Abstract

At a given wavelength, we determine all possible solution pairs (ϕ, d absorbing substrate that achieve a given unpolarized-light reflectance R_u. The trajectory of the point that represents a solution pair in the ϕ- d plane depends significantly on the extinction coefficient of the substrate and on whether R_u is or the normal-incidence reflectance ${\overline{R}}_{\text{O}}$ of the uncoated substrate. When R_u ${\overline{R}}_{\text{O}}$, the specified reflectance is achieved over a limited range of ϕ. At the least possible incidence angle, the film thickness ≅ 1/8th wave, with the exact equality holding if the substrate is transparent. As an application of these results we consider SiO₂ films on Si detectors that produce R_u = 0.75, 0.6667, and 0.50 at laser wavelengths of 337, 488, and 633 nm. If the first three detectors of the four-detector photopolarimeter (FDP) are coated to have these reflectance levels, with the reflectance diminishing in the direction of propagation of the light beam, and the last detector is anti-reflection-coated (e.g., with a quarter-wave Si₃N₄ layer), equipartition of energy among the four detectors is accomplished for incident unpolarized light. Such condition is desirable in the operation of the FDP.¹ The ellipsometric parameters of the coated surfaces and the determinant of the FDP instrument matrix are also calculated.

© 1990 Optical Society of America