  We show that the dynamics of high-intensity laser pulses undergoing
self-focused propagation in a nonlinear medium can be understood in terms of
the topological constraints imposed by the formation and evolution of
spatiotemporal optical vortices (STOVs). STOVs are born from point phase
defects on the sides of the pulse nucleated by spatiotemporal phase shear.
These defects grow into closed loops of spatiotemporal vorticity that initially
exclude the pulse propagation axis, but then reconnect to form a pair of
toroidal vortex rings that wrap around it. STOVs constrain the intrapulse flow
of electromagnetic energy, controlling the focusing-defocusing cycles and pulse
splitting inherent to nonlinear pulse propagation. We illustrate this in two
widely studied but very different regimes, relativistic self-focusing in plasma
and non-relativistic self-focusing in gas, demonstrating that STOVs mediate
nonlinear propagation irrespective of the detailed physics.
