Prediction of random and chaotic dynamics in nonlinear optics

Prediction of random and chaotic dynamics in nonlinear optics

Applied Math And Analysis Seminar

Amir Sagiv (Columbia)

Tuesday, April 21, 2020 -
3:15pm to 4:15pm
Location: 
119 Physics

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. Not all is lost, however. The statistics of many interactions are predictable by a universal model. Computationally, the universal model is efficiently solved using 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 and analysis at the intersection of probability and approximation theory.

Last updated: 2019/12/14 - 2:31pm