Simple wave solutions for the Maxwell equations in bianisotropic, nonlinear media, with application to oblique incidence

We analyze the propagation of electromagnetic waves in nonlinear, bianisotropic, nondispersive, homogeneous media using simple waves and six-vector formalism. The Maxwell equations are formulated as an eigenvalue problem, whose solutions are equivalent to the characteristic propagation directions. We solve the oblique incidence of plane waves in vacuum on a half space of nonlinear material, and present a method to calculate the reflected and transmitted fields for all angles of incidence and all polarizations of the incident field. Numerical examples for reflection and transmission illustrate the field dependence of the Brewster angle, and the birefringence of an anisotropic material.