GENERALIZED DIMENSIONS OF LASER ATTRACTORS

We use generalized dimensions to compare the dynamics of an optically pumped NH3 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 D2 as an estimate for the Hausdorff dimension D0 can differ substantially from D0, and shows little sensitivity to attractor changes.