Perturbation theory for Maxwell's equations in anisotropic materials with shifting boundaries

TL;DR

This paper develops a modified perturbation theory for Maxwell's equations in anisotropic materials with shifting boundaries, enabling accurate calculation of eigenfrequency shifts without approximation, especially in strongly anisotropic media.

Contribution

It introduces an optimized smoothing function approach for precise perturbation analysis in anisotropic dielectric interfaces, improving upon previous approximation methods.

Findings

Accurately calculates eigenfrequency shifts in anisotropic materials.

Demonstrates improved results over traditional methods in strong-anisotropy cases.

Applicable to small boundary shifts in anisotropic dielectric interfaces.

Abstract

Perturbation theory is a kind of estimation method based on theorem of Taylor expansion, and is useful to investigate electromagnetic solutions of small changes. By considering a sharp boundary as a limit of smoothed systems, previous study has solved the problem when applying standard perturbation theory to Maxwell's equations for small shifts in isotropic dielectric interfaces. However, when dealing with anisotropic materials, an approximation is conducted and leads to an unsatisfactory error. Here we develop a modified perturbation theory for small shifts in anisotropically dielectric interfaces. By using optimized smoothing function for each component of permittivity, we obtain a method to calculate the intrinsic frequency shifts of anisotropic permittivity field when boundaries shift, without approximation. Our method shows accurate results when calculating eigenfrequency's shifts in strong-anisotropy materials, and can be widely used for small shifts in anisotropically dielectric interfaces.