Analysis of a dephased complex-coupled distributed-feedback laser by the power-series method

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 (|kappa(g)|/|kappa(n)|) and of the phase difference between the index and the gain gratings. For coupling coefficient |kappa|l < ., the laser shows a mode degeneracy at specific values of the ratio |kappa(g)|/|kappa(n)| for cleaved facets. At phase differences pi/2 and 3pi/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 npi, n =, ..., and maximum at phase differences pi/2 and 3pi/2.