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Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems, Todd Blanton Smith
Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems, Todd Blanton Smith
Electronic Theses and Dissertations
In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in …
Optical Nonlinear Interactions In Dielectric Nano-Suspensions, Ramy El-Ganainy
Optical Nonlinear Interactions In Dielectric Nano-Suspensions, Ramy El-Ganainy
Electronic Theses and Dissertations
This work is divided into two main parts. In the first part (chapters 2-7) we consider the nonlinear response of nano-particle colloidal systems. Starting from the Nernst-Planck and Smoluchowski equations, we demonstrate that in these arrangements the underlying nonlinearities as well as the nonlinear Rayleigh losses depend exponentially on optical intensity. Two different nonlinear regimes are identified depending on the refractive index contrast of the nanoparticles involved and the interesting prospect of self-induced transparency is demonstrated. Soliton stability is systematically analyzed for both 1D and 2D configurations and their propagation dynamics in the presence of Rayleigh losses is examined. We …
Optical Solitons In Periodic Structures, Konstantinos Makris
Optical Solitons In Periodic Structures, Konstantinos Makris
Electronic Theses and Dissertations
By nature discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one-and two-dimensional nonlinear waveguide arrays. In recent years such lattice structures have been implemented or induced in a variety of material systems including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness leads to new families of optical solitons that have no counterpart whatsoever in continuous systems. In the first part of this dissertation, a …
Soliton Solutions Of Nonlinear Partial Differential Equations Using Variational Approximations And Inverse Scattering Techniques, Thomas Vogel
Electronic Theses and Dissertations
Throughout the last several decades many techniques have been developed in establishing solutions to nonlinear partial differential equations (NPDE). These techniques are characterized by their limited reach in solving large classes of NPDE. This body of work will study the analysis of NPDE using two of the most ubiquitous techniques developed in the last century. In this body of work, the analysis and techniques herein are applied to unsolved physical problems in both the fields of variational approximations and inverse scattering transform. Additionally, a new technique for estimating the error of a variational approximation is established. Note that the material …
Discrete Surface Solitons, Sergiy Suntsov
Discrete Surface Solitons, Sergiy Suntsov
Electronic Theses and Dissertations
Surface waves exist along the interfaces between two different media and are known to display properties that have no analogue in continuous systems. In years past, they have been the subject of many studies in a diverse collection of scientific disciplines. In optics, one of the mechanisms through which optical surface waves can exist is material nonlinearity. Until recently, most of the activity in this area was focused on interfaces between continuous media but no successful experiments have been reported. However, the growing interest that nonlinear discrete optics has attracted in the last two decades has raised the question of …
Optical Wave Propagation In Discrete Waveguide Arrays, Jared Hudock
Optical Wave Propagation In Discrete Waveguide Arrays, Jared Hudock
Electronic Theses and Dissertations
The propagation dynamics of light in optical waveguide arrays is characteristic of that encountered in discrete systems. As a result, it is possible to engineer the diffraction properties of such structures, which leads to the ability to control the flow of light in ways that are impossible in continuous media. In this work, a detailed theoretical investigation of both linear and nonlinear optical wave propagation in one- and two-dimensional waveguide lattices is presented. The ability to completely overcome the effects of discrete diffraction through the mutual trapping of two orthogonally polarized coherent beams interacting in Kerr nonlinear arrays of birefringent …
Discrete Nonlinear Wave Propagation In Kerr Nonlinear Media, Joachim Meier
Discrete Nonlinear Wave Propagation In Kerr Nonlinear Media, Joachim Meier
Electronic Theses and Dissertations
Discrete optical systems are a subgroup of periodic structures in which the evolution of a continuous electromagnetic field can be described by a discrete model. In this model, the total field is the sum of localized, discrete modes. Weakly coupled arrays of single mode channel waveguides have been known to fall into this class of systems since the late 1960's. Nonlinear discrete optics has received a considerable amount of interest in the last few years, triggered by the experimental realization of discrete solitons in a Kerr nonlinear AlGaAs waveguide array by H. Eisenberg and coworkers in 1998. In this work …