Given a transparent film of refractive index n₁ on an absorbing substrate of complex refractive index n₂-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.

© 1985 Optical Society of America

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