Pattern formation and competition in nonlinear optics

Pattern formation and competition occur in a nonlinear extended medium if dissipation allows for attracting sets, independently of initial and boundary conditions. This intrinsic patterning emerges from a reaction diffusion dynamics (Turing chemical patterns). In optics, the coupling of an electromagnetic field to a polarizable medium and the presence of losses induce a more general (diffraction-diffusion) mechanism of pattern formation. The presence of a coherent phase propagation may lead to a large set of unstable bands and hence to a richer variety with respect to the chemical case. A review of different experimental situations is presented, including a discussion on suitable indicators which characterize the different regimes. Vistas on perspective new phenomena and applications include an extension to atom optics. (C) 1999 Elsevier Science B.V. All rights reserved.