Qualitative Analysis of Maxwell-Duffing Models in Nonlinear Optics

Honors College Thesis

Public Deposited

Citeable URL: https://ir.library.oregonstate.edu/concern/honors_college_theses/hq37vt94s

Descriptions

Attribute Name	Values
Creator	Tro, Sara K.
Abstract	In this thesis we analyze a model for Kerr optical materials consisting of Maxwell's equations along with the dispersive Duffing model. We consider Duffing models with cubic and quintic polynomial nonlinearities. We assume a traveling wave solution to this nonlinear electromagnetic system and analyze it using the theory of dynamical systems. A bifurcation analysis is conducted that depends on parameters $\alpha$, the Kerr nonlinearity coefficient, $\Gamma$, the damping term, and $v$, the velocity of the traveling wave. We predict saddles and unstable nodes and spirals when we have damping, i.e., $\Gamma\neq0$, and saddles and centers when $\Gamma=0$ and the system is conservative.
Resource Type	Honors College Thesis
Date Issued	2019-06-07
Degree Level	Bachelor's
Degree Name	Honors Bachelor of Science (H.B.S.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2019
Advisor	Bokil, Vrushali A.
Committee Member	Gibson, Nathan L. Cozzi, Elaine
Non-Academic Affiliation	Oregon State University. Honors College
Déclaration de droits	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

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