IP3* ~ Sunday, May 21, 1995 ~ 5:00 PM*
## Pattern Evolution in Large Aspect Ratio Nonlinear Optical Systems

Large aspect ratio nonlinear optical systems provide potential technological benefits in massively parallel optical computing systems and in the generation of high power laser outputs for space communications. Patterns, including traveling waves, rolls, squares, hexagons and topological defects have been observed in recent experiments in nonlinear optics. The ability to generate and control complex spatio-temporal evolutions is important to development of the technology.
The speaker will illustrate how universal order parameter equation descriptions in terms of complex Swift-Hohenberg, complex Ginzburg-Landau type pde's. arise naturally in the description of the emergence of patterns near a Hopf bifurcation point in a large aspect ratio laser. Such models prove to be remarkably robust in predicting pattern selection, not only near, but well beyond the initial bifurcation point. For many important laser systems, the physically relevant Maxwell-Bloch mathematical models prove to be extremely stiff and the relevant order parameter equation must be coupled to a mean flow. As a consequence, the domain of stable patterns is extremely narrow and a weakly turbulent behavior becomes evident in both experimental observations and numerical simulations.

**Jerome V. Moloney**

Department of Mathematics, University of Arizona

*3/15/95*