Eur. Phys. J. D 12, 15-20 (2000)
https://doi.org/10.1007/s100530070037

Geometrical frustration in 2D optical patterns

¹ Institut Non Linéaire de NiceUMR 6618 du CNRS, Université de Nice Sophia Antipolis, 1361 route des Lucioles, 06560 Valbonne, France
² Istituto Nazionale di Ottica, 50125 Firenze, Italy

Received: 27 December 1999
Revised: 29 March 2000
Published online: 15 October 2000

Abstract

In the case of 2D optical patterns, frustration comes from the interplay between the physical constraints (light-matter interaction) and the geometrical constraints (cavity length and structure). Depending on the dynamical parameters, we are able to single out two distinct behaviors. For small diffusion and close to threshold, the system is forced to fulfill the geometrical constraints giving rise to a phase dynamics of quasicrystals. For larger diffusion, the system fragmentates into spatial domains giving rise to a competition between different patterns. By means of a geometrical argument, we show that the spatial distribution of domains is related to the symmetry imposed by the geometrical constraint and that the domain borders are disinclination defects. These defects being the nucleation centers of spatial domains, they trigger the onset of pattern competition.