Completeness and orthogonality of quasinormal modes in leaky optical cavities

Abstract

It is shown that for the scalar analog of electrodynamics in one dimension, the quasinormal modes of a leaky cavity form a complete set inside the cavity, provided the cavity is defined by a discontinuity in the refractive index. This condition is sufficiently general to apply to a number of interesting examples. The quasinormal modes are also orthogonal under a modified definition of the inner product. The completeness and orthogonality hold even though the cavity is not a Hermitian system by itself. These properties allow the discrete quasinormal modes to be used as the basis for dynamics of the scalar wave in the cavity.