We develop a dynamical model suitable for the description of two mutually coupled semiconductor lasers in a face-to-face configuration. Our study considers the propagation of the electric field along the compound system as well as the evolution of the carrier densities within each semiconductor laser. Mutual injection, passive optical feedback, and multiple reflections are accounted for in this framework, although under weak to moderate coupling conditions. We systematically describe the effect of the coupling strength on the spectrum of monochromatic solutions and on the respective dynamical behavior. By assuming single-longitudinal-mode operation, weak mutual coupling and slowly varying approximation, the dynamical model can be reduced to rate equations describing the mutual injection from one laser to its counterpart and vice versa. A good agreement between the complete and simplified models is found for small coupling. For larger coupling, higher-order terms lead to a smaller threshold reduction, reflected itself in the spectrum of the monochromatic solutions and in the dynamics of the optical power.
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