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

流氓波（RW）最初被观察到的巨振幅波发生在公海比高斯统计预测的更频繁。这一概念随后从海洋学扩展到物理学的其他领域，以描述巨大振幅的波浪，或者一般来说，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、检测和传播的物理科学，已被证明是探测异常波的特别肥沃的土壤。这是因为例如在光纤系统中可以相对容易地在真实的时间内生成大量的统计数据阵列。 到目前为止，已经在理论上和/或实验上在许多非线性光学系统中发现了RW。然而，这些研究的大部分，一直关注RW产生保守的，弱非线性光学介质，远离任何内部共振的介质原子。** 我建议探索非高斯统计和RW激发在非线性介质中的光学共振附近的物理机制。具体来说，我将研究极端的统计事件，触发的前向和后向受激拉曼散射和吸收或放大非线性介质的条件下，入射光脉冲的中心频率是接近的介质的内部共振频率的噪声源。 共振非线性介质涉及光场能量的增益或损失，并且通常不支持任何驻波结构，例如孤子。然而，我们以前的研究表明，这样的系统是有利于非高斯统计，因此RW的出现。因此，我建议解决一个基本的问题，在这样的系统中的RW的物理性质。** 所提出的工作和产生的结果将阐明非高斯统计产生和共振非线性系统中的流氓波激发的基本方面。所获得的见解将证明是非常宝贵的实现RW激励控制。自然的下一步将是猜想设计一个RW源，允许RW生成（或多或少）统计控制的方式。因此，研究RW控制，也许，他们的统计操纵可以打开令人兴奋的机会，设计新的高强度波动脉冲源。这样的源可以填补高强度相干源（例如激光器）和低强度部分相干源（例如发光二极管）之间的差距，从而结合两种源类型的优点。 这种新型光源可以在任意环境下的超宽带光通信中得到应用。最后，提出的基本探索光学流氓波及其产生机制可能提供新的见解流氓波的性质和激发机制的海洋学，原始流氓波的栖息地。

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.