Subject Area
Mathematics, Applied
Abstract
Solitons are self-reinforcing localized wave packets that have remarkable stability features that arise from the balanced competition of nonlinear and dispersive effects in the medium. Traditionally, the dominant order of dispersion has been the lowest (second), however in recent years, experimental and theoretical research has shown that high, even order dispersion may lead to novel applications. Here, the focus is on investigating the interplay of dominant quartic (fourth-order) dispersion and the self-phase modulation due to the nonlinear Kerr effect in laser systems. One big factor to consider for experimentalists working in laser systems is the effect of noise on the inputs to these systems. Therefore, I numerically analyze the generation of localized states arising from dominant quartic dispersion where noise is added on the inputs to the laser system and the resulting robustness of these states. In addition, I also examine the interaction of solitary waves with dominant quartic dispersion in different media and how these results can differ from the conventional case of dominant quadratic dispersion. The results show that the behavior that is exhibited for the quadratic case for generation of pulses is maintained and furthermore, there are increased opportunities for stable localized states in quartic Kerr media.
Degree Date
Spring 2024
Document Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
Advisor
Alejandro Aceves
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
Hetzel, Sabrina, "Generation, Dynamics, and Interaction of Quartic Solitary Waves in Nonlinear Laser Systems" (2024). Mathematics Theses and Dissertations. 26.
https://scholar.smu.edu/hum_sci_mathematics_etds/26
Included in
Dynamic Systems Commons, Non-linear Dynamics Commons, Optics Commons, Partial Differential Equations Commons
