  Surface plasmon polaritons enable light concentration within subwavelength
regions, opening thereby new avenues for miniaturizing the device and
strengthening light-matter interactions. Here we realize effective
electro-optic modulation in low-loss plasmonic waveguides with the aid of
graphene, and the devices are fully integrated in the silicon-on-insulator
platform. By advantageously exploiting low-loss plasmonic slot-waveguide modes,
which weakly leak into a substrate while feature strong fields within the
two-layer-graphene covered slots in metal, we successfully achieve a tunability
of 0.13 dB/um for our fabricated graphene-plasmonic waveguide devices with
extremely low insertion loss, which outperforms previously reported
graphene-plasmonic devices. Our results highlight the potential of graphene
plasmonic leaky-mode hybrid waveguides to realized active ultra-compact devices
for optoelectronic applications.
