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

异常浪（RW）最初被观测到是在公海出现的巨大振幅波，比高斯统计预测的频率要高。这个概念后来从海洋学扩展到物理学的其他领域，用来描述振幅巨大的波浪，或者一般来说，描述服从重尾概率分布的极端统计事件。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，已被证明是探索异常波的一个特别肥沃的土壤。这是因为人们可以相对容易地在光纤系统中实时生成大量的统计数据。迄今为止，rw已经在许多非线性光学系统中被理论和/或实验发现。然而，这些研究的大部分都是关于保守的弱非线性光学介质中RW的产生，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激励的物理机制。具体来说，我将研究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和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失，通常不支持任何固定波结构，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，我建议解决这种系统中rw的物理性质的一个基本问题。******提出的工作和产生的结果将揭示共振非线性系统中非高斯统计产生和异常波激发的基本方面。所获得的见解将证明对实现RW激励的控制是无价的。下一步自然是推测设计一个RW源，允许RW以（或多或少）统计控制的方式产生。因此，对RW控制的研究，也许，他们的统计操作，可以为设计高强度波动脉冲的新来源提供令人兴奋的机会。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，结合了两种光源类型的优点。新光源可以在随机环境下的超宽带光通信中找到应用。最后，本文提出的光学异常波及其产生机制的基础性探索，可为异常波的原始栖息地——海洋学中的异常波性质和激发机制提供新的认识。

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.