Time-independent perturbation theory for quasinormal modes in leaky optical cavities

If a cavity is leaky, its ``modes'' are quasinormal modes (QNM's) with complex frequencies, and they do not constitute a Hermitian system. Nevertheless, the time-independent perturbation arising from a small change of the dielectric-constant distribution can be formulated in terms of these discrete QNM's, resulting in a generalization of the usual perturbation scheme to a non-Hermitian situation. In particular, shifts for the imaginary parts of the eigenvalues are obtained as well. This paper presents this theory for scalar waves in one dimension.