A continuous family of Exact Dispersive Quasi-Normal Modal (DQNM) Expansions for dispersive photonic structures

TL;DR

This paper introduces a continuous family of DQNM expansion formalisms for dispersive photonic structures, allowing flexible modal analysis applicable to complex materials like anisotropic and non-reciprocal media.

Contribution

It presents a novel family of DQNM expansions parameterized continuously, addressing non-uniqueness and over-completeness in modal analysis of dispersive photonic systems.

Findings

Applicable to dispersive, anisotropic, and non-reciprocal materials

Demonstrated on a 2-D scattering model with measured permittivity data

Shows flexibility in modal expansion formalism

Abstract

In photonics, Dispersive Quasi-Normal Modes (DQNMs) refer to optical resonant modes, solutions of spectral problems associated with Maxwell's equations for open photonic structures involving dispersive media. Since these DQNMs are the constituents determining optical responses, studying DQNM expansion formalisms is the key to model the physical properties of a considered system. In this paper, we emphasize the non-uniqueness of the expansions related to the over-completeness of the set of modes and discuss a family of DQNM expansions depending on continuous parameters that can be freely chosen. These expansions can be applied to dispersive, anisotropic, and even non-reciprocal materials. As an example, we particularly demonstrate the modal analysis on a 2-D scattering model where the permittivity of a silicon object is drawn directly from actual measurement data.