The condition of zero reflection of p- and s-polarized light by a transparent bilayer on an absorbing substrate is derived in the form |gν(ø,Ni)| ≤ 1, where gν is a function of the angle of incidence ø, the refractive indices Ni(i = 0,1,2,3) of the system, and the polarization state ν (= p or s). As an application, the air-Si3N4-SiO2-Si system is considered at two laser wavelengths λ = 6328 and 3250 Å. The thicknesses of the two films of the bilayer and the unextinguished reflectance are determined as functions of ø, and the results appear graphically and in tables. Extinction of the s polarization is accompanied by low overall residual reflectance (e.g., for incident unpolarized light, it is 1.6% for λ = 6328 Å at ø = 45°). On the other hand, suppression of the p polarization at a high incidence angle is accompanied by high s reflectance (e.g. = 96%for λ = 3250 Å at ø = 83°). This demonstrates that efficient bilayer reflection polarizers are possible.
R. M. A. Azzam and Karim Javily, "Antireflecting and polarizing transparent bilayer coatings on absorbing substrates at oblique incidence," Appl. Opt. 24, 519-526 (1985)