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The guiding characteristics of a grating waveguide is presented for the general case of oblique incidence. The formulation of the three-dimensional boundary-value problem is carried out rigorously, taking into account the hybrid nature of the guided modes. First of all, the TE and TM modes in each constituent region of the waveguide structures are investigated. Secondly, the TE and TM modes are coupled by the surfaces of the grating, resulting in new physical effect of extra stop bands. Numerical results are obtained extensively to illustrate the new physical effect, and to evaluate the effect of grating profiles.
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