Abstract

Cooperative behaviors have long been known to affect dramatically the dynamics of distributed ' nonequilibrium systems. They are, in particular, responsible for self-organization phenomena that commonly manifest themselves through the formation of coherent patterns — or dissipative structures — associated with instabilities resulting from the interplay of nonlinearities and diffusion processes. In the field of nonlinear optics, Lugiato and Lefever (LL) suggested in 1987 a very simple optical system to demonstrate in a paradigmatic way the universality of self-organization phenomena [1]. The system is an externally driven passive diffractive optical cavity filled with a Kerr material that can be modeled by a single complex second order partial differential equation (pde) with cubic nonlinearity. The originality of the LL approach is that their model is analogous to reaction-diffusion equations encountered in chemistry or in developmental biology. This allows them to describe pattern formation as being due to a fundamental mechanism analogous to the well-known Turing instability of nonlinear-diffusive systems.

© 2000 IEEE