Computational Nonlinear Optics
Par Stefan Skupin, CELIA, CNRS-Université de Bordeaux
Mardi 22 Novembre, 14h, Salle des séminaires (215), 2ème étage, Bâtiment A4N
After a short general introduction, I will focus on optics in so-called nonlocal nonlinear media. It is nowadays well appreciated that nonlocality has a dramatic impact on the dynamics in nonlinear systems. Nonlocality is usually associated with transport processes or inter-molecular long-range interactions. After a brief introduction to nonlocal nonlinear systems, with special emphasize on optics, I will first talk about wave collapse in systems with attractive spatially nonlocal nonlinearities. I will present rigorous collapse criteria for systems with singular nonlocal nonlinear interaction, similar to those known for the famous local nonlinear Schroedinger equation. In the second part of my talk I will switch to self-organization of light in optical media with competing nonlinearities. Self-organization constitutes one of the most fascinating phenomena appearing in nonlinear systems. During the process, strong interactions among the system components lead to the formation of spatial structures and long-range ordering. We recently demonstrated that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns. Signatures of this long-range ordering turn out to be observable in the propagation of light in optical waveguides and even in free space.