The classical problem of three-wave mixing in a nonlinear optical medium is investigated using the homotopy analysis method (HAM). We show that the power series basis builds a generic polynomial expression that can be used to study three-wave mixing for arbitrary input parameters. The phase-mismatched and perfectly phase matched cases are investigated. Parameters that result in generalized sum- and difference-frequency generation are studied using HAM with a power series basis and compared to an explicit finite-difference approximation. The convergence region is extended by increasing the auxiliary parameter.

中文翻译：

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应用于非线性光介质二阶混频的同伦分析方法

使用同伦分析法（HAM）研究了非线性光学介质中三波混频的经典问题。我们展示了幂级数基础构建了一个通用多项式表达式，可用于研究任意输入参数的三波混频。研究了相位不匹配和完美相位匹配的情况。使用具有幂级数基础的 HAM 研究导致广义和频和差频生成的参数，并与显式有限差分近似进行比较。通过增加辅助参数来扩展收敛区域。