Abstract

The spontaneous formation of periodic spatial patterns is a common feature of a range of physical systems that are excited beyond an instability threshold. The symmetry properties of the emerging spatial structures depend both on bulk and boundary characteristics of the system. In two spatial dimensions hexagonal structures are generic. Analysis of the bifurcation structure of a mean field model of pattern formation reveals that other, non hexagonal symmetries are valid solutions, yet they generally have smaller growth rates than the observed hexagonal structures. Several recent works have considered techniques for stabilization and selection of optical patterns [1], and a simple technique based on amplitude filtering in the Fourier plane has been demonstrated experimentally[2].

© 1998 IEEE