Symmetry properties of two-dimensional anisotropic photonic crystals.

A theoretical study of two-dimensional photonic crystals made of anisotropic material is presented. Detailed computation principles including a treatment of the TE and TM polarizations are given for a photonic crystal made of either uniaxially or biaxially anisotropic materials. These two polarizations can be decoupled as long as any one of the principal axes of the anisotropic material is perpendicular to the periodic plane of the photonic crystal. The symmetry loss due to the anisotropy of the material and the variation of the Brillouin zones relative to the tensor orientations are also analyzed. Furthermore, the symmetry properties of the two-dimensional photonic band structure are studied, and the resulting effect on the photonic bandgap and the dispersion properties of photonic crystal are analyzed as a function of the orientation of the anisotropic material.