Localized electromagnetic waves in a layered periodic dielectric medium with a defect

Abstract

Electromagnetic waves propagating perpendicularly to the layers in a layered periodic dielectric medium with an embedded defect are studied. We develop an analytical method to obtain the solution to the spectral problem for such a one-dimensional system with an arbitrary configuration of the period cell and of the defect. It is shown that the defect induces localized electromagnetic modes with a discrete spectrum of frequencies located in the band gaps of an unchanged continuous spectrum. We derive equations for the gaps, for the discrete spectrum, and for the localization rate. For a case of a two-layer periodic medium with an embedded one-layer defect we carry out a complete analysis of the dependence of the frequency and of the rate of localization of a defect-induced mode on the parameters of the defect and of the periodic medium.