  We theoretically demonstrate the possibility of generating a spatiotemporal
optical vortex (STOV) beam in a dielectric slab waveguide. The STOV is
generated upon reflection of a spatiotemporal optical pulse from an integrated
metal-dielectric structure consisting of metal strips "buried" in the
waveguide. For describing the interaction of the incident pulse with the
integrated structure, we derive its "vectorial" spatiotemporal transfer
function (TF) describing the transformation of the electromagnetic field
components of the incident pulse. We show that if the TF of the structure
corresponds to the TF of a spatiotemporal differentiator with a $\pi/2$ phase
difference between the terms describing temporal and spatial differentiation,
then the envelope of the reflected pulse will contain an STOV in all nonzero
components of the electromagnetic field. The obtained theoretical results are
in good agreement with the results of rigorous numerical simulation of the STOV
generation using a three-strip metal-dielectric integrated structure. We
believe that the presented results pave the way for the research and
application of STOV beams in the on-chip geometry.
