Integrated Lasers with Transition-Metal-Dichalcogenide Heterostructures: Analysis and Design Utilizing Coupled-Mode Theory for Two-Dimensional Materials

We assess the continuous-wave and dynamic performance of a photonic laser cavity consisting of a silicon-rich-nitride-on-insulator disk resonator overlaid with a transition-metal dichalcogenide (TMD) bilayer heterostructure (${\mathrm{WSe}}_{2}/{\mathrm{Mo}\mathrm{S}}_{2}$) acting as the gain medium. The optically pumped TMD heterostructure fosters an interlayer exciton with long radiative recombination lifetime, providing light emission in the near-infrared ($\ensuremath{\sim}1130$ nm). Following a meticulous design process, we propose a silicon-on-insulator-compatible, monolithically integrated optical source capable of emitting milliwatt power inside an integrated waveguide, featuring a low pump-power threshold of $\ensuremath{\sim}16\phantom{\rule{0.2em}{0ex}}{\mathrm{kW}/\mathrm{cm}}^{2}$, and exhibiting an estimated total quantum efficiency of approximately 1.7%. The proposed laser cavity is analyzed and designed using a rigorous theoretical framework based on perturbation theory and temporal coupled-mode theory, capable of treating nanophotonic cavities of any geometry and material composition comprising both bulk and/or sheet gain media. The framework is built upon fundamental electromagnetic and semiclassical gain equations, rendering it general and adaptable to different cavity configurations and gain-media descriptions. It constitutes a powerful tool for the efficient analysis of contemporary micro- and nanophotonic semiconductor lasers, since it is capable of predicting fundamental laser characteristics, providing design directives, deriving continuous-wave design metrics, and evaluating the dynamic response of realistic laser cavities.