Prediction of random and chaotic dynamics in nonlinear optics
The control and prediction of interactions between high-power, nonlinear laser beams is a longstanding open problem in optics and mathematics. One of the traditional underlying assumptions in this field has been that these dynamics are governed by a deterministic model. Lately, however, we have shown that at the presence of input noise, high-power laser beams lose their initial phase information in nonlinear propagation. Thus, at long propagation distances, a beam's phase becomes random, and so long-range interactions between multiple beams become random too. Not all is lost, however. Even though each interaction is unpredictable, the statistics of many interactions are predictable. Moreover, the above “loss of phase” result implies that these statistics, in fact, follow a universal model.
This universal model is efficiently solved using a novel stochastic computational method we developed. Our algorithm efficiently estimate probability density functions (PDF) of PDEs with random or uncertain input. This is a new and general problem in numerical uncertainty-quantification (UQ), which leads to surprising results and analysis.