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

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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.