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The scattering characteristics of dielectric periodic structures are discusses based on Floquet modes analysis and hybrid finite element methods in the paper. Propagating and evanescent Floquet modes are analyzed theoretically. The hybrid finite element method is developed. Then the effects of structure parameters, dielectric material, incident angle and frequency on propagation directions and power of Floquet modes are studied through numerical simulations and analysis. Meaning conclusions are drawn. Thus, this paper is of both theoretical and practical interest for the design and analysis of DPSs.