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 f(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.
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