Effect of Amplitude-Phase Coupling on the Formation of Dissipative Topological Defects in Coupled Lasers

Finding a globally stable defect-free state can be exploited for solving computationally hard optimization problems, which occur in a wide range of fields. We present the effect of amplitude-phase coupling (linewidth enhancement factor, α) on the formation of dissipative topological defects in a one-dimensional ring array of coupled lasers. We have found that the probability of topological defects (ρ) depends on several parameters, such as system size (number of lasers (N)), amplitude-phase coupling, coupling strength, and pump strength. Specifically, it increases monotonically with the system size. It is also found to be the lowest for a large amplitude-phase coupling factor. The probability of topological defects decreases significantly when the lasers operate close to the threshold. For different types of coupling between the lasers, the relation for the probability of topological defects is found as \({\varvec{\rho}}_{{{\varvec{NN}}}} > {\varvec{\rho}}_{{{\varvec{NU}}}} > {\varvec{\rho}}_{{{\varvec{NNN}}}}\) .