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 (‖κ<sub><i>g</i></sub>‖/‖κ<sub><i>n</i></sub>‖) and of the phase difference between the index and the gain gratings. For coupling coefficient ‖κ‖<i>l</i> < ., the laser shows a mode degeneracy at specific values of the ratio ‖κ<sub><i>g</i></sub>‖/‖κ<sub><i>n</i></sub>‖ 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 <i>n</i>π, <i>n</i> =, …, and maximum at phase differences π/2 and 3π/2.
© 2000 Optical Society of America
(140.3490) Lasers and laser optics : Lasers, distributed-feedback
(140.3580) Lasers and laser optics : Lasers, solid-state
(230.6080) Optical devices : Sources
(270.3430) Quantum optics : Laser theory
Muhammad Arif and Mohammad A. Karim, "Analysis of a Dephased Complex-Coupled Distributed-Feedback Laser by the Power-Series Method," Appl. Opt. 39, 954-961 (2000)