The Dynamics of Spatially Extended Lasers

The dynamics of spatially extended lasers is studied both experimentally and theoretically in order to understand instabilities and losses of spatial coherence in the output intensity. Analysis first begins with small bore CO _2 lasers in which experimental evidence of time-dependent and stationary complex spatial structures is shown. A comparison of the data with a theoretical model supports the notion that the observed phenomena result from the nonlinear interaction of transverse cavity modes with the active medium. The sequence of events in which going from a simple pattern (symmetric pattern) to a complex pattern is studied in a large bore CO_2 laser by considering a qualitative theory of bifurcations. In particular demonstrated is that the spatiotemporal behavior of lasers can be characterized by group theory, that structures experimentally observed are created from the symmetry breaking of the O(2) X T ^2 group, and that spontaneous symmetry breaking is at the origin of a gradual increase of complexity in space and time. After each bifurcation a new frequency is added until two or three frequencies in the intensity usually produce local chaotic behavior. At that point almost any degree of spatial symmetry is lost. Numerical integration of the laser equations is carried out to make a further analysis. In particular the numerical code shows the appearance of defects. As a measure of complexity (turbulence) a function to indicate loss of spatial coherence (correlation function) is introduced. The presence of defects on the correlation function is to produce a loss of coherence. This function also can indicate whenever there is loss of a frequency component in the temporal signal. Experimental results of measuring this function will be discussed.