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 n2-jk2 can be coated by a transparent thin film of refractive index n1 and normalized thickness ζ so that the ratio of complex reflection coefficients for the pand s polarizations of the film-covered substrate ρ is the inverse of that of the film-free substrate ρ¯ at a given angle of incidence φ. A pair of parallel (metallic) mirrors, one uncoated and the other coated with a ρ-inverting layer, causes a beam displacement without change of polarization and with a certain net reflectance (insertion loss) ℜ. In this paper the constraint on n1,n2,k2 for ρ inversion (ρρ¯ = 1) is represented by a family of constant -n1 contours in the n2k2 plane at φ = 45, 60, and 75°. Along each solution curve, ζ and ℜ are also plottedvs n2 at constant n1. 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