Given a transparent film of refractive index n1 on an absorbing substrate of complex refractive indexn2-jk2, we examine the constraint on n1, n2, and k2 such that the film-substrate system acts as an external-reflection retarder of specified retardance Δ at a specified angle of incidence φ. The constraint, which takes the form ƒ(n1,n2,k2;φ,Δ) = 0, is portrayed graphically by equi-n1 contours in the n2,k2 plane at φ = 45, 70° and for Δ = ±90 and ±180°, corresponding to quarterwave and halfwave retarders (QWR and HWR), respectively. The required film thickness as a fraction of the film thickness period and the polarization-independent device reflectance R are also studied graphically as functions of the optical constants. It is found that as n2 → 0, R → 1, so that a metal substrate such as Ag is best suited for high-reflectance QWR (φ > 45°) and HWR (φ ≤ 45°). However, films that achieve QWR at φ ≤ 45° are excellent antireflection coatings of the underlying dielectric, semiconductor, or metallic substrate.
R. M. A. Azzam and Bruce E. Perilloux, "Constraint on the optical constants of a film-substrate system for operation as an external-reflection retarder at a given angle of incidence," Appl. Opt. 24, 1171-1179 (1985)