Asymmetric band diagrams in photonic crystals with a spontaneous nonreciprocal response

Abstract

We study the propagation of electromagnetic waves in layered photonic crystals formed by materials with a spontaneous nonreciprocal response, such as Tellegen (axion) media or topological insulators. Surprisingly, it is proven that stratified Tellegen photonic crystals that break simultaneously the space inversion and time-reversal symmetries have always symmetric dispersion diagrams. Interestingly, we show that by combining chiral and nonreciprocal materials the photonic band diagrams can exhibit a spectral asymmetry such that $\ensuremath{\omega}(\mathbf{k})\ensuremath{\ne}\ensuremath{\omega}(\ensuremath{-}\mathbf{k})$. Furthermore, it is demonstrated that in some conditions two juxtaposed Tellegen medium layers have an electromagnetic response analogous to that of a biased ferrite slab.