Modulational Instabilities in Passive Optical Resonators

Spatio-temporal effects play an important role in the transition to turbulence in diverse physical systems. In both Rayleigh-Benard convection and Taylor Couette flow, for example, the onset of a new temporal motion (e.g. periodic to quasiperiodic) is accompanied by the sudden appearance of small periodic spatial scales in the fluid 1. We shall show that a similar situation applies in nonlinear optics. In particular, it has recently been shown that the plane wave Ikeda map describing the dynamics of a ring cavity is more unstable to fluctuations with a transverse spatial structure than to plane wave perturbations 2. As a consequence this simple map cannot provide a correct description of the instabilities. Instead we predict new and diverse routes to optical turbulence under different physical conditions.