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For planar multilayered structures composed of thin-film waveguides with anisotropic or gyrotropic media, resonant polarization conversion and anomalous lateral beam shift are considered. If an oblique gaussian beam is incident under the optimum condition, polarization of the field incident on the top region is almost completely converted to cross polarization; under the other condition, instead of the polarization conversion, the corresponding system produces a large beam shift—nearly twice the ordinary beam shift of a prism coupling structure. The interpretation of the physical mechanism for these phenomena is presented with numerical examples. New schemes for modulation and optical switching applications are proposed.