Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection

The single-mode rate equations for a semiconductor laser subject to optical injection are investigated analytically. We determine the first branch of periodic solutions for low values of the injection field. For larger values of the injection field, we derive a third-order pendulum equation for the phase difference of the laser field of the form psi triple prime + psi' = Lambda cos(psi), where Lambda groups all the key laser parameters. This equation captures several aspects of the numerical 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 also obtain very good agreement with the numerically computed spectrum.