Leaky modes of dielectric cavities

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.