Quadratic corrections to the metaplectic formulation of resonant mode conversion

TL;DR

This paper investigates quadratic order corrections to the dispersion matrix in mode conversion, improving the matching between local and far-field solutions, with potential for higher-order extensions.

Contribution

It introduces quadratic corrections to the metaplectic formulation of mode conversion, enhancing solution matching accuracy and outlining a method for higher-order corrections.

Findings

Quadratic corrections improve local and far-field solution matching.

Numerical validation confirms the effectiveness of the corrections.

Method can be extended to arbitrary order for more precise modeling.

Abstract

The effects of quadratic order terms in the dispersion matrix near a mode conversion are considered. It is shown that including the corrections due to these quadratic terms gives a better matching between the local solution in the mode conversion region, and the far-field WKB solutions for the incoming and outgoing waves. This matching is demonstrated by comparison of the asymptotic solution with a numerical solution for a simple one-dimensional conversion. This procedure for obtaining the corrections due to quadratic order terms can be extended to arbitrary order and, in principle, an outline for performing such an extension is given.