Transverse patterns in nascent optical bistability

We study the Swift-Hohenberg equation describing a passive optical cavity driven by an external coherent field, valid close to the onset of optical bistability. A linear analysis shows that the system can sustain nontrivial stationary structures for small positive detunings. A weakly nonlinear analysis in the vicinity of the instability points reveals the existence of stable hexagonal structures which eventually give way to rolls. Numerical simulations support such a bifurcation scenario.