The dynamical behaviour of a semiconductor ring laser

We review theoretical results on the dynamics of solitary single longitudinal mode and single transversal mode semiconductor ring lasers. These analyses are based on a rate equation model for the slowly varying envelopes of the counter-propagating fields in the ring cavity which has been proposed by Sorel et al. [Opt. Lett. 27, 1992 (2002); IEEE J. Quantum Electron. 39, 1187 (2003)]. The model shows several operating regimes. The lasers are found to operate bidirectionally up to twice the threshold, where unidirectional operation starts. Just above threshold, the lasers operate in a regime where the two counterpropagating modes are continuous wave, while as the injected current is increased, a regime appears where the intensities of the two counterpropagating modes undergo alternate sinusoidal oscillations. To understand these dynamical features, we discuss a reduction of this basic rate equation model derived by Van der Sande et al. [accepted for publication in J. Phys. B (2008)]. The reduction has been achieved using asymptotic methods based on the typical relative scaling of the dynamical time scales of the system. Physical conditions for the emergence of the operating regimes are assessed quantitatively in terms of nonlinear (saturation processes) and linear coupling (backscattering) between the counter-propagating modes.