Periodic bi-isotropic crystals with spectral asymmetry

We study periodic layered structures formed by bi-isotropic media with the aim of exploring nonreciprocal effects in the corresponding photonic band diagrams. We prove that under some conditions the photonic band diagrams can exhibit spectral asymmetry such that ω(k_z) ≠ ω(-k_z). Surprisingly, this is only possible when the photonic crystal contains both chiral and Tellegen materials. Furthermore, we demonstrate that the band structure of layered Tellegen photonic crystals that break simultaneously the space inversion and time reversal symmetries is always symmetric for propagation along the direction normal to the stratification. We explain this result by identifying another symmetry that protects the band diagrams of asymmetries. Moreover, we show that Tellegen structures which cannot be reduced to conventional structures under a duality transformation have nondegenerated Bloch eigenmodes.