This project deals with the mathematical and computational modeling of light as it propagates in photonic micro and nanostructures. In one example, a new and improved model will be proposed and used to describe novel optical pulse propagation in photonic crystal fibers such as the recently observed phenomena of supercontinuum generation which cannot be well understood with the existing slowly varying envelope approximation. A second component of this project studies light localization and steering in optical fiber arrays and in particular the role imperfections in the manufacturing of such devices have in enhancing or suppressing light localization. The model considered here is a set of coupled stochastic differential equations. Finally, we will begin to address the question of which optical phenomena that has been observed in micro-devices can also happen in the nano-devices. In all instances, the mathematical and computational outcomes will be presented to and compared with leading experimentalist efforts.
This research effort is of interdisciplinary nature and the use of mathematical modeling will help improve performance of optical devices used in medical applications such as coherent tomography and in advanced fiber lasers aimed at producing powers in the multi-kilowatt regime. State of the art lasers based on the model studied here, will likely prove to be relevant for homeland security. This project will support the advancement of two women (a PhD student and a junior faculty) in their careers as Applied Mathematics professionals.
