Constraint on the optical constants of a film-substrate system for operation as an external-reflection retarder at a given angle of incidence.

Constraint on the optical constants of a film-substrate system for operation as an external-reflection retarder at a given angle of incidence," Appl. Given a transparent film of refractive index n 1 on an absorbing substrate of complex refractive index n 2-jk 2 , we examine the constraint on ni, n2, and k 2 such that the film-substrate system acts as an external-reflection retarder of specified retardance A at a specified angle of incidence. The constraint, which takes the form f(ni,n 2 ,k 2 ;0,A) = 0, is portrayed graphically by equi-nj contours in the n 2 ,k 2 plane at k = 45, 700 and for A = +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 (> 45°) and HWR (< 450). However, films that achieve QWR at k < 450 are excellent antireflection coatings of the underlying dielectric, semiconductor, or metallic substrate.