Persistent Link:
http://hdl.handle.net/10150/186972
Title:
Patterns, fishing and nonlinear optics.
Author:
Geddes, John Bruce.
Issue Date:
1994
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Motivated by a conversation with my brother, a deep sea fisherman off the east coast of Scotland, I review the concepts which unify the topic of pattern formation in nonequilibrium systems. As a specific example of a pattern-forming system, I go on to examine pattern formation in nonlinear optics and I discuss two nonlinear optical systems in considerable detail. The first, counterpropagating laser beams in a nonlinear Kerr medium, results in the prediction and numerical observation of hexagonal patterns in a self-focusing medium, and of square patterns in a self-defocusing medium. Furthermore, a novel Hopf bifurcation is observed which destabilises the hexagons and an explanation in terms of a coupled-amplitude model is given. The other system, namely the mean-field model of propagation in a nonlinear cavity, also gives rise to hexagonal patterns in a self-focusing medium. By extending this model to include the vector nature of the electric field, polarisation patterns are predicted and observed for a self-defocusing medium. Roll patterns dominate close to threshold, while farther from threshold labyrinthine patterns are found. By driving the system very hard, a transition to a regime consisting of polarisation domains connected by fronts is also observed. Finally, numerical algorithms appropriate for solving the model equations are discussed and an alternative algorithm is presented which may be of use in pattern-forming systems in general.
Type:
text; Dissertation-Reproduction (electronic)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Moloney, Jerome

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titlePatterns, fishing and nonlinear optics.en_US
dc.creatorGeddes, John Bruce.en_US
dc.contributor.authorGeddes, John Bruce.en_US
dc.date.issued1994en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractMotivated by a conversation with my brother, a deep sea fisherman off the east coast of Scotland, I review the concepts which unify the topic of pattern formation in nonequilibrium systems. As a specific example of a pattern-forming system, I go on to examine pattern formation in nonlinear optics and I discuss two nonlinear optical systems in considerable detail. The first, counterpropagating laser beams in a nonlinear Kerr medium, results in the prediction and numerical observation of hexagonal patterns in a self-focusing medium, and of square patterns in a self-defocusing medium. Furthermore, a novel Hopf bifurcation is observed which destabilises the hexagons and an explanation in terms of a coupled-amplitude model is given. The other system, namely the mean-field model of propagation in a nonlinear cavity, also gives rise to hexagonal patterns in a self-focusing medium. By extending this model to include the vector nature of the electric field, polarisation patterns are predicted and observed for a self-defocusing medium. Roll patterns dominate close to threshold, while farther from threshold labyrinthine patterns are found. By driving the system very hard, a transition to a regime consisting of polarisation domains connected by fronts is also observed. Finally, numerical algorithms appropriate for solving the model equations are discussed and an alternative algorithm is presented which may be of use in pattern-forming systems in general.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairMoloney, Jeromeen_US
dc.contributor.committeememberErcolani, Nicholasen_US
dc.contributor.committeememberIndik, Roberten_US
dc.identifier.proquest9517582en_US
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