Complete method to determine transmission and reflection characteristics at a planar interface between arbitrarily oriented biaxial media

TLDR: In this paper, a complete, systematic methodology is provided for calculating all properties of the transmitted and reflected light waves, including phase-velocity indices of refraction, angles of reflection and reflection, polarization angles, walk-off angles, and Poynting-vector relative magnitudes.

Abstract: The general case of monochromatic plane-wave reflection and refraction at oblique incidence from a planar biaxial–biaxial interface is presented for arbitrary principal-axes orientation in each region. A complete, systematic methodology is provided for calculating all properties of the transmitted and reflected light waves. The singularities that arise when one or both regions are taken to be isotropic are addressed, to our knowledge for the first time. Example calculations are presented for all cases. Finally, the methodology yields all wave parameters, including phase-velocity indices of refraction, angles of refraction and reflection, polarization angles, walk-off angles, and Poynting-vector relative magnitudes. Some common applications of this theory include multilayer structure analysis and the determination of internal angles for second-harmonic generation.