  We identify a class of modal solutions for spatio-temporal optical vortex
(STOV) electromagnetic pulses propagating in dispersive media with orbital
angular momentum (OAM) orthogonal to propagation. We find that symmetric STOVs
in vacuum can carry half-integer intrinsic orbital angular momentum (OAM); for
general asymmetric STOVs in a dispersive medium, the OAM is quantized in
integer multiples of a parameter that depends on the STOV symmetry and the
group velocity dispersion. Our results suggest that STOVs propagating in
dispersive media are accompanied by a polariton-like quasiparticle. The modal
theory is in excellent agreement with measurements of free space propagation of
STOVs.
