Leaky Modes of Dielectric Cavities

TL;DR

This paper investigates the leaky electromagnetic modes in dielectric cavities like slabs, spheres, and cylinders, providing mathematical proofs of completeness and numerical analysis of their relationship with cavity resonances.

Contribution

It introduces a comprehensive analysis of leaky modes in various dielectric geometries, including proofs of their completeness and numerical results linking them to cavity resonances.

Findings

Leaky modes form a complete set for dielectric cavities.

Numerical results illustrate the connection between leaky modes and resonances.

Completeness proofs support the theoretical framework.

Abstract

In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out (and also by getting absorbed within the medium). We analyze the leaky modes of a parallel-plate slab, a solid glass sphere, and a solid glass cylinder, by examining those solutions of Maxwell's equations (for dispersive as well as non-dispersive media) which admit of a complex-valued oscillation frequency. Under certain circumstances, these leaky modes constitute a complete set into which an arbitrary distribution of the electromagnetic field residing inside a dielectric body can be expanded. We provide completeness proofs, and also present results of numerical calculations that illustrate the relationship between the leaky modes and the resonances of dielectric cavities formed by a simple parallel-plate slab, a glass sphere, and a glass cylinder.