Chaotic behavior in transverse-mode laser dynamics

We analyze chaotic behavior found in numerical simulations of the transverse pattern dynamics of a laser demonstrating that in some cases chaos originates in phase dynamics and is of low dimension. Investigations of both a Ginzburg-Landau equation for the complex field amplitude of the laser output and a Kuramoto-Sivashinsky-type equation for only the phase of that complex field equation find the same behavior. Both equations can be expanded in terms of spatial modes and in the chaotic regime the behavior of the modal amplitudes seems relatively independent. However, the fluctuations of the modal amplitudes are sufficiently correlated so that the spatiotemporal dynamics is a form of low dimensional chaos rather than a more complex turbulent behavior or even one that might merit the term spatiotemporal chaos.