了探究PPLN 外部谐振倍频腔的输出模式，从菲涅尔-基尔霍夫衍射积分公式出发，采用快速傅里叶变换法(FFT)和Fox-Li 迭代法数值模拟高斯反射率圆形平凹倍频腔输出基模的场强分布、相位分布和光束质量M2 因子，同时与圆形双凹倍频腔做了比较。计算结果表明，两类倍频谐振腔输出基模均为高斯分布，腔长变化对两类倍频腔输出光束质量的影响较小。平凹倍频腔输出光束质量M2=1.296，远场发散角θ=58.084 μrad；而双凹倍频腔输出光束质量M2=6.930，θ= 310.56 μrad。平凹倍频腔输出光束质量明显优于双凹倍频腔。

To study the output mode distribution of the frequency doubling resonant in PPLN, the field distributions and beam quality M2 factor of the plano-concave resonator or dual-cavity were calculated and compared. The output fundamental modes of them with tilted Gaussian-reflectivity mirrors were simulated with Fourier transformation method and Fox-Li iterative method. The results show that the output fundamental mode of the frequency doubling external resonants is Gaussian distribution, and cavity length changes have less effect on the output beam quality. The output beam quality of the plano-concave resonator is M2=1.296, divergence angle θ=58.084 μrad, and the Dual-cavity is M2=6.930, θ= 310.56 μrad. The output beam quality of the plano-concave resonator is superior to the Dual-cavity.