Abstract

Rare and extreme events are ubiquitous in many complex systems, from rogue waves in the ocean to financial crisis. In optics, extreme events have been identified in pulses propagating in nonlinear optical fibers and in the temporal dynamics of some semiconductor laser systems. Many questions remain unsolved concerning the minimum ingredients necessary to produce extreme events and how to control them. In this work, we study a dissipative, quasi 1D spatially extended system (a broad area line VCSEL with integrated saturable absorber of original design [1]) and show experimentally the occurrence in certain parameter regions of high amplitude and rare pulses (Fig. 1). Our system has the peculiar property of not displaying a complex dynamics (and thus extreme events) without spatial coupling. It is thus in stark contrast to existing studies in active dissipative systems where extreme events were found in the chaotic temporal dynamics of zero-dimensional systems [2]. We analyze the role of spatial coupling in the generation of extreme events. We experimentally demonstrate that the spatio-temporal dynamics has a characteristic correlation length smaller than the lasing area. Using cross-correlation measurements by recording the dynamics at two different locations simultaneously, we rule out the mechanism of collision of coherent structure as a mechanism for rogue wave formation in our system, as found e.g. in [3]. With the help of numerical simulations, we can identify several dynamical regimes giving rise to different long-tail probability density distributions. We calculate the Lyapunov spectrum of the numerically integrated dynamics and relate the presence of spatio-temporal chaos in our system to the occurrence of extreme events.

© 2015 IEEE