Solitons and vortices in lasers

Nonlinear optical resonators, particularly active resonators, of large Fres nel number show a rich structure formation, which relates for example, lase rs with fluids, superfluids, or chemical systems. "Localized structures" ar e structures of particular interest because of their particle-like properti es. In nonlinear optics vortices and spatial solitons are such localized st ructures. We give in this article the mathematical background for pattern formation i n nonlinear active resonators, elucidating the relation of optics with othe r fields of physics, and demonstrate experimentally the existence, properti es, and dynamics of: (i) vortices in lasers, (ii) bright spatial solitons in lasers with saturable absorber and (iii) spatial solitons in degenerate parametric mixing. All these structure s are by definition bistable so that they are potentially useful for parall el optical information processing.