We characterize the geometric and dynamic phase introduced by a lossless dielectric multilayer into an elliptically polarized input wave with oblique incidence. The phases are conveniently mapped on the Poincaré sphere as a function of the Stokes vector of the input field. The geometric phase interval of the transmitted wave is determined by the difference of the phases of the overall transmission coefficients for the TE and TM waves. The same conclusion is obtained for the reflected wave. To exemplify the theory, we show the surface plots of the geometric phase intervals as a function of the incident angle and the phase thickness of a single layer and a periodic multilayer.
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