Abstract

Hexagonal optical patterns appear as a result of a transverse instability of coun- terpropagating laser beams in a nonlinear medium. In large aspect ratio experiments, where transverse boundary conditions play only a weak role, a single spatial scale characterizes the hexagons. This scale results from a compatibility condition between different mechanisms. In transverse nonlinear optics a resonance occurs when a nonlinear phase shift resulting from, e.g., a cubic nonlinearity, cancels the linear diffractive phase shift because of propagation. The resulting transverse patterns have a characteristic spatial scale given by $\sqrt{\lambda l}$ where λ is the optical wavelength and Í is the length of the nonlinear medium.

© 1996 Optical Society of America