Full Field Propagation Models And Methods For Extreme Nonlinear Optics

Persistent Link:
http://hdl.handle.net/10150/347238
Title:
Full Field Propagation Models And Methods For Extreme Nonlinear Optics
Author:
Whalen, Patrick
Issue Date:
2015
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:
This dissertation examines models, methods, and applications of electric field pulse propagation in nonlinear optics. Standard nonlinear optical propagation models such as the NLS equation are derived using a procedure invoking a slowly-varying wave approximation which amounts to discarding second order derivatives in the propagation direction. This work follows a more intuitive procedure emphasizing unidirectionality, the core trait of laser light propagation, by projecting a nonlinear wave system onto a unidirectional subspace. The projection method is discussed as a general theory and then applied to a series of different electric field configurations. Two important full-field propagation models are examined. The unidirectional pulse propagation equations (UPPE's) are generated from Maxwell's equations with the sole approximation being that of unidirectionality. The second model studied is the MKP equation which is a canonical full-field propagation equation particularly amenable to mathematical analysis due to its status as a conserved system. Applications unique to full-field propagation including electric field shock and harmonic walk-off induced collapse arrest are studied through numerical simulations. An emphasis is placed on the mid-infrared to long-infrared wavelength regime where significant differences between envelope models and electric field models manifest as a result of extremely weak dispersion. Presented are the first embedded Runge-Kutta exponential time-differencing (RKETD) methods of fourth order with third order embedding and fifth order with third order embedding for non-Rosenbrock type nonlinear systems. A procedure for constructing RKETD methods that accounts for both order conditions and stability is outlined. In the stability analysis, the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before. An effective time-stepping strategy based on reducing both ETD function evaluations and rejected steps is described. Comparisons of performance with adaptive-stepping integrating factor (IF) are carried out on a set of canonical partial differential equations including the standard z-propagated UPPE.
Type:
text; Electronic Dissertation
Keywords:
Applied Mathematics
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Moloney, Jerome V.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleFull Field Propagation Models And Methods For Extreme Nonlinear Opticsen_US
dc.creatorWhalen, Patricken_US
dc.contributor.authorWhalen, Patricken_US
dc.date.issued2015-
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.abstractThis dissertation examines models, methods, and applications of electric field pulse propagation in nonlinear optics. Standard nonlinear optical propagation models such as the NLS equation are derived using a procedure invoking a slowly-varying wave approximation which amounts to discarding second order derivatives in the propagation direction. This work follows a more intuitive procedure emphasizing unidirectionality, the core trait of laser light propagation, by projecting a nonlinear wave system onto a unidirectional subspace. The projection method is discussed as a general theory and then applied to a series of different electric field configurations. Two important full-field propagation models are examined. The unidirectional pulse propagation equations (UPPE's) are generated from Maxwell's equations with the sole approximation being that of unidirectionality. The second model studied is the MKP equation which is a canonical full-field propagation equation particularly amenable to mathematical analysis due to its status as a conserved system. Applications unique to full-field propagation including electric field shock and harmonic walk-off induced collapse arrest are studied through numerical simulations. An emphasis is placed on the mid-infrared to long-infrared wavelength regime where significant differences between envelope models and electric field models manifest as a result of extremely weak dispersion. Presented are the first embedded Runge-Kutta exponential time-differencing (RKETD) methods of fourth order with third order embedding and fifth order with third order embedding for non-Rosenbrock type nonlinear systems. A procedure for constructing RKETD methods that accounts for both order conditions and stability is outlined. In the stability analysis, the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before. An effective time-stepping strategy based on reducing both ETD function evaluations and rejected steps is described. Comparisons of performance with adaptive-stepping integrating factor (IF) are carried out on a set of canonical partial differential equations including the standard z-propagated UPPE.en_US
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectApplied Mathematicsen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorMoloney, Jerome V.en_US
dc.contributor.committeememberMoloney, Jerome V.en_US
dc.contributor.committeememberMoysey, Brioen_US
dc.contributor.committeememberKolesik, Miroslaven_US
dc.contributor.committeememberVenkataramani, Shankaren_US
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