The problem of wave guidance in thin-film dielectric waveguides is formulated using the modematching method in the sense of least squares. The result is applied to analysis of the first-order Bragg interactions in a three-layered dielectric waveguide having a sinusoidal surface corrugation. The precise numerical results of the dispersion relation near the first-order stopband are presented for both of the lowest TE and TM modes and compared with those obtained by a conventional perturbation approximation.
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