  Compact, high-speed electro-optic phase modulators play a vital role in
various large-scale applications including phased arrays, quantum and neural
networks, and optical communication links. Conventional phase modulators suffer
from a fundamental tradeoff between device length and optical loss that limits
their scaling capabilities. High-finesse ring resonators have been
traditionally used as compact intensity modulators, but their use for phase
modulation have been limited due to the high insertion loss associated with the
phase change. Here, we show that high-finesse resonators can achieve a strong
phase change with low insertion loss by simultaneous modulation of the real and
imaginary parts of the refractive index, to the same extent i.e. $\frac{\Delta
n}{\Delta k} \sim 1$. To implement this strategy, we utilize a hybrid platform
that combines a low-loss SiN ring resonator with electro-absorptive graphene
(Gr) and electro-refractive WSe$_2$. We achieve a phase modulation efficiency
($V_{\frac{\pi}{2}} \cdot L_{\frac{\pi}{2}}$) of 0.045 V $\cdot$ cm with an
insertion loss (IL$_{\frac{\pi}{2}}$) of 4.7 dB for a phase change of
$\frac{\pi}{2}$ radians, in a 25 $\mu$m long Gr-Al$_2$O$_3$-WSe$_2$ capacitor
embedded on a SiN ring of 50 $\mu$m radius. We find that our
Gr-Al$_2$O$_3$-WSe$_2$ capacitor can support an electro-optic bandwidth of 14.9
$\pm$ 0.1 GHz. We further show that the $V_{\frac{\pi}{2}} \cdot
L_{\frac{\pi}{2}}$ of our SiN-2D platform is at least an order of magnitude
lower than that of electro-optic phase modulators based on silicon, III-V on
silicon, graphene on silicon and lithium niobate. This SiN-2D hybrid platform
provides the impetus to design compact and high-speed reconfigurable circuits
with graphene and transition metal dichalcogenide (TMD) monolayers that can
enable large-scale photonic systems.
