  Research on graphene has revealed its unique optical properties, including
strong coupling with light, high-speed operation, and gate-variable optical
conductivity, which promise to satisfy the needs of future electro-optic (EO)
modulators. In particular, recent work demonstrated a broadband EO modulator
based on the interband absorption of graphene with overall length only
40{\mu}m. However, compared with the size of on-chip electronic components it
is still bulky. On-chip optical interconnects require EO modulation at the
nanoscale. The key to achieve nanoscale graphene EO modulation is to greatly
enhance light-graphene interaction based on novel waveguides and platforms.
Herein, we present our recent exploration of graphene EO modulators based on
graphene sandwiched in dielectric or plasmonic waveguides. With a suitable gate
voltage, the dielectric constant of graphene can be tuned to be very small due
to the effect of intraband electronic transition, resulting in "graphene-slot
waveguides" and greatly enhanced absorption modes. Up to 3-dB modulation depth
can be achieved within 800nm long silicon waveguides, or 120nm long plasmonic
waveguides based on small signal analysis. They have the advantages of
nanoscale footprints, small insertion loss, low power consumption, and
potentially ultrahigh speed, as well as being CMOS-compatible.
