On-chip low-loss all-optical MoSe$_2$ modulator

Monolayer transition metal dichalcogenides (TMDCs), like MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, feature direct bandgaps, strong spin-orbit coupling, and exciton-polariton interactions at the atomic scale, which could be harnessed for efficient light emission, valleytronics, and polaritonic lasing, respectively. Nevertheless, to build next-generation photonic devices that make use of these features, it is first essential to model the all-optical control mechanisms in TMDCs. Herein, a simple model is proposed to quantify the performance of a 35$\,$\textmu m long Si$_3$N$_4$ waveguide-integrated all-optical MoSe$_2$ modulator. Using this model, a switching energy of 14.6$\,$pJ is obtained for a transverse-magnetic (TM) and transverse-electric (TE) polarised pump signals at $\lambda =\,$480$\,$nm. Moreover, maximal extinction ratios of 20.6$\,$dB and 20.1$\,$dB are achieved for a TM and TE polarised probe signal at $\lambda =\,$500$\,$nm, respectively, with an ultra-low insertion loss of $