Quarter-wave layers with 50% reflectance for obliquely incident unpolarized light.

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 phi are determined. Two distinct solution branches are obtained that correspond to light reflection above and below the polarizing angle, phi(p), of zero reflection for p polarization. The real p and s amplitude reflection coefficients have the same (negative) sign for the solution branch phi>phi(p) and have opposite signs for the solution branch phior=(square root 2+1)square root n2. A monochromatic design that uses a high-index TiO2 thin film on a low-index MgF2 substrate at 488 nm wavelength is presented as an example.