The conditions under which light interference in a transparent quarter-wave layer of refractive index n1 on a transparent substrate of refractive index n2 leads to 50% reflectance for incident unpolarized light at an angle φ are determined. Two distinct solution branches are obtained that correspond to light reflection above and below the polarizing angle, φp , of zero reflection for p polarization. The real p and s amplitude reflection coefficients have the same (negative) sign for the solution branch φ>φp and have opposite signs for the solution branch φ<φp . Operation at φ<φp is the basis of a 50%–50% beam splitter that divides an incident totally polarized light beam (with p and s components of equal intensity) into reflected and refracted beams of orthogonal polarizations [ Opt. Lett. 31, 1525 (2006) ] and requires a film refractive indexn1⩾(2√+1)n2−−√ . A monochromatic design that uses a high-index TiO2 thin film on a low-index MgF2substrate at 488 nm wavelength is presented as an example.
Journal of the Optical Society of America A
R. M. A. Azzam and F. F. Sudradjat, "Quarter-wave layers with 50% reflectance for obliquely incident unpolarized light," J. Opt. Soc. Am. A 24, 850-855 (2007)