Stability of spiralling solitary waves in Hamiltonian systems.

We present a rigorous criterion for stability of spiralling solitary structures in Hamiltonian systems incorporating the angular momentum integral and demonstrate its applicability to the spiralling of two mutually incoherent optical beams propagating in a photorefractive material.

Polarization dynamics of Bragg solitons.

The families of vectorial Bragg solitons existing in transversely periodic media and their stability properties are studied in detail. Two qualitatively distinct types of polarization instabilities have been found. One leads to the significant radiation transfer into nonsolitonic forms, while the other mainly redistributes energy between two soliton components.

Two-dimensional clusters of solitary structures in driven optical cavities.

Using analytical and numerical approaches we study clusters of the two-dimensional localized structures of light excited in the externally driven optical cavities. Stability and instability properties of clusters of two, three, and four structures are analyzed in detail. We develop a technique for calculation of the expression for the interaction potential through modified Bessel functions that has applicability going beyond the model under consideration. Qualitative differences between stability properties of triangular and square structures are found that emphasize the role of diagonal interactions in the latter.

Giant excess noise and transient gain in misaligned laser cavities.

The excess noise factor is calculated analytically for a very general class of optical cavities, and is shown to have a superexponential dependence on cavity misalignment, easily attaining values of order 10(10). The physical basis is shown to be "ransient gain" associated with amplified spontaneous emission. Similarly dramatic effects of symmetry breaking can be expected in other physical systems with non-normal modes.