Non-Gaussian statistics and optical rogue waves in resonant nonlinear systems

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Rogue waves (RW) were originally observed as giant amplitude waves occurring in high seas more frequently than predicted by Gaussian statistics. The concept has subsequently been extended from oceanography to other areas of physics to describe waves of enormous amplitudes, or, in general, extreme statistical events obeying heavy-tailed probability distributions. Photonics, which is a physical science of light generation, detection and propagation in material media, has proven to be an especially fertile ground for rogue wave exploration. This is because one can relatively easily generate vast arrays of statistical data in real time in fiber optical systems, for example. To date, RWs have been discovered theoretically and/or experimentally in a multitude of nonlinear optical systems. The bulk of these studies, however, have been concerned with RW generation in conservative, weakly nonlinear optical media, far from any internal resonances of medium atoms. I propose to explore physical mechanisms for non-Gaussian statistics and RW excitation in nonlinear media near optical resonance(s). Specifically, I will study extreme statistical events, triggered by noisy sources in forward and backward stimulated Raman scattering and absorbing or amplifying nonlinear media under the condition that the central frequency of an incident light pulse is close to an internal resonance frequency of the medium. Resonant nonlinear media involve gain or loss of the optical field energy and do not, in general, support any stationary wave structures such as solitons. Yet, our previous research indicates that such systems are conducive to non-Gaussian statistics and hence RW emergence. Thus, I propose to address a fundamental issue of the physical nature of RWs in such systems. The proposed work and generated results will shed light on fundamental aspects of non-Gaussian statistics generation and rogue wave excitation in resonant nonlinear systems. The gained insights will prove invaluable for attaining control of RW excitation. The natural next step will be to conjecture devising an RW source, allowing for RW generation in a (more-or-less) statistically controlled manner. Thus, the studies into RW control and, perhaps, their statistics manipulation can open exciting opportunities to design novel sources of high-intensity fluctuating pulses. Such sources can fill in the gap between high-intensity coherent sources such as lasers and low-intensity partially coherent ones, such as light-emitting diodes, combining the advantages the the two source types. The new sources can find applications to ultra wide band optical communications through random environments. Finally, the proposed fundamental explorations into optical rogue waves and their generating mechanisms may offer new insights into rogue wave nature and excitation mechanisms in oceanography, the original rogue wave habitat.