  Doped graphene emerges as a strong contender for active plasmonic material in
the mid-infrared wavelengths due to the versatile external-control of its
permittivity-function and also its highly-compressed graphene surface plasmon
(GSP) wavelength. In this paper, we design active plasmonic waveguide devices
based on electrical-modulation of doped graphene nanoribbons (GNRs) on a
voltage-gated inhomogeneous dielectric layer. We first develop figure-of-merit
(FoM) formulae to characterize the performance of passive and active graphene
nanoribbon waveguides. Based on the FoMs, we choose optimal GNRs to build a
plasmonic shutter, which consists of a GNR placed on top of an inhomogeneous
SiO$_2$ substrate supported by a Si nanopillar. Simulation studies show that
for a simple 50nm-long plasmonic shutter, the modulation contrast can exceed
30dB. The plasmonic shutter is further extended to build a 4-port active power
splitter and an 8-port active network, both based on GNR cross-junction
waveguides. For the active power splitter, the GSP power transmission at each
waveguide arm can be independently controlled by an applied gate-voltage with
high modulation contrast and nearly-equal power-splitting proportions. From the
construct of the 8-port active network, we see that it is possible to scale up
the GNR cross-junction waveguides into large and complex active waveguide
networks, showing great potential in an exciting new area of mid-infrared
graphene plasmonic integrated nanocircuits.
