The cumulative retardance Δt introduced between the p and the s orthogonal linear polarizations after two successive total internal reflections (TIRs) inside a right-angle prism at complementary angles Φ and 90°−Φ is calculated as a function of Φ and prism refractive index n. Quarter-wave retardation (QWR) is obtained on retroreflection with minimum angular sensitivity when n=(√2+1)1/2=1.55377 and Φ=45°. A QWR prism made of N-BAK4 Schott glass (n=1.55377 at λ=1303.5 nm) has good spectral response (<5° retardance error) over the 0.5-2 μm visible and near-IR spectral range. A ZnS-coated right-angle Si prism achieves QWR with an error of <±2.5° in the 9-11 μm (CO2 laser) IR spectral range. This device functions as a linear-to-circular polarization transformer and can be tuned to exact QWR at any desired wavelength (within a given range) by tilting the prism by a small angle around Φ=45°. A PbTe right-angle prism introduces near-half-wave retardation (near-HWR) with a ≤2% error over a broad (4≤λ≤12.5 μm) IR spectral range. This device also has a wide field of view and its interesting polarization properties are discussed. A compact (aspect ratio of 2), in-line, HWR is described that uses a chevron dual Fresnel rhomb with four TIRs at the same angle Φ=45°. Finally, a useful algorithm is presented that transforms a three-term Sellmeier dispersion relation of a transparent optical material to an equivalent cubic equation that can be solved for the wavelengths at which the refractive index assumes any desired value.
R. M. A. Azzam and H. K. Khanfar, "Polarization properties of retroreflecting right-angle prisms," Appl. Opt. 47, 359-364 (2008).