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Coupling between the modes in a planar optical waveguide induced by a boundary step discontinuity, by a single groove and by a grating with arbitrary cross section, is investigated theoretically. Analytical expressions for the coupling mode coefficients are obtained by the mode-matching method, containing the angular dependence in explicit form for both TE and TM incidence. An analogy of Brewster's law for a planar waveguide with a single step boundary discontinuity is obtained. The results for gratings are compared with the coupled-mode theory and the total field analysis.