Photonic band structures of optically anisotropic periodic arrays

Abstract

We use a plane-wave expansion to calculate the photonic band structures of anisotropic dielectric composites. The composites consist of a periodic array of anisotropic dielectric spheres embedded in air. Calculations are carried out for spheres that are optically uniaxial or biaxial, Faraday active, or naturally optically active. Anisotropy in the sphere dielectric function is found to split degenerate bands and to narrow or even close band gaps, analogous to Stark or Zeeman splitting in conventional band structures. At long wavelengths, the lowest bands are well described by effective indices of refraction, which are in fairly good agreement with an anisotropic Maxwell-Garnett approximation.