published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

This dissertation presents theories of multiwave mixing in two- and three-level media. The first part of the dissertation treats the semiclassical theories in two-level media. Chapter 2 gives the simple semiclassical theory of four-wave mixing when the two pump frequences differ by more than the reciprocal of the population-difference lifetime. This difference washes out the pump spatial holes as well as one of the two reflection gratings. We compare the results to the degenerate treatment of Abrams and Lind and find significant differences in the reflection coefficient spectra. Chapter 3 presents the semiclassical theory of multiwave in a squeezed vacuum characterized by unequal in-phase and in-quadrature dipole decay times. For a highly squeezed vacuum, we find sharp resonances in both probe absorption and reflection coefficients, which provide sensitive ways to measure the amount of squeezing in the vacuum. The second part of the dissertation treats the quantum theories in two- and three-level media. Chapter 4 develops the fourth-order quantum theory of multiwave mixing to describe the effects of sidemode saturation in two-level media. We derive explicit formulas for the fourth-order quantum coefficients and show that the fourth-order quantum theory reproduces the third-order semiclassical coefficient obtained by truncating a continued fraction. We apply the results to cavity problems and find significant differences in the sideband spectra given by the second- and fourth-order treatments, particularly as the sidemode approaches the laser threshold. The final chapter presents a quantum theory of multiwave mixing in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong pump intensities and good broad-band squeezing for low pump intensities.

The effect of linear absorption on TE0 nonlinear guided waves and the effect of linear absorption, input-beam misalignment and nonlinear saturation on soliton emission from a nonlinear waveguide have been numerically investigated using the beam propagation method. In the first case the distribution of the absorption is found to have a dramatic effect on the propagation of the nonlinear guided waves. In the second case results reminiscent of the lossless case are found to survive in the presence of these complications.

Stochastic analysis procedures have been recently applied to analyze nonlinear dynamical systems. In this study, nonlinear responses, stochastic and/or chaotic, are examined and interpreted from a probabilistic perspective. A multi-point-moored ocean structural system under regular and irregular wave excitations is analytically examined via a generalized stochastic Melnikov function and Markov process approach. Time domain simulations and associated experimental observations are employed to assist in the interpretation of the analytical predictions. Taking into account the presence of random noise, a generalized stochastic Melnikov function associated with the corresponding averaged system, where a homoclinic connection exists near the primary resonance, is derived. The effects of random noise on the boundary of regions of possible existence of chaotic response is demonstrated via a mean-squared Melnikov criterion. The random wave field is approximated as random perturbations on regular and nearly regular (with very narrow-band spectrum) waves by adding a white noise component, or using a filtered white noise process to fit the JONSWAP spectrum. A Markov process approach is then applied explicitly to analyze the response. The evolution of the probability density function (PDF) of nonlinear stochastic response under the Markov process approach is characterized by a deterministic partial differential equation called the Fokker-Planck equation, which in this study is solved by a path integral solution procedure. Numerical evaluation of the path integral solution is based on path sum, and the short-time propagator is discretized accordingly. Short-time propagation is performed by using a fourth order Runge-Kutta scheme to calculate the most probable (i.e. mean) position in the phase space and to establish the fact that discrete contributions to the random response are locally Gaussian. Transient and steady-state PDF's can be obtained by repeat application of the short-time propagation. Based on depictions of the joint probability density functions and time domain simulations, it is observed that the presence of random noise may expedite the occurrence of "noisy" chaotic response. The noise intensity governs the transition among various types of stochastic nonlinear responses and the relative strengths of coexisting response attractors. Experimental observations confirm the general behavior depicted by the analytical predictions. / Graduation date: 1995

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 72-80). Also available in print.

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Thesis (Ph. D in Physics.)--University of California, Los Angeles, June 1962. / Typewritten. Includes vita and abstract. Bibliography references : p. 157-160.

Thesis (Ph. D.)--Princeton University, 1996. / Includes bibliographical references (leaves 233-242).

Thesis (Ph. D.)--Duke University, 2007. / Includes bibliographical references.

Thesis (Ph.D.)--University of Rhode Island, 2009. / Includes bibliographical references (leaves 69-71).