Homotopy analysis method applied to second-order frequency mixing in nonlinear optical dielectric media

TL;DR

This paper applies the homotopy analysis method to analyze second-order frequency mixing in nonlinear optical media, providing a flexible polynomial approach for different phase-matching conditions and comparing results with finite-difference methods.

Contribution

It introduces a homotopy analysis method-based polynomial framework for three-wave mixing, applicable to arbitrary parameters and phase-matching scenarios, extending convergence through auxiliary parameters.

Findings

Power series basis models three-wave mixing for arbitrary inputs.

The method accurately predicts sum- and difference-frequency generation.

Convergence is improved by adjusting the auxiliary parameter.

Abstract

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.