Transverse laser patterns. II. Variational principle for pattern selection, spatial multistability, and laser hydrodynamics

We show that the stationary transverse patterns, formed by the interaction of the modes of a frequency-degenerate family, are selected by the laser according to a specific variational principle. We discuss the phenomenon of spatial multistability, which consists in the coexistence of two or more different configurations for the same values of the control parameters. We establish a general connection between laser physics and hydrodynamics, by reformulating the dynamical equations of the laser in the form of hydrodynamical equations for a compressible fluid, similar to the law of mass conservation and to the Bernoulli equation. This result provides a general framework for the discussion of the relations between optical and hydrodynamical turbulence.