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One of the more challenging aspects of optical thin film design has been to design the s- and p-polarizations of a filter to have the same reflectance as each other at a given angle of incidence. There have been various contributions in the literature for over half of a century to the understanding of this behavior. Some of these works are reviewed and their results are illustrated in newer graphic formats with examples. Baumeister, in 1961, reported in Optica Acta on “The Transmission and Degree of Polarization of Quarter-wave Stacks at Non-normal Incidence.” In 1970, Costich described a method of transforming massive media to nonpolarizing effective massive media. He applied two design techniques to the problem of making polarization independent metal-dielectric-metal interference filters and polarization independent beam splitters. The polarization dependence of interference coatings may be reduced by combining two approaches. The first is the use of a polarization insensitive layer combination, and the second is to transform the massive media to effective massive media having little polarization splitting of their effective indices. In 1976, Thelen reported on nonpolarizing interference films inside a glass cube. He described another method using only quarter-wave layers including the equations to accomplish this and he refers to the work of Baumeister reported from 1961. He points out some limitations to the Costich approach. Henderson showed the benefits of using three materials instead of only two in a 1978 paper. Two materials could be made non-polarizing for one wavelength and angle, but three materials would provide non-polarizing performance over a broader wavelength range. At normal incidence, a layer-pair of quarter waves of high and low indices is the basic building block to stack one layer-pair upon another to create a high reflection at a given wavelength band centered at the design wavelength for which the layers are quarter-waves. When plotted on a Fresnel Reflectance Amplitude diagram, each quarter-wave forms a semicircle at the design wavelength, and the layer pair then covers 360°. In the case of non-polarizing designs, the building blocks composed of three materials are formed from four quarter-waves or 720° of phase change. These have the property at the design wavelength and angle to advance the reflectance equally for both the s- and p-polarization. There is an apparent similarity here between the effect of this medium-index layer and the typical halfwave thickness high index layer as an achromatizing layer for a three material broadband four quarter-wave antireflection coating design. There is also a similarity on a reflectance amplitude diagram to the mathematical shape of a Limacon for both the s- and p-polarization. The s- polarization has an obvious internal Limacon loop and the p-loop expands to appear more as a spiral in some cases. The Herpin/Epstein concept might lead one to consider accomplishing the function of the three-material designs with only two materials. The possibilities and limitations of only two-material designs are examined.
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