Abstract
Simple and asymptotically exact dispersion relations describing the symmetric first-order Bragg interactions in an active planar dielectric waveguide have been deduced for the case of even TE modes. Either the index or the gain is assumed to have a sinusoidal variation in the propagation direction. The guided wave is absolutely unstable in the first-order Bragg region and the characteristics of this instability have been examined. The mode theory is used to obtain the exact dispersion relation from which, by a perturbation expansion, the first-order dispersion relations are determined.
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