Single-reflection film–substrate half-wave retarders with nearly stationary reflection properties over a wide range of incidence angles

The complex reflection coefficient for the p polarization of a transparent film on an absorbing or transparent substrate can be made equal to the negative of that for the s polarization, and hence the film–substrate system acts as a half-wave retarder (HWR), by proper selection of film refractive index N₁, film thickness d, and angle of incidence ϕ.This condition, which generally holds only at normal incidence, becomes possible at oblique incidence also if N₁ is within a certain range, $1<N_1<{\widehat{N}}_1$. For a given substrate and given N₁, a procedure is described to determine ϕ_HWR and d_HWR that achieve a HWR. As N₁ is increased from 1 to the upper limit ${\widehat{N}}_1$, ϕ_HWR decreases from 90° to 0 monotonically. d_HWR approximately equals (exactly equals when the substrate is a perfect dielectric or a perfect conductor) an odd multiple of half of the film-thickness period evaluated at ϕ_HWR. Significantly, we find that the film–substrate HWR retains nearly the same characteristics of normal-incidence reflection over the range of angle from 0 up to (and beyond) ϕ_HWR. Detailed data are presented of HWR’s that use transparent films on metallic (Al and Ag), semiconducting (Si), and dielectric (glass) substrates at two laser wavelengths (0.6328 and 10.6 μm). Film–substrate HWR’s permit the realization of simple polarization-insensitive parallel-mirror beam displacers, 90° rooftop reflectors, and biconical axicons and waxicons.