Dynamics of two lasers coupled via mutual cavity-loss modulation

Abstract

A mathematical model for synchronization of two single-mode semiconductor lasers is built within the framework of the rate equations approximation. The model has the form of a system of nonlinear ordinary differential equations for electron concentrations and photon densities in both lasers. The lasers are coupled in such a way that the cavity losses of each device are proportional to the light intensity emitted by the other. Besides, the equations take into account the nonlinear (quadratic) losses. The system is analyzed by the methods of bifurcation theory and multiple scale techniques. It is shown that the model exhibits different behavior at strong and weak coupling between the lasers. At strong coupling, there is no oscillation in the system,
though the phenomena of bistability and hysteresis are possible. At weak coupling, a stable limit cycle and spiky relaxation oscillations may emerge. It is found that synchronous oscillations of the photon density in lasers occur in antiphase. The proposed synchronization scheme could be useful in obtaining long-period pulsations.