  Vanadium dioxide (${\rm VO}_2$) is a phase change material (PCM) that
exhibits a large change in complex refractive index on the order of unity upon
switching from its dielectric to its metallic phase. Although this property is
key for the design of ultracompact optical modulators of only a few microns in
footprint, the high absorption of ${\rm VO}_2$ leads to appreciable insertion
loss (IL) that limits the modulator performance. In this paper, through theory
and numerical modeling, we report on a new paradigm, which demonstrates how the
use of a hybrid plasmonic waveguide to construct a ${\rm VO}_2$ based modulator
can improve the performance by minimizing its IL while achieving high
extinction ratio (ER) in comparison to a purely dielectric waveguide. The
hybrid plasmonic waveguide that contains an additional metal layer with even
higher loss than ${\rm VO}_2$ enables unique approaches to engineer the
electric field (E-field) intensity distribution within the cross section of the
modulator. The resulting figure-of-merit, FoM = ER/IL, is much higher than what
is possible by simply incorporating ${\rm VO}_2$ into a silicon wire waveguide.
A practical modulator design using this new approach, which also includes input
and output couplers yields ER = 3.8 dB/{\mu}m and IL = 1.4 dB/{\mu}m (FoM =
2.7), with a 3-dB optical bandwidth >500 nm, in a device length = 2 {\mu}m, and
cross-sectional dimensions = 200 nm $\times$ 450 nm. To the best of our
knowledge, this is one of the smallest modulator designs proposed to date that
also exhibits amongst the highest ER, FoM, and optical bandwidth, in comparison
to existing designs. In addition to ${\rm VO}_2$, we investigate two other PCMs
incorporated within the waveguide structure. The improvements obtained for
${\rm VO}_2$ modulators do not extend to other PCMs.
