Subhexagons and ultrahexagons as a result of a secondary instability

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Abstract
Simulating two-dimensional optical pattern formation in sodium vapor, we show that hexagonal patterns can be unstable against their own spatial harmonics or subharmonics. The instability results in ultrahexagons 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 the instabilities is discussed on the basis of order parameter equations obtained from symmetry considerations.