Asymptotic approach to the analysis of mode-hopping in semiconductor ring lasers

We investigate the directional mode-hopping in semiconductor ring lasers in the limit of small noise intensity. We show how only long time scales are involved in the hopping process. In such limit, the initial stochastic rate equations can be reduced to an auxiliary Hamiltonian system, and the dependence of the hopping on the laser parameters can be investigated. The predictions made from the reduced model agree well with the results obtained by simulating the full rate-equation system.