  Dissipative nonlinear wave dynamics have been investigated extensively in
mode-locked lasers with single transverse-mode, whereas there are few studies
related to three-dimensional nonlinear dynamics within lasers. Recently,
spatiotemporal mode-locking (STML) was proposed in lasers with small modal
(i.e., transverse-mode) dispersion, which has been considered to be critical
for achieving STML in those cavities because the small dispersion can be easily
balanced. Here, we demonstrate that STML can also be achieved in multimode
lasers with much larger modal dispersion, where we find that the intracavity
saturable absorber plays an important role for counteracting the large modal
dispersion. Furthermore, we observe a new STML phenomenon of passive nonlinear
auto-selection of single-mode mode-locking, resulting from the interaction
between spatiotemporal saturable absorption and spatial gain competition. Our
work significantly broadens the design possibilities for useful STML lasers
thus making them much more accessible for applications, and extends the
explorable parameter space of the novel dissipative spatiotemporal nonlinear
dynamics that can be achieved in these lasers.
