Ray-Optics Analysis of Inhomogeneous Uniaxially Anisotropic Media

Uniaxial optical anisotropy in the geometrical-optics approach is a classical problem and most of the theory is known for at least fifty years. Although the subject appears frequently in the literature, it is nearly silent about wave propagation through inhomogeneous anisotropic media. At the same time, 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 anisotropic properties. The method presented in this report is a clear outline of how to assess the optical properties of uniaxially anisotropic media. c © Koninklijke Philips Electronics N.V. 2008 iii TN-2007/00892 Unclassified Conclusions: Since the literature is nearly silent about wave propagation via inhomogeneous anisotropic media, we have developed a general and complete ray-tracing method in the geometrical-optics approach. We can use the method to calculate ray paths with polarized ray tracing in the bulk material of inhomogeneous anisotropic media in three dimensions, provided the properties of the medium change slowly over one wavelength. In addition, this model enables one to calculate the optical properties of interfaces with arbitrary orientation and/or anisotropic properties. Finally, we have derived vector equations which are general, concise and easy to apply. In combination with these vector equations, the ray-tracing method presented in this report becomes a clear outline of how to apply the classical theory in practice. Furthermore, we have applied the method to a number of optically anisotropic systems. We have investigated an anisotropic cylinder, the influence of anisotropy in immersion lithography, the Freédericksz transition (applied in two different designs) and an artificial anisotropic gradient-index lens. Finally, we have briefly discussed the domains of geometrical optics and wave optics and the distinction between them in terms of the transport equations and the degree of inhomogeneity. iv c © Koninklijke Philips Electronics N.V. 2008 Unclassified TN-2007/00892