Nonlinear dynamics of semiconductor microring lasers

Semiconductor ring lasers (SRLs) are a particular type of semiconductor lasers where the laser cavity consists of a ring-shaped waveguide. Due to their symmetry, SRLs can emit in one of two counter-propagating modes and are therefore recognized to be promising sources in photonic integrated circuits. In particular, this possibility of bistable directional operation has paved the way for encoding digital information in the emission direction of SRLs with record low values for switching times and energies [1].
We have applied a singular perturbation technique to reduce a set of rate equa- tions for a SRL to two equations for the relative modal intensity and the phase difference between the two counter-propagating modes [2]. Not only do these re- duced equations simplify the bifurcation analysis of the possible steady-state solu- tions considerably, they also allow for a two-dimensional phase-space description of the laser. In particular, the shape of the invariant manifolds of the saddle point in the system is studied and a full bifurcation analysis of this two-dimensional laser system is carried out. This approach also reveals that semiconductor ring lasers are an optical prototype of nonlinear systems with Z2 symmetry.
We investigate both theoretically and experimentally the stochastic switching between two counter-propagating lasing modes of a SRL. Experimentally, the resi- dence time distribution cannot be described by a simple one parameter Arrhenius exponential law and reveals the presence of two different mode-hop scenarios with distinct time scales. The topological phase-space picture of the two-dimensional dynamical system gives insight into the observed features [3]. Expanding on the mode-hopping study in the bistable region, we also show how the operation of the device can be steered to multistable dynamical regimes, predicted by the two- dimensional model. By analyzing the phase-space in this model, we predict how the stochastic transitions between multiple stable states take place and confirm it experimentally [4].
Finally, we show theoretically and experimentally that by perturbing the Z2 symmetry, SRLs can be driven into a regime of excitability. The global shape of the invariant manifolds of the saddle in the vicinity of a homoclinic loop are shown to determine the origin of excitability and the features of the excitable pulses [5]

[1] M. T. Hill et. al., Nature 432, 206-209 (2004). [2] G. Van der Sande et. al., J. Phys. B 41, 095402 (2008). [3] S. Beri et. al., Phys. Rev. Lett. 101, 093903 (2008). [4] L. Gelens et. al., Phys. Rev. Lett. 102, 193904 (2009). [5] S. Beri et. al., Phys. Lett. A 374, 739-743 (2010).