The optical thin film systems correcting the differential phase shift and preserving the state of polarization are investigated.
First, the thin film theory derived from Maxwell equations is utilized to obtain thin film matrix representations, and the complex admittances, which is the generalized refractive index, for metal thin film and for total internal reflection are derived. The ratio of the parallel and perpendicular components of the electric field, which is related to the state of polarization, is discussed. From these results, dielectricmetal film systems are designed to give differential phase shifts 0˚, 90˚, 180˚ and 270˚ in reflection. Total reflection in thin film system is useful in correcting differential phase shift. Glass ($n_0=1.80$)-$MgF_2$-air system (case of one dielectric film) and glass ($n_0 =1.52$)-ZnS-$MgF_2$-air system (case of two dielectric film) are designed in order to preserve polarization at the wavelength of He-Ne laser beam.
Throughout the present thin film design, computer optimization technique is extensively used. The merit function and its derivatives are analytically calculated for the optimization of the system. In order to give a quarterwave(90˚) differential phase shift and simultaneously high reflectance at 0.633μm and 10.6μm, twenty-layer thin film systems are designed by computer optimization process. It is found that the chromatic differential phase shifts of the film systems vary not more than 0.15˚ and 0.80˚, respectively.
The same computer optimization technique is used in the design of four separated dielectric film system which suppress the change in the polarization state of He-Ne laser beam and $CO_2$ laser beam passing through a four spherical mirror system. The stability of the system for random thickness error is checked. In the final design, $TiO_2$ film system and PbTe film system are used for He-Ne laser beam and for $CO_2$ laser beam, respectively.
