Theoretical study of a passively mode-locked integrated laser based on transition-metal dichalcogenides and graphene

We assess the theoretical performance of a mode-locked silicon-rich-nitride ring laser, which is partly overlayed with a ${\mathrm{MoS}}_2/{\mathrm{WSe}}_2$ bilayer and partly with a graphene monolayer. Through an external vertical optical pump at 740 nm, the transition-metal dichalcogenide (TMD) bilayer can be inverted and provide gain at 1128 nm while the graphene monolayer acts as the fast broadband saturable absorber. We show that under modest pumping conditions, we can reach a stable mode-locked regime that can deliver on-chip pulsed output with milliwatt peak power and down to 400 fs in duration. The ring laser is studied by rigorously modeling the TMD bilayer as a semiclassical three-level system and incorporating the resulting resonant polarization to the nonlinear Schrödinger equation (NLSE). Within the NLSE formalism we are able to also incorporate material and waveguide dispersion as well as the significant Kerr-type nonlinearity of the silicon-rich-nitride waveguide. Furthermore, we discuss all the necessary physical and mathematical approximations needed to numerically solve the propagation problem, based on an implementation of the split-step Fourier method with the atomic polarization term. Our mathematical treatment is very general and can be adapted to any two-dimensional-material-enhanced traveling wave source. Finally, this work shows the feasibility and potential of TMD bilayers as well as graphene for the development of efficient integrated pulsed on-chip sources.