提出了一种基于亥姆霍兹方程的有限差分方法用于有源非稳腔的模式计算。从理论上分析了光场传输的有限差分计算方法, 并由此出发, 建立了针对有源非稳腔模式的数值计算模型。基于这个计算模型, 能够较为精确、快速地获得激光谐振腔输出的光场分布。分别给出了空腔条件下和非均匀增益条件下的数值模拟结果, 前者还与用快速傅里叶变换法获得的数值模拟结果进行了对比。数值模拟的结果表明, 所用方法结果可信、计算速度较快, 可有效用于大菲涅耳数有源非稳腔的模式计算。

A finite difference method based on Helmholtz equation is presented for the mode calculation of active unstable resonator. The finite difference method for the optical field transmission is analyzed theoretically, and the numerical calculation model for active unstable resonator is established. The optical field distribution of laser resonator output can be obtained accurately and quickly based on the calculation model. The numerical sim. ulation results for bare cavity mode and active cavity mode with non-uniform gain are presented respectively. The simulation results for bare cavity mode are also compared with the modes calculated by fast Fourier transform, and it shows that the numerical simulation methods and the calculated modes are reliable, time-saving, and can be used for model calculation with large Fresnel number.