Polarization ray tracing in anisotropic optically active media. II. Theory and physics

Refraction, reflection, and amplitude relations are derived that apply to polarization ray tracing in anisotropic, optically active media such as quartz. The constitutive relations for quartz are discussed. The refractive indices and polarization states associated with the two modes of propagation are derived as a function of wave direction. A procedure for refracting at any uniaxial or optically active interface is derived that computes both the ray direction and the wave direction. A method for computing the optical path length is given, and Fresnel transmission and ref lection equations are derived from boundary conditions on the electromagnetic fields. These ray-tracing formulas apply to uniaxial, optically active media and therefore encompass uniaxial, non-optically active materials and isotropic, optically active materials