Chair of Computational Mathematics Seminar: Mathematical modeling in optics and photonics I: Introduction

by Alejandro Aceves

Professor of Applied Mathematics and Department Chair
Southern Methodist University, Dallas, TX, US

Abstract:
There is a long story of the role nonlinearity plays in optics and photonics. From the early experiments in second harmonic generation to the demonstration of optical solutions in fiber optics, the field continues to evolve in several directions. In these series of talks, I will start by a general introduction to the topic and quickly move into current trends where mathematical modeling plays a key role in the understanding of nonlinear optics phenomena. In my last presentation, rather than presenting well developed ideas, I will attempt to provide examples mostly from recent experiments in need of better models. They will highlight optical phenomena for weakly and for strongly nonlinear effects. Topics I hope to cover include pulses in novel waveguides with leading fourth order dispersion, spatio-temporal dynamics in multi-mode fibers, optical rogue waves and second harmonics filaments.
In the first seminar I will present a introduction of what constitutes light matter interaction in optical media. Beginning with Maxwell’s equations, we will derive mathematical models of current use in nonlinear optics and photonics.