Nonlinear-time-series analysis of chaotic laser dynamics

We report on the analysis of experiments on a neodymium-doped yttrium aluminum garnet laser with an intracavity frequency-doubling crystal. Three modes of the laser were excited in differing polarization configurations. The total intensity of infrared light was observed and then analyzed using methods of nonlinear-time-series analysis. We present clear evidence using global false nearest neighbors that when all polarizations are parallel, the intensity is chaotic with two positive Lyapunov exponents and the system can be embedded in dimension 7. The noise level in this operating condition, which we call type I chaos, is small. When one of the polarizations is perpendicular to the others, the intensity is again chaotic with positive Lyapunov exponents, but there is substantial noise in the signal of high dimensional origin, and no finite embedding dimension appears possible. We call this type II chaos. We suggest that the origin of this phenomenon is the intrinsic quantum noise associated with the generation of green light, which is 25 times more intense in the type II operating configuration than in the first. In past experiments with this system we have found that the type I chaos can be controlled to unstable periodic orbits while type II cannot. In each type of chaotic laser operation we use local false nearest neighbors to demonstrate that the local dimension of the dynamics is 7. This means seven differential equations can capture the full dynamics of these regimes of the laser. We evaluate local and global false nearest neighbors to support our conclusions and determine the Lyapunov spectrum of each type of chaotic behavior. The predictability of type II chaos is shown to be much less than that of type I, and we make local polynomial models in reconstructed-state space to demonstrate that we can predict rather well for type I chaos. Finally we suggest a fairly standard model for the interaction of the infrared light with the nonlinear frequency doubling medium and with a two-level of the active medium.