The first demonstration of optical rogue waves in a microstructured optical fibre [1] triggered a major scientific interest in the understanding of the physical mechanisms behind the origin and development of optical rogue waves, the probability of observing them, and the type of optical systems capable of generating these extreme events [2]. For nonlinear optical cavities, experimental evidence of deterministic rogue waves was first provided in lasers with injected signals [3]. The dynamics of many of these systems, however, are confined to one spatial dimension or less.

In this talk we describe a mechanism for the generation of fully two-dimensional spatio- temporal rogue waves in the presence of turbulence of interacting optical vortices. We consider the dynamics in the transverse plane of the complex Ginzburg-Landau (CGL) and complex Swift-Hohenberg equations in the presence of an external forcing. Without spatio- temporal coupling, chaos, turbulence and, consequently, rogue waves are forbidden. With spatio-temporal coupling and below the locking threshold, we demonstrate phase instabilities leading to amplitude instabilities and then to regimes of defect-mediated turbulence with interacting optical vortices [4]. Depending on the density of the moving vortices, short distance interactions lead to sudden, rare, large and randomly positioned peaks of the light intensity. The statistics of these events is highly non-Gaussian and the probability density function is well described by the Weibull distribution [4]. The small aspect ratio, the full 2D character and the quick dynamics represent the major advantages of transverse optical devices for studying the generation and control of rare events with applications, by universality, in hydrodynamics and oceanography. We note that the CGL model equations have a broad range of applications in optics, ranging from broad area lasers to optical parametric oscillators, and to polaritons in semiconductor microcavities.

References:

[1] D. R. Solli, C. Ropers, P. Koonath, and B. Jalai, “Optical rogue waves,” Nature 450, 1054 (2007)

[2] J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photonics 8, 755 (2014)

[3] C. Bonatto et al., “Deterministic Optical Rogue Waves,” Phys. Rev. Lett. 107, 053901 (2011)

[4] C. Gibson, A. M. Yao and G.-L. Oppo, “Optical rogue waves in vortex turbulence,” Phys. Rev. Lett. 116, 043903 (2016)