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Compact, high-speed electro-optic phase modulators play a vital role invarious large-scale applications including phased arrays, quantum and neuralnetworks, and optical communication links. Conventional phase modulators sufferfrom a fundamental tradeoff between device length and optical loss that limitstheir scaling capabilities. High-finesse ring resonators have beentraditionally used as compact intensity modulators, but their use for phasemodulation have been limited due to the high insertion loss associated with thephase change. Here, we show that high-finesse resonators can achieve a strongphase change with low insertion loss by simultaneous modulation of the real andimaginary parts of the refractive index, to the same extent i.e. $\frac{\Deltan}{\Delta k} \sim 1$. To implement this strategy, we utilize a hybrid platformthat 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 aninsertion 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$_2$ capacitorembedded on a SiN ring of 50 $\mu$m radius. We find that ourGr-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 $V_{\frac{\pi}{2}} \cdotL_{\frac{\pi}{2}}$ of our SiN-2D platform is at least an order of magnitudelower than that of electro-optic phase modulators based on silicon, III-V onsilicon, graphene on silicon and lithium niobate. This SiN-2D hybrid platformprovides the impetus to design compact and high-speed reconfigurable circuitswith graphene and transition metal dichalcogenide (TMD) monolayers that canenable large-scale photonic systems.

2D material platform for overcoming the amplitude-phase tradeoff in ring modulators