טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentManela Ofer
SubjectNonlinear Dynamics and Effects in Periodic Optical Systems
DepartmentDepartment of Physics
Supervisor ? 18? Mordechai Segev
Full Thesis textFull thesis text - English Version


Abstract

This Thesis mainly deals with phenomena occurring when waves propagate in nonlinear periodic or quasiperiodic systems. Most ideas we explore are universal, and can be found, e.g., in optics, fluid dynamics, matter waves, plasma physics, and cold atom systems. Here, I predict the existence of self-localized second-band vortex solitons in two dimensional lattices, and study their properties. I found that their phase forms an array of counter-rotating vortices. I also identify composite solitons in which a second-band vortex is jointly trapped with a mode arising from the first band. When such a composite entity is unstable, it disintegrates while exchanging angular momentum between its constituents, eventually stabilizing into another form of composite soliton. In adition, I predict the existence of localized nondiffracting beams in two-dimensional linear periodic systems. I explain the reasoning for the existence of these beams, constructed some examples, study their properties, and show that they exhibit symmetry-properties and phase-structure characteristic to the band(s) they are associated with. Next, I study the interaction of Bloch modes in nonlinear periodic structures. I show that two Bloch modes launched into a nonlinear lattice evolve into a comb or a supercontinuum of spatial frequencies, exhibiting a sensitive dependence on the momentum difference of the two initially-excited modes. I explain this as a combined result of the nonlinear Four-Wave-Mixing and the linear exchange of lattice momentum. In addition, I propose a new type of optical elements: diffractive optical elements with a spatially-varying nonlinear refractive index. Such a component acts as a diffractive optical element whose properties depend on the intensity of the incoming beam. I present a method for designing such elements, and as specific examples I study three types of nonlinear diffractive optical elements: Nonlinear Fresnel Zone Plates, Two-foci Nonlinear Fresnel Zone Plate, and Fresnel Zone Plate to Grating interpolator. Finally, I study the nonlinear Harper equation, and find a set of nonlinear extended eigenmodes and the corresponding nonlinear spectra. I show that the spectra form deformed versions of the Hofstadter butterfly, and that the nonlinear eigenmodes can be classified in two families: modes that are "continuation" of the linear modes of the system, and new modes that have no counterparts in the linear spectrum. In addition, I proposed an optical realization of the (linear and nonlinear) Hofstadter butterflies implemented in modulated waveguide arrays.