First-order perturbation theory of eigenmodes for systems with interfaces

TL;DR

This paper develops an exact first-order perturbation theory for eigenmodes in systems with interfaces, revealing that higher-order terms can influence first-order frequency shifts and providing a generalized correction formula for complex materials.

Contribution

It introduces a comprehensive first-order perturbation framework that accounts for higher-order effects and applies to diverse material types and geometries.

Findings

Higher-order terms can affect first-order eigenfrequency shifts.

The diagonal approximation is not always sufficient for accurate results.

A general correction formula for complex materials is derived.

Abstract

We present an exact first-order perturbation theory for the eigenmodes in systems with interfaces causing material discontinuities. We show that when interfaces deform, higher-order terms of the perturbation series can contribute to the eigenmode frequencies in first order in the deformation depth. This means that the usual diagonal approximation is not necessarily equal to the firstorder approximation, rendering the well known single-mode result insufficient. Extracting the true first-order correction from all higher-order terms enables us to recover the diagonal formalism in a modified form. A general formula for the single-mode first-order correction to electromagnetic eigenmodes is derived, capable of treating dispersive, magnetic, and chiral materials with arbitrary shapes.