Modeling Complex Nonlinear Optical Systems
Final rept. 10 Jul 2003-9 Jul 2006
NEW MEXICO UNIV ALBUQUERQUE DEPT OF MATHEMATICS AND STATISTICS
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This research dealt with the modeling of light propagation in nonlinear periodic media including bragg grating fiber arrays and periodic nonlinear 2-dimensional waveguides. The goals set were to find conditions for stable pulse propagation in the arrays and for the search of light bullets, their stability and propagation characteristics in the two dimensional waveguide. We also established conditions for optical trapping in a defect. This is a topic of great interest in the search of all optical logic systems and buffers. A second component of the project dealt with existence and stability of Bose Einstein condensates in periodic magnetic traps. There has been an extensive experimental effort on BEC trapping and our work developed a solid theoretical framework to explore such trapping mechanisms. Tools used in this research include Dynamical systems, numerical methods for nonlinear partial differential equations, asymtotic analysis. The project had also an important educational component as it served to train 3 graduate students in Applied Mathematics and provided a seed for a new crop of students working in this field.
- Quantum Theory and Relativity