Spatiotemporal pattern formation and chaos in passive optical systems

The interaction and competition of transverse cavity modes in passive optical systems can lead to the formation of spatial field structures whose symmetry differs from that of the empty cavity, while the time behaviour can become irregular. After having introduced dynamical equations in which the spatial dependence of the electric field is described by frequency-degenerate Gauss-Laguerre (GL) modes, the stationary solutions corresponding to a single or many modes are calculated and their stability is discussed. A scan of the parameter space allows for the identification of several interesting dynamical regimes. An extensive study of the chaotic states is performed in order to understand the relation between GL mode excitation and the relevant active degrees of freedom. Based on this analysis, the conditions for the onset of spatiotemporal chaos, for its characterisation and experimental observation are finally discussed.