Stability of self-pulsing due to Hopf bifurcation in semiconductor lasers

A formulation is given of the stability criterion for oscillations arising at Hopf bifurcations in semiconductor lasers. A second-order perturbation expansion is utilized to provide nonlinear rate equations for the laser. The rate equations contain terms whose second-order partial derivatives are required in the definition of stability parameters. Using these parameters, a simple statement of the stability criterion is possible. Numerical calculations are included, using typical device parameters, and show the existence of both stable and unstable Hopf oscillations.