Extreme events and phase dynamics in a forced semiconductor ring laser
The study of extreme events in optical systems has attracted lots of attention essentially due to their formal similarity to emblematic oceanic rogue waves . Due to this origin, optical fibers have long been the system of choice for their analysis . However, the understanding of extreme events is challenging and potentially useful in many nonlinear systems beyond oceanography and optical experiments may shed light on many generic phenomena leading to the appearance of rogue events. This is especially true when single shot spatially and temporally resolved measurements can be performed together with the accumulation of very large data sets. Such measurements are of course notoriously difficult to achieve in nonlinear fiber optics due to the involved time scales which often oblige the experimentalist to make use of spectral measurement techniques.
In this contribution, we analyse the nucleation of extreme events in a fast (nanosecond time scale) spatially extended oscillatory medium with coherent forcing. In particular, we focus on the predictability of individual events and their analysis in terms of the (spatio-temporally resolved) phase dynamics of the system.
The experimental system is a strongly multimode ring semiconductor laser  consisting of a millimetric semiconductor active medium enclosed in a 1-m long optical cavity under coherent external forcing. While similar experiments have often been performed in single mode lasers (described by lowdimensional dynamical systems ) the description of this particular experiment requires the use of partial differential equations taking into account the propagation of the electric field. In the single-mode case, the many accessible dynamical regimes are well documented both experimentally and theoretically and include frequency and phase locking, bistability, excitability and chaos. In the multimode case (and especially with the geometrical characteristics of this particular experiment), the system is much less documented in particular due to the stiffness of the model equations and its very large number of degrees of freedom.
We analyze our results thanks to a set of partial differential equations describing the field and semiconductor medium evolution . In some cases the full set of PDEs can be reduced to a single soliton forming equation, namely a modified Ginzburg- Landau equation with nearly resonant forcing [5,6], providing both a simple numerical system and a connection to a much broader class of systems. Indeed, this model markedly differs from the nonlinear Schrödinger equation not only due to the presence of dissipation, but also due to its oscillatory nature. Here, we analyze the impact of phase dynamics in the formation of coherent structures in this system, from phase solitons to extreme events. In phase-unstable regimes, where usually strong multimode competition occurs, we attempt the prediction of extreme events based on local phase space reconstruction.
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