Consequences of spatial antisymmetry on light

TLDR: In this article, light propagation in two and three dimensional lattices for which the index of refraction exhibits spatial antisymmetry is investigated in the ray and photonic crystal regimes.

Abstract: Light propagation in two and three dimensional lattices for which the index of refraction exhibits spatial antisymmetry is investigated in the ray and photonic crystal regimes. In these regimes, all the two dimensional antisymmetry groups for which light fails to propagate are identified. In the ray-regime, it is observed that in tilings described by 7 of the 46 two dimensional antisymmetric groups, light is localized within a fundamental domain and does not propagate through the tiling, in contrast to the behavior in the other 39 groups. To understand the above phenomenon, a rule based on the number of anti-mirror planes passing through a single Bravais lattice point is derived. In the wave regime for photonic crystals, it is observed that there are no propagating eigensolutions for the same 7 tilings as above, whereas propagating solutions and energy pass band dispersion curves can be obtained for the other 39 groups. The reasons underlying this peculiar behavior are analyzed using the topological approach for modeling flow in dynamical billiards to shed light on the applicability of Bloch’s theorem for these periodic antisymmetric lattices.