Leaky Modes of Solid Dielectric Spheres

TL;DR

This paper analyzes the leaky electromagnetic modes of solid dielectric spheres, demonstrating their completeness and relationship to resonances, which enhances understanding of light decay in dielectric media.

Contribution

It provides a theoretical framework and numerical analysis showing leaky modes form a complete set and relate closely to cavity resonances in dielectric spheres.

Findings

Leaky modes can form a complete basis for electromagnetic fields inside dielectric spheres.

Numerical results illustrate the connection between leaky modes and cavity resonances.

The study offers a completeness proof outline for leaky modes in dielectric spheres.

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 solid dielectric spheres by examining solutions of Maxwell's equations for simple homogeneous, isotropic, linearly dispersive media that admit complex-valued oscillation frequencies. We show that, under appropriate circumstances, these leaky modes constitute a complete set into which an initial electromagnetic field distribution inside a dielectric sphere can be expanded. We provide the outline of a completeness proof, and also present results of numerical calculations that illustrate the close relationship between the leaky modes and the resonances of solid dielectric spherical cavities.