Polarization properties of retroreflecting right-angle prisms

The cumulative retardance
t 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
and 90°   is calculated as a function of
and prism refractive index n. Quarter-wave retardation (QWR) is obtained on retroreflection with minimum angular sensitivity when n 
2  112  1.55377 and   45°. A QWR prism made of N-BAK4 Schott glass (n  1.55377 at   1303.5 nm) has good spectral response (5° retardance error) over the 0.5–2 m 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 m (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   45°. A PbTe right-angle prism introduces near-half-wave retardation (near-HWR) with a 2% error over a broad
4  12.5 m 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   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.