The Exact Photonic Band Structure for a Class of Media with Periodic Complex Moduli

Abstract

An exact formula for the photonic band structure (and hence the dispersion relation) is found for a certain class of periodic media. These media have the special property that the spatially fluctuating part of their complex electrical permittivity and magnetic permeability, when Fourier transformed, vanishes in half of Fourier space. As a result the band structure is proved to be exactly the same as for a lossy homogeneous medium, at least when the frequency is not too high.