Pattern formation and competition in nonlinear optics

Pattern formation and competition occur in a nonlinear extended medium if d issipation allows for attracting sets, independently of initial and boundar y conditions. This intrinsic patterning emerges from a reaction diffusion d ynamics (Turing chemical patterns). In optics, the coupling of an electroma gnetic field to a polarizable medium and the presence of losses induce a mo re general (diffraction-diffusion) mechanism of pattern formation. The pres ence of a coherent phase propagation may lead to a large set of unstable ba nds and hence to a richer variety with respect to the chemical case. A revi ew of different experimental situations is presented, including a discussio n on suitable indicators which characterize the different regimes. Vistas o n perspective new phenomena and applications include an extension to atom o ptics. (C) 1999 Elsevier Science B.V. All rights reserved.