Nonlinear dynamics of partially-coherent waves: experimental and theoretical studies in statistical light

自然界中的大多数波只是部分相干的，波动（热，量子或其他）赋予它们的动力学统计特性。 特别是在非线性的情况下，运输是复杂的有限相关的存在。 涨落引起扰动，既可以产生也可以抑制不稳定性。 在前一种情况下，噪声提供了自由能和能量破坏源，而在后一种情况下，统计失相可以抑制非线性模式耦合和能量转移。 本论文的目的是利用统计光的非线性传播，从实验和理论两方面研究这些效应，其出发点是观察到完全凝聚的多体系统通常可以用一个宏观波函数来描述，这与激光的相干光场完全相似。 在部分凝聚系统中，有限温度效应引起统计行为，这在非相干光的传播中具有对应性。 本研究利用这些关系，解释了许多方面的非线性光束传输的根本新的，场论的方式。 其结果是为各种不同的光学现象提供了一个统一的框架，从而导致了一系列新的实验方向。 然而，新的观点不仅提出了新的解释，还提出了几种从未在任何领域进行过的相关性研究。 研究这种行为对于理解统计动力学和非线性模式耦合至关重要，这既是基础科学的基础，也具有重要的技术意义。光学成像的力量推动了这项工作的智力价值，因为与其他领域相关（但往往隐藏在其中）的复杂波动动力学可以直接可视化。 事实上，光学系统作为模拟复杂凝聚态行为的光学模拟器的能力有很大的潜力（类似于使用光学信号处理进行高度并行计算）。 从教学的角度来看，光的熟悉和成像的容易性给光学系统带来了巨大的教学优势。 实际上，这种通过光子学方法的物理学可以通过相对简单的实验来证明，而这些系统中的波动动力学可以像场论中的任何主题一样复杂。 因此，一个强大的教育组成部分是这项工作的一个主题，教学项目与研究计划相结合。 从工作的结果将直接纳入调查课程，既振兴本科班，并说明基本原则领域理论研究生课程。 希望这里提出的模型系统和研究计划将为普林斯顿大学内外更大的基于光学的科学计划提供支持。该项目由数学和物理科学理事会物理部的光学物理计划和材料研究部的凝聚态物理计划共同支持。

Most waves in nature are only partially coherent, with fluctuations (thermal, quantum, or other) imparting a statistical character to their dynamics. Particularly in the nonlinear case, transport is complicated by the presence of finite correlations. Fluctuations seed perturbations and can either generate or suppress instability. In the former case, noise provides a free-energy and symmetry-breaking source, while in the latter case statistical de-phasing can inhibit nonlinear mode coupling and energy transfer. The purpose of this work is to study these effects, both experimentally and theoretically, using the nonlinear propagation of statistical light.The starting point is the observation that fully-condensed, many-body systems can often be described by a single, macroscopic wavefunction, in complete analogy with the coherent light field from a laser. In partially-condensed systems, finite-temperature effects give rise to statistical behavior, which has correspondences in the propagation of incoherent light. This research takes advantage of these relations, interpreting many aspects of nonlinear beam propagation in fundamentally new, field-theoretic ways. The result is a unifying framework for a variety of disparate optical phenomena, leading to a series of new experimental directions. Even more than novel interpretations, though, the new perspectives suggest several types of correlation studies that have never been performed for any field. Studying such behavior is crucial to the understanding of statistical dynamics and nonlinear mode coupling, which is both fundamental to basic science and of great technological importance.The power of optical imaging drives the intellectual merit of this work, as complicated wave dynamics relevant to (but often hidden in) other fields can be directly visualized. Indeed, there is much potential in the ability of optical systems to serve as optical simulators for modeling complex condensed-matter behavior (similar to the use of optical signal processing for highly parallel computing). From a teaching perspective, the familiarity of light and the ease of imaging give optical systems an enormous pedagogical advantage. Practically, this physics through photonics approach can be demonstrated through experiments that are relatively simple to perform, while the wave dynamics in these systems can be as complex as any topic in field theory. A strong educational component is therefore a main theme of this work, with instructional projects coherently integrated with the research plan. Results from the work will be incorporated directly into the investigators courses, both to invigorate undergraduate classes and to illustrate basic principles in field-theoretic graduate courses. It is hoped that the model systems and research plans proposed here will feed into a larger optics-based science program, both within and beyond Princeton University.This project is jointly supported by the Optical Physics program in the Physics Division and the Condensed Matter Physics program in the Division of Materials Research of the Mathematical and Physical Sciences Directorate.