Instabilities and Chaos in Multimode Homogeneously Broadened Lasers

The experiments of Hillman, et al. [1] with a ring dye laser indicate that single-mode homogeneously broadened oscillation is intrinsically unstable at high pumping levels. Motivated by this work, we have considered various formulations of the general multimode problem. We find that certain aspects of these experiments, such as the transition from single to multimode oscillation with increased pumping, can be understood within the thin-sheet gain model in which spatial hole burning is completely ignored. (We hope by the time of our presentation to be more precise about the comparison of theory and experiment.) Following the bifurcation of the single-mode steady state and the onset of two modes symmetrically displaced about line center, there is a period-doubling route to chaos which is not evident in the experiments thus far. The familiar "gain clamping" assumption of single-mode oscillation in a homogeneously broadened laser is incorrect at high pumping levels, even in the absence of spatial hole burning. Our results appear to be consistent with the arguments advanced by Hillman, et al. on the basis of a model in which the atoms are driven by the field but do not react back on it.