Characterizing the reflectance of periodic layered media

Abstract

It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor in an infinite periodic structure. We argue that such a procedure may become meaningless when dealing with structures with not very many periods. We propose an alternative approach based on a factorization of the multilayer transfer matrix in terms of three fundamental matrices of simple interpretation. We show that the trace of the transfer matrix sorts the periodic structures into three types with properties closely related to one (and only one) of the three fundamental matrices. We present the reflectance associated to each one of these types, which can be considered as universal features of the reflection in these media.