Generalized dimensions of laser attractors

We use generalized dimensions to compare the dynamics of an optically pumped ${\mathrm{NH}}_3$ ring laser with that of the Lorenz model. While for pure single-mode emission we find excellent agreement between dimension spectra of the laser and the Lorenz attractor, for conditions of existence of a second counterpropagating mode, dimensions are found to be higher. Thus the dimension spectra reflect the larger phase space occupied by the attractor. As a further result of that comparison, we find that the frequently used correlation dimension ${\mathit{D}}_2$ as an estimate for the Hausdorff dimension ${\mathit{D}}_0$ can differ substantially from ${\mathit{D}}_0$, and shows little sensitivity to attractor changes.