  Multimode nonlinear optics offers to overcome a long-standing limitation of
fiber optics, tightly phase locking several spatial modes and enabling the
coherent transport of a wavepacket through a multimode fiber. A similar problem
is encountered in the temporal compression of multi-mJ pulses to few-cycle
duration in hollow gas-filled fibers. Scaling the fiber length to up to six
meters, hollow fibers have recently reached 1 TW of peak power. Despite the
remarkable utility of the hollow fiber compressor and its widespread
application, however, no analytical model exists to enable insight into the
scaling behavior of maximum compressibility and peak power. Here we extend a
recently introduced formalism for describing mode-locking to the spatially
analogue scenario of locking spatial fiber modes together. Our formalism
unveils the coexistence of two soliton branches for anomalous modal dispersion
and indicates the formation of stable spatio-temporal light bullets that would
be unstable in free space, similar to the temporal cage solitons in
mode-locking theory. Our model enables deeper understanding of the physical
processes behind the formation of such light bullets and predict the existence
of multimode solitons in a much wider range of fiber types than previously
considered possible.
