Equalization of the Complex Reflection Coefficients for the Parallel and Perpendicular Polarizations of an Absorbing Substrate Coated by a Transparent Thin Film

By coating an absorbing substrate of complex refractive index n 2 − jk 2 with a transparent thin film of certain refractive index n 1 and (normalized) thickness ζ, the complex reflection coefficients R p and R s for the p and s polarizations can be equalized (R p = R s) at a given angle of incidence φ. Consequently, such a film-substrate system reflects incident monochromatic light without any change of polarization, for all incident polarizations. The constraint on n 1,n 2 and k 2, such that R p = R s at a given φ, is studied numerically and graphically. The constraint is found to be virtually independent of φ, and a highly accurate, φ-free, analytical approximation is determined. The associated film thickness ζ and the polarization-independent intensity reflectance R of the film-substrate system are examined as functions of the optical constants. ζ is also found to be virtually invariant with φ, and a highly accurate explicit expression that specifies its dependence on n 1,n 2 and k 2 is given. ℜ has an upper limit,ℜmax= tan4(φ/2), that is determined by φ only.