The object of this paper is to present a coordinate-free method in solving the problem of wave reflection from the surface of an anisotropic medium. Based on the direct manipulation of vectors, dyadics, and their invariants, the method eliminates the use of coordinate systems. It facilitates solutions and provides results in a greater generality. The paper contains the following results in coordinate-free forms: (1) the dispersion equation, (2) the laws of reflection and refraction, (3) the Booker quartic equation, and (4) the transmission and reflection coefficient matrices.

Lithium niobate nanoparticulate clad on the core of single mode optical fiber for temperature and magnetic field sensing Appl. Phys. Lett. 101, 043102 (2012) Ultrafast all-optical magnetic switching in NaTb(WO4)2 Appl. Phys. Lett. 96, 201108 (2010) Aberration-free imaging for light and electrons Appl. Phys. Lett. 93, 161105 (2008) Precision polarimetry with real-time mitigation of optical-window birefringence Rev. Sci. Instrum. 79, 013108 (2008) Linear birefringence measurement at 157 nm Rev. Sci. Instrum. 74, 1386 (2003 Additional information on J. Appl. Phys. This paper considers of a coordinate-free approach to wave propagation in anisotropic media. Based on the direct manipulation of vectors, dyadics, and their invariants, the approach eliminates the use of coordinate systems. It facilitates solutions and provides results in a greater generality. The paper contains the following results in coordinate-free forms: The formulation of eigenvalue problems, the dispersion equation, the polarization of waves in magnetic crystals, and the determination of the directions of field vectors.