将不均匀介质势函数进行泰勒展开,取其前3项近似,与描述光腔模式的亥姆霍兹方程中的特殊函数结合,根据光腔边界条件推导出光腔模式的本征解、激光输出功率以及不均匀介质与激光模式的相位与强度分布关系表达式。将表达式应用于氧碘化学激光器的功率与输出耦合率的非线性拟合以及近场光强分布的分析,预测趋势与文献结果相符。

Nonuniform laser medium will cause the variations of phase and intensity distributions of laser modes. It is difficult to solve the wave equations associated with nonuniform laser medium. In this paper,the potential function of nonuniform laser medium was approximately expressed by the primary three items of its Taylor series expansion,and then coupled into the special function in Helmholtz equations describing the laser modes in a resonator. According to the boundary conditions of a typical resonator,we derived the expression for the eigen-solutions of laser modes,the expression for the output laser power,and the expressions for the relations between nonuniform laser medium and phase/intensity distributions of laser modes. Applying the derived expressions in the nonlinear curve-fitting for output power vs. out-coupling rate and the analysis for near field intensity distribution in the case of a chemical oxygen-iodine laser,we found the trends of prediction consist with the results in literatures.