We derive the transmission coefficient, T (ω), for grazing incidence of crystals with spatial dispersion accounting for the excitation of multiple modes with different wave vectors k for a given frequency ω. The generalization of the Fresnel formulas contains the refraction indices of these modes as determined by the dielectric function (ω, k ). Near frequencies ω e , where the group velocity vanishes, T (ω) depends also on an additional parameter determined by the crystal microstructure. The transmission T is significantly suppressed, if one of the excited modes is decaying into the crystal. We derive these features microscopically for the Josephson plasma resonance in layered superconductors.
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