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 Title
 OPTICAL PROPAGATION OF SELFSUSTAINING WAVEFRONTS AND NONLINEAR DYNAMICS IN PARABOLIC MULTIMODE FIBERS.
 Creator

Mills, Matthew, Christodoulides, Demetrios, Hagan, David, Dogariu, Aristide, Kaup, David, University of Central Florida
 Abstract / Description

The aim of this thesis is to introduce my work which has generally been focused on opticalwavefronts that have the unusual property of resisting commonplace phenomena such as diffraction and dispersion. Interestingly, these special beams are found both in linear and nonlinear situations. For example, in the linear regime, localized spatiotemporal waves which resemble the spherical harmonic symmetries of the hydrogen quantum orbitals can simultaneously negotiate both diffractive and...
Show moreThe aim of this thesis is to introduce my work which has generally been focused on opticalwavefronts that have the unusual property of resisting commonplace phenomena such as diffraction and dispersion. Interestingly, these special beams are found both in linear and nonlinear situations. For example, in the linear regime, localized spatiotemporal waves which resemble the spherical harmonic symmetries of the hydrogen quantum orbitals can simultaneously negotiate both diffractive and dispersiveeffects. In the nonlinear regime, dressed optical filaments can be arranged to propagate multiphoton produced plasma channels orders of magnitude longer than expected.The first portion of this dissertation will begin by surveying the history of diffractionfree beamsand introducing some of their mathematical treatments. Interjected throughout this discussion will be several relevant concepts which I explored during my first years a CREOL. The discussion will then be steered into a detailed account of diffraction/dispersion free wavefronts which display hydrogenlike symmetries. The second segment of the document will cover the highly nonlinear process of optical filamentation. This chapter will almost entirely investigate the idea of the dressed filament, an entity which allows for substantial prolongation of this light string. I will then conclude by delving into the topicof supercontinuum generation in parabolic multimode fibers which, in the upcoming years, has great potential of becoming important in optics.
Show less  Date Issued
 2015
 Identifier
 CFE0005977, ucf:50767
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005977
 Title
 OPTICAL SOLITONS IN PERIODIC STRUCTURES.
 Creator

Makris, Konstantinos, Christodoulides, Demetrios, University of Central Florida
 Abstract / Description

By nature discrete solitons represent selftrapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of selflocalized states has been successfully observed in both oneand twodimensional 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,...
Show moreBy nature discrete solitons represent selftrapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of selflocalized states has been successfully observed in both oneand twodimensional 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 liquidcrystal 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 theoretical investigation of linear and nonlinear optical wave propagation in semiinfinite waveguide arrays is presented. In particular, the properties and the stability of surface solitons at the edge of Kerr (AlGaAs) and quadratic (LiNbO3) lattices are examined. Heterostructures of two dissimilar semiinfinite arrays are also considered. The existence of hybrid solitons in these latter types of structures is demonstrated. Rabitype optical transitions in zmodulated waveguide arrays are theoretically demonstrated. The corresponding coupled mode equations, that govern the energy oscillations between two different transmission bands, are derived. The results are compared with direct beam propagation simulations and are found to be in excellent agreement with coupled mode theory formulations. In the second part of this thesis, the concept of paritytimesymmetry is introduced in the context of optics. More specifically, periodic potentials associated with PTsymmetric Hamiltonians are numerically explored. These new optical structures are found to exhibit surprising characteristics. These include the possibility of abrupt phase transitions, band merging, nonorthogonality, nonreciprocity, double refraction, secondary emissions, as well as power oscillations. Even though gain/loss is present in this class of periodic potentials, the propagation eigenvalues are entirely real. This is a direct outcome of the PTsymmetry. Finally, discrete solitons in PTsymmetric optical lattices are examined in detail.
Show less  Date Issued
 2008
 Identifier
 CFE0002013, ucf:47610
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002013
 Title
 STANDING WAVES OF SPATIALLY DISCRETE FITZHUGHNAGUMO EQUATIONS.
 Creator

Segal, Joseph, Moore, Brian, University of Central Florida
 Abstract / Description

We study a system of spatially discrete FitzHughNagumo equations, which are nonlinear differentialdifference equations on an infinite onedimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for...
Show moreWe study a system of spatially discrete FitzHughNagumo equations, which are nonlinear differentialdifference equations on an infinite onedimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for all 1pulse solutions. We determine the range of parameter values that allow for the existence of standing waves. We use numerical methods to demonstrate the stability of our solutions and to investigate the relationship between the existence of standing waves and propagation failure of traveling waves.
Show less  Date Issued
 2009
 Identifier
 CFE0002892, ucf:48021
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002892
 Title
 DESIGN AND ASSESSMENT OF COMPACT OPTICAL SYSTEMS TOWARDS SPECIAL EFFECTS IMAGING.
 Creator

Chaoulov, Vesselin, Rolland, Jannick, University of Central Florida
 Abstract / Description

A main challenge in the field of special effects is to create special effects in real time in a way that the user can preview the effect before taking the actual picture or movie sequence. There are many techniques currently used to create computersimulated special effects, however current techniques in computer graphics do not provide the option for the creation of realtime texture synthesis. Thus, while computer graphics is a powerful tool in the field of special effects, it is neither...
Show moreA main challenge in the field of special effects is to create special effects in real time in a way that the user can preview the effect before taking the actual picture or movie sequence. There are many techniques currently used to create computersimulated special effects, however current techniques in computer graphics do not provide the option for the creation of realtime texture synthesis. Thus, while computer graphics is a powerful tool in the field of special effects, it is neither portable nor does it provide work in realtime capabilities. Realtime special effects may, however, be created optically. Such approach will provide not only realtime image processing at the speed of light but also a preview option allowing the user or the artist to preview the effect on various parts of the object in order to optimize the outcome. The work presented in this dissertation was inspired by the idea of optically created special effects, such as painterly effects, encoded in images captured by photographic or motion picture cameras. As part of the presented work, compact relay optics was assessed, developed, and a working prototype was built. It was concluded that even though compact relay optics can be achieved, further push for compactness and costeffectiveness was impossible in the paradigm of bulk macrooptics systems. Thus, a paradigm for imaging with multiaperture microoptics was proposed and demonstrated for the first time, which constitutes one of the key contributions of this work. This new paradigm was further extended to the most general case of magnifying multiaperture microoptical systems. Such paradigm allows an extreme reduction in size of the imaging optics by a factor of about 10 and a reduction in weight by a factor of about 500. Furthermore, an experimental quantification of the feasibility of optically created special effects was completed, and consequently raytracing software was developed, which was later commercialized by SmARTLens(TM). While the art forms created via raytracing were powerful, they did not predict all effects acquired experimentally. Thus, finally, as key contribution of this work, the principles of scalar diffraction theory were applied to optical imaging of extended objects under quasimonochromatic incoherent illumination in order to provide a path to more accurately model the proposed optical imaging process for special effects obtained in the hardware. The existing theoretical framework was generalized to nonparaxial in and outoffocus imaging and results were obtained to verify the generalized framework. In the generalized nonparaxial framework, even the most complex linear systems, without any assumptions for shift invariance, can be modeled and analyzed.
Show less  Date Issued
 2005
 Identifier
 CFE0000513, ucf:46447
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0000513