A novel power-series method to solve the coupled-wave equations is introduced. The method is used to calculate the threshold gain margins of a complex-coupled distributed-feedback laser as functions of the ratio of gain coupling to index coupling (|κg|/|κn|) and of the phase difference between the index and the gain gratings. For coupling coefficient |κ|l < 0.9, the laser shows a mode degeneracy at specific values of the ratio |κg|/|κn| for cleaved facets. At phase differences π/2 and 3π/2 between the gain and the index gratings, an antireflection-coated complex-coupled laser becomes multimode, and a different mode starts to lase. The effect of facet reflectivity (both magnitude and phase) on the gain margin of a complex-coupled DFB laser is also investigated. Although the gain margin varies slowly with the magnitude of the facet’s reflectivity, it shows large variations as a function of the phase. Spatial hole burning was found to be minimum at phase difference nπ, n = 0, 1 … , and maximum at phase differences π/2 and 3π/2.
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