Applied Math Seminar: Prediction of random and chaotic dynamics in nonlinear optics

Seminar | January 15 | 4-5 p.m. | 939 Evans Hall | Note change in location

 Amir Sagiv, Columbia University

 Department of Mathematics

The prediction of interactions between nonlinear laser beams is a longstanding open problem. A traditional assumption is that these interactions are deterministic. We have shown, however, that in the nonlinear Schrodinger equation (NLS) model of laser propagation, beams lose their initial phase information in the presence of input noise. Thus, the interactions between beams become unpredictable as well.

Computationally, these predictions are enabled through a novel spline-based stochastic computational method. Our algorithm efficiently estimates probability density functions (PDF) that result from differential equations with random input. This is a new and general problem in numerical uncertainty-quantification (UQ), which leads to surprising results at the intersection of probability and transport theory.