Interaction and stability of periodic and localized structures in optical bistable systems

We analytically and numerically study the role of the homogeneous zero mode on the interaction between two modulational instabilities. Periodic and localized structures (LSs) are considered in two transverse dimensions. We consider a real-order parameter description for a passive optical cavity driven by an external coherent field, valid close to the onset of optical bistability. A global description of pattern formation in both monostable and bistable regimes is given. We show that the interaction between the modulational modes and the zero mode modifies the existence and the stability of diffractive patterns. In particular, this interaction induces a coexistence between two different types of phase locked hexagonal structures. We also consider the interaction between two separated LSs. An analytical expression for the interaction potential in terms of modified Bessel functions is derived. Numerical simulations confirm the analytical predictions.