Relevance of symmetry for the synchronization of chaotic optical systems and the related Lang-Kobayashi model limitations

Synchronization of chaotic semiconductor lasers has now been demonstrated experimentally in a variety of coupling schemes. Coupling methods include configurations where the transmitter laser system is itself chaotic and drives a receiver system, both lasers are individually chaotic, and both lasers induce the chaos through mutual coupling. The dynamics for each of these scenarios is in many cases adequately captured by the Lang-Kobayashi rate equation model. Such a simplified model, however, ignores fundamental aspects of the laser dynamics, such as the frequency and carrier density material susceptibility dependence, spatial hole burning effects, proper boundary conditions, and the fact that lasers may exhibit pronounced rnultilongitudinal dynamic behavior with and without the presence of a weak external feedback or injection. The model also cannot distinguish between many of the possible coupling geometries realizable in experiments. Using an interactive simulator based on the rigorous microscopic description of the light-matter interaction, we explore the unidirectionally coupled configuration, the relevance of symmetry for the synchronization achieved between two identical lasers, and the differences that arise when the traditional analysis through the Lang-Kobayashi model is compared to the full nonlinear partial differential equation model results.