Keywords
Nonlinear optics, Solitons, Wave propagation, Nonlinear Dynamics
Abstract
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 theoretical investigation of linear and nonlinear optical wave propagation in semi-infinite 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. Hetero-structures of two dissimilar semi-infinite arrays are also considered. The existence of hybrid solitons in these latter types of structures is demonstrated. Rabi-type optical transitions in z-modulated 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 parity-time-symmetry is introduced in the context of optics. More specifically, periodic potentials associated with PT-symmetric Hamiltonians are numerically explored. These new optical structures are found to exhibit surprising characteristics. These include the possibility of abrupt phase transitions, band merging, non-orthogonality, non-reciprocity, 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 PT-symmetry. Finally, discrete solitons in PT-symmetric optical lattices are examined in detail.
Notes
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Graduation Date
2008
Advisor
Christodoulides, Demetrios
Degree
Doctor of Philosophy (Ph.D.)
College
College of Optics and Photonics
Department
Optics and Photonics
Degree Program
Optics
Format
application/pdf
Identifier
CFE0002013
URL
http://purl.fcla.edu/fcla/etd/CFE0002013
Language
English
Release Date
June 2008
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
STARS Citation
Makris, Konstantinos, "Optical Solitons In Periodic Structures" (2008). Electronic Theses and Dissertations. 3723.
https://stars.library.ucf.edu/etd/3723