Symmetry-breaking bifurcations in two mutually delay-coupled lasers

Abstract

We consider a symmetric system of delay differential equations arising from a model of two mutually delay-coupled semiconductor lasers. The system is described using the Lang-Kobayashi rate equations whose basic solutions are called compound laser modes (CLMs). We employ a group-theoretic approach to find solutions and to identify symmetry-breaking steady-state and Hopf bifurcations. This classification allows us to predict the symmetry group of a bifurcating branch of solutions from a symmetry- breaking bifurcation. Methods and techniques used in this study can be extended to larger symmetric laser networks.