Ph.D Student | Manela Ofer |
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Subject | Nonlinear Dynamics and Effects in Periodic Optical Systems |

Department | Department of Physics |

Supervisor | ? 18? Mordechai Segev |

Full Thesis text |

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.