Simple explicit equations are derived that determine the angles of incidence at which the parallel and perpendicular polarization components of light are extinguished on reflection from a transparent film coating a high-reflectance (metallic) substrate. The polarizing angles obtained from our approximate expressions are in excellent agreement with those determined by iterative numerical solution of the exact nonlinear equations that govern such angles. For the approximation to be valid, the intensity reflectance of the film-substrate interface, evaluated at the critical angle of the film-ambient interface, must exceed 0.5.
Journal of the Optical Society of America A
R. M. A. Azzam, "Explicit equations for the polarizing angles of a high-reflectance substrate coated by a transparent thin film," J. Opt. Soc. Am. A 2, 480-482 (1985)