Cascaded third harmonic generation in hybrid graphene-semiconductor waveguides

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.