Refraction of light on flat boundary of liquid crystals or anisotropic metamaterials

Refraction of light at a boundary between an isotropic dielectric and an optically anisotropic material - liquid crystalline or metamaterial - is elaborated, especially the dependence on the angle between the anisotropic material birefringence optical axis and the material surface. Different regimes of negative and positive refraction are shown, caused by the liquid-crystalline optical response or potential negative-positive anisotropic metamaterial, identifying distinct regimes of refraction and reflection. The theoretical analysis is verified with finite-difference time-domain simulations and presented in the context of selected related literature. More broadly, this work is a contribution towards developing and understanding anisotropic liquid crystal-type soft metamaterials to achieve novel photonic phenomena based on optical anisotropy.