Dynamics of Evanescently-Coupled Laser Pairs With Unequal Pumping: Analysis Using a Three-Variable Reduction of the Coupled Rate Equations

The five coupled rate equations used to describe laterally-coupled pairs of lasers with weak coupling and unequal pumping are reduced to a new system of three equations. This enables approximate closed-form steady-state solutions and explicit expressions for the boundaries between regions of stable and unstable dynamics to be found. The results of applying these approximations to specific cases of coupled laser pairs are shown to be in good agreement with results obtained from numerical solutions of the original set of five equations as well as earlier results from the literature. In addition the approximations based on the reduced set of equations allow a systematic investigation of the effects of material, device and operating conditions on trends and novel features in the dynamics of laterally-coupled laser pairs. The algebraic results give insight into trends with parameters without the need for extensive numerical computation and should therefore be of use in modelling two-element VCSEL arrays for numerous potential applications.