SUBHEXAGONS AND ULTRAHEXAGONS AS A RESULT OF A SECONDARY INSTABILITY

Simulating two-dimensional optical pattern formation in sodium vapor, we show that hexagonal patterns can be unstable against their own spat ial harmonics or subharmonics. The instability results in ultrahexagon s or subhexagons, respectively. The formation of ultrahexagons is due to interaction with a second solution branch with a wave number nearly resonant to the harmonics of the primary hexagon. The mechanism of th e instabilities is discussed on the basis of order parameter equations obtained from symmetry considerations.