A design procedure is described to determine the thicknesses of single-layer coatings of a given dielectric on a given metallic substrate so that any input polarization of light is preserved after two reflections at the same angle of incidence from a parallel-mirror beam displacer or an axicon. This is achieved by equalizing the net complex p and s reflection coefficients (also called the radial and azimuthal eigenvalues of an axicon) after two reflections. The net polarization-independent reflectance (insertion loss) of the device is computed and found to exceed the net minimum parallel reflectance of the uncoated device for incidence above a certain angle. Thus the dielectric films serve (1) protective, (2) polarization-corrective, and (3) reflectance-enhancement functions simultaneously. The sensitivity of the designs (deviation from the condition of polarization preservation) to small film-thickness and angle-of-incidence errors is examined. Results are presented graphically and in tables of applications of the method to beam displacers and axicons for He-Ne laser light, λ = 0.6328 µm, using Al2O3 (or Si2O3)/Al and MgF2/Al film-substrate systems, and for CO2 laser light, λ = 10.6 µm, using ZnS or ThF4 films on an Ag substrate.
R. M. A. Azzam and M. Emdadur Rahman Khan, "Polarization-preserving single-layer-coated beam displacers and axicons," Appl. Opt. 21, 3314-3322 (1982)