MECHANISM FOR PERIOD-DOUBLING BIFURCATION IN A SEMICONDUCTOR-LASER SUBJECT TO OPTICAL-INJECTION

The single-mode rate equations for a semiconductor laser subject to op tical injection are investigated analytically. We determine the first branch of periodic solutions for low values of the injection field. Fo r larger values of the injection field, we derive a third-order pendul um equation for the phase difference of the laser field of the form ps i triple prime + psi' = Lambda cos(psi), where Lambda groups all the k ey laser parameters. This equation captures several aspects of the num erical bifurcation diagram, namely, the fixed amplitude of the period- one solution and the period-doubling bifurcation. Finally, we compute the optical power spectrum utilizing the perturbation solutions of the phase equation before and after the period-doubling transition. We al so obtain very good agreement with the numerically computed spectrum.