DYNAMICAL TRANSVERSE LASER PATTERNS .1. THEORY

We consider a cylindrically symmetrical laser with spherical mirrors a nd describe the dynamics in terms of the competition among different G auss-Laguerre modes of the cavity. In this paper we focus on the case in which the mode competition leads the laser to a dynamical: state th at, according to the values of the central parameters, can be periodic or quasiperiodic. The linear stability analysis of the single-mode st ationary solutions, in which the laser oscillates with the fundamental TEM(00) or the TEM(01) mode, provides an initial guideline in our se arch for; the various spatiotemporal patterns which emerge. We conside r cases in which the gain line activates one, two, or three frequency- degenerate families of modes. The motion of optical vortices, from the simple rotation to creation and annihilation in pairs is analyzed, to gether with the correlated movement or the peaks of the intensity dist ribution in the: traverse plane. We study also the patterns which appe ar-when the cylindrical symmetry of the system is broken. The paramete rs of our calculations correspond closely to those which characterize Na-2 lasers, CO2 lasers, and Nd-doped yttrium aluminum garnet lasers.