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The symmetric first-order Bragg interactions of the optical guided wave in a periodically corrugated dielectric layered structure are investigated for the case of TE mode. The dispersion relation that clarified the propagation characteristics of the optical guided wave in this system is derived systematically by a singular perturbation method using multiple space scales. The obtained formulation is possible to give analytically an estimation of the system, and its numerical results give a designing basis at composing the filter of the optical guided wave and resonator of the semiconductor lasers.