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

无赖波(RW)最初被观测到是在公海出现的巨幅波，其频率比高斯统计预测的要高。这个概念后来从海洋学扩展到物理学的其他领域，用来描述巨大幅度的波，或者，一般说来，极端统计事件服从重尾概率分布。光子学是一门研究光在物质介质中产生、探测和传播的物理科学，已被证明是探索无赖波的特别肥沃的土壤。例如，这是因为人们可以相对容易地在光纤系统中实时产生大量的统计数据。到目前为止，在许多非线性光学系统中已经从理论和/或实验上发现了RW。然而，这些研究的大部分都是关于在保守的、弱非线性的光学介质中产生RW，远离介质原子的任何内部共振。*我建议探索光学共振附近非线性介质中非高斯统计和RW激发的物理机制(S)。具体地说，我将研究极端统计事件，在入射光脉冲的中心频率接近介质的内共振频率的条件下，由前向和后向受激拉曼散射以及吸收或放大非线性介质中的噪声源触发的极端统计事件。共振非线性介质涉及光场能量的增益或损耗，通常不支持任何驻波结构，如孤子。然而，我们之前的研究表明，这样的系统有利于非高斯统计，因此RW的出现。因此，我建议解决此类系统中RW的物理性质的一个基本问题。*所提出的工作和所产生的结果将有助于揭示共振非线性系统中非高斯统计产生和流氓波激励的基本方面。所获得的见解将被证明对于实现RW激励的控制是非常有价值的。自然的下一步将是猜测设计RW源，允许以(或多或少)统计控制的方式生成RW。因此，对RW控制的研究，以及它们的统计操纵，可能会为设计高强度波动脉冲的新来源打开令人兴奋的机会。这种光源可以填补高强度相干光源(如激光)和低强度部分相干光源(如发光二极管)之间的空白，结合了这两种光源的优点。这种新型光源可以在随机环境中应用于超宽带光通信。最后，提出的对光学无赖波及其产生机制的基础性探索可能会为研究海洋无赖波的本质和激发机制提供新的见解，海洋学是原始的无赖波栖息地。

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.