Hexagons and Squares in a Passive Nonlinear Optical System
Geddes, John B. Indik, R. A. Moloney, J. V. Firth, Willie J.
Pattern formation is analyzed and simulated in a nonlinear optical system involving all three space dimensions as well as time in an essential way. This system, counterpropagation in a Kerr medium, is shown to lose stability, for sufficient pump intensity, to a nonuniform spatial pattern. We observe hexagonal patterns in a self-focusing medium, and squares in a self-defocusing one, in good agreement with analysis based on symmetry and asymptotic expansions.