Tunable optical anisotropy in three-dimensional photonic crystals

Artificial optical birefringence can be realized in three-dimensional photonic crystals with a uniaxial structural symmetry: e.g., woodpile photonic crystals with a tetragonal lattice structure in the long-wavelength limit. The ordinary and extraordinary indices of refraction are determined from calculation of the reflection coefficient for a plane wave incident on the surface of a semi-infinite photonic crystal at different angles. We find that the anisotropy can be widely tuned by simply changing the width and thickness of the dielectric rod. A large relative negative anisotropy over 33% is found. A transition from positive anisotropy to negative anisotropy can be readily achieved. At certain parameters, a structurally anisotropic nanostructure can behave like an optically isotropic medium. Our study opens a window to use artificial nanostructures to create an arbitrary optical anisotropy that is not possible in natural crystals.