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The familiar coupled mode equations are extended in a self-consistent fashion to include radiation and other partial wave coupling effects in distributed feedback (DFB) and distributed Bragg reflector (DBR) lasers, as well as orthogonal radiating couplers. This general formulation takes into account the joint interaction of the two coherent contradirectional guided waves with arbitrarily shaped gratings. In addition to the modified coupled mode equations, which contain added constants characterizing the interactions, expressions for radiated waves are also obtained. A particular waveguide geometry is studied in detail. The interaction constants are evaluated for all Bragg orders up to the fourth and various blazing angles. Then the equations are solved for both a DBR and DFB laser. In the former case it is shown that the reflection is smaller than that computed without the interaction constants. Furthermore, reflection is asymmetrical relative to the Bragg condition. The DFB laser is shown to have an asymmetrical longitudinal mode structure even for symmetrical boundary conditions and to have only slightly higher thresholds than previously calculated.
Streifer et al. (Fri,) studied this question.