The quest for ever higher information capacities has brought about a renaissance in multimode optical waveguide systems. This resurgence of interest has recently initiated a flurry of activities in nonlinear multimode fiber optics. The sheer complexity emerging from the presence of a multitude of nonlinearly interacting modes has led not only to new opportunities in observing a host of novel optical effects that are otherwise impossible in single-mode settings, but also to new theoretical challenges in understanding their collective dynamics. In this dissertation, we present a consistent thermodynamical framework capable of describing in a universal fashion the exceedingly intricate behavior of such nonlinear highly multimoded photonic configurations at thermal equilibrium. By introducing pertinent extensive variables, we derive new equations of state and show that any nonlinear multimoded optical systems that preserve power and energy will thermalize and settle to a Rayleigh-Jeans distribution. This thermalization processes are universal, regardless of the nonlinearity involved or the band structure of the systems. Moreover, each system has an unique equilibrium temperature and chemical potential once the initial conditions are determined. In addition, we show that both the "internal energy" and optical power in many-mode arrangements always flow in such a way so as to satisfy the second law of thermodynamics. The laws governing isentropic processes are derived and the prospect for realizing Carnot-like cycles is also presented. Subsequently, the prospect of all-optical cooling is investigated where the beam quality of an multimoded optical beam can be significantly improved through thermodynamic principles, driven by the second law of thermodynamics. We next provide an optical Sackur-Tetrode equation of nonlinear chain networks which explicitly gives the total relative entropy of such system in terms of the three extensive variables. Archetypical process including Joule expansion, heat conductivity, etc. are discussed basing on this formalism. In addition to shedding light on fundamental issues, our work may pave the way towards a new generation of high power multimode optical structures and could have ramifications in other many-state nonlinear systems, ranging from Bose-Einstein condensates to optomechanics.
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Doctor of Philosophy (Ph.D.)
College of Optics and Photonics
Optics and Photonics
Optics and Photonics
Length of Campus-only Access
Doctoral Dissertation (Campus-only Access)
Wu, Fan, "Thermodynamic Theory of Heavily Multimoded Nonlinear Optical Systems" (2020). Electronic Theses and Dissertations, 2020-. 153.