Dynamics of pattern formation in the Turing optical instability

Abstract

The transient dynamical evolution of spatial pattern formation in a nonlinear passive optical system in a Fabry-Pérot cavity driven by an external coherent field is studied. The associated decay of the unstable homogeneous state of the system is described analytically, with the inclusion of noise effects, in terms of a stochastic amplitude equation for the unstable mode in the direction of instability. As a result, the time scale on which the pattern is formed as well as the anomalous transient fluctuations of the field intensity are explicitly calculated. Our results show that the behavior of these fluctuations depends strongly on the position within the cavity. Finally, the symmetry-restoring effect of fluctuations is also discussed.