Phase properties of high-reflectance two-material periodic mirrors: application to oblique-incidence tunable filters

Mathematical expressions are developed for the phase-shift derivative with respect to the wavelength, in the case of nonquarter-wave, two-material, high-reflectance, periodic mirrors. These expressions are applied to the case of oblique incidence, and a condition relating the layer indices, which provides identical phase dispersion curves for both the P and S polarizations, is derived. The use of such mirrors in Fabry-Perot filters results in a common peak wavelength for both polarizations when the filter is used at oblique incidence, instead of the two separate spectral peaks usually observed. This property, which is illustrated by several numerical examples, is of great interest for the design of tunable filters, in which the angle of incidence is frequently used as a tuning parameter.