Ray-optics analysis of inhomogeneous biaxially anisotropic media.

Firm evidence of the biaxial nematic phase in liquid crystals, not induced by a magnetic or electric field, has been established only recently. The discovery of these biaxially anisotropic liquid crystals has opened up new areas of both fundamental and applied research. The advances in biaxial liquid-crystal-related topics call for a good overview on the propagation of waves through biaxially anisotropic media. Although the literature sporadically discusses biaxial interfaces, the propagation of waves through inhomogeneous biaxially anisotropic bulk materials has never been fully addressed. For this reason, we present a novel ray-tracing method for inhomogeneous biaxially anisotropic media. In the geometrical-optics approach, we clearly show how to assess the optical properties of inhomogeneous biaxially anisotropic media in three dimensions.

General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media.

Uniaxial optical anisotropy in the geometrical-optics approach is a classical problem, and most of the theory has been known for at least fifty years. Although the subject appears frequently in the literature, wave propagation through inhomogeneous anisotropic media is rarely addressed. The rapid advances in liquid-crystal lenses call for a good overview of the theory on wave propagation via anisotropic media. Therefore, we present a novel polarized ray-tracing method, which can be applied to anisotropic optical systems that contain inhomogeneous liquid crystals. We describe the propagation of rays in the bulk material of inhomogeneous anisotropic media in three dimensions. In addition, we discuss ray refraction, ray reflection, and energy transfer at, in general, curved anisotropic interfaces with arbitrary orientation and/or arbitrary anisotropic properties. The method presented is a clear outline of how to assess the optical properties of uniaxially anisotropic media.