  We study cascaded harmonic generation of hybrid surface plasmons in
integrated planar waveguides composed of a graphene layer and a
doped-semiconductor slab. We derive a comprehensive model of cascaded third
harmonic generation through phase-matched nonlinear interaction of fundamental,
second harmonic and third harmonic plasmonic modes supported by the structure.
We show that hybrid graphene-semiconductor waveguides can simultaneously
phase-match these three interacting harmonics, increasing the total
third-harmonic output by a factor of 5 compared to the non-cascaded regime.
