Constraint on the optical constants of a transparent film on an absorbing substrate for inversion of the ratio of complex p and s reflection coefficients at a given angle of incidence.

An absorbing substrate of complex refractive index n(2)-jk(2) can be coated by a transparent thin film of refractive index n(1) and normalized thickness zeta so that the ratio of complex reflection coefficients for the p and s polarizations of the film-covered substrate rho is the inverse of that of the film-free substrate rho at a given angle of incidence phi. A pair of parallel (metallic) mirrors, one uncoated and the other coated with a rho-inverting layer, causes a beam displacement without change of polarization and with a certain net reflectance (insertion loss) ?. In this paper the constraint on n(1),n(2),k(2) for rho inversion (rhorho = 1) is represented by a family of constant -n(1) contours in the n(2)k(2) plane at phi = 45, 60, and 75 degrees . Along each solution curve, zeta and ? are also plottedvs n(2) at constant n(1). Analysis of the effect of small errors of incidence angles, film refractive index, and thickness is presented for two specific designs using Al mirrors at 650 and 950 nm.