Photonic pseudogaps for periodic dielectric structures

Abstract

We consider the problems of existence and structure of gaps (pseudogaps) in the spectra associated with Maxwell equations and equations that govern the propagation of acoustic waves in periodic two-component media. The dielectric constant e is assumed to be real and positive, and the value of e = eb on the background is supposed to be essentially larger than the value of e = ea on the embedded component. We prove the existence of pseudogaps in the spectra of the relevant operators. In particular, we give an accurate treatment of the term “pseudogap.” We also show that if the contrast eb/ea approaches infinity, then the bands of the spectrum shrink to a discrete set which can be identified with the set of eigenvalues of a Neumann-type boundary value problem and thus can be effectively calculated.