Non-uniqueness of the Quasinormal Mode Expansion of Electromagnetic Lorentz Dispersive Materials

TL;DR

This paper explores the non-uniqueness in the modal expansion of electromagnetic responses in Lorentz dispersive materials, analyzing different formulas and their accuracy through numerical validation.

Contribution

It introduces a unified formalism for modal expansion in Lorentz dispersive media and discusses the impact of linearization choices on excitation coefficients.

Findings

Different formulas for modal expansion are validated.

Numerical results compare the accuracy of these formulas.

A method for orthogonalizing degenerate modes is provided.

Abstract

Any optical structure possesses resonance modes and its response to an excitation can be decomposed onto the quasinormal and numerical modes of discretized Maxwell's operator. In this paper, we consider a dielectric permittivity that is a N-pole Lorentz function of the pulsation $\omega$. We propose a common formalism and obtain different formulas for the modal expansion. The non-uniqueness of the excitation coeffcient is due to a choice of the linearization of Maxwell's equation with respect to $\omega$ and of the form of the source term. We make the link between the numerical discrete modal expansion and analytical formulas that can be found in the literature. We detail the formulation of dispersive Perfectly Matched Layers (PML) in order to keep a linear eigenvalue problem. We also give an algorithm to regain an orthogonal basis for degenerate modes. Numerical results validate the different formulas and compare their accuracy.