Efficient Lasing in MoS$_2$/WSe$_2$-Based Metasurfaces Enabled by Quasi-Dark Magnetic Dipole Resonance

TL;DR

This work tackles efficient lasing from ultrathin dielectric metasurfaces by leveraging long-lived interlayer excitons in a MoS2/WSe2 heterobilayer gain medium. It designs a silicon-rich nitride metasurface that supports a quasi-dark magnetic-dipole qBIC, symmetry-broken to enable outcoupling, and couples it to the interlayer excitons to achieve lasing around the near-IR. A temporal coupled-mode theory (CMT) framework, validated against nonlinear time-domain simulations, yields a low lasing threshold (~6 kW/cm^2) with ~3.7% efficiency and robust operation; thermal analysis shows stable performance up to several MW/cm^2 on suitably engineered substrates. The results establish an efficient, accurate route to design metasurface lasers with 2D gain media and paves the way for ultrathin, high-performance light-emitting surfaces.

Abstract

The novel combination of a strongly-resonant optical metasurface with the MoS$_2$/WSe$_2$ hetero-bilayer is proposed for efficient free-space lasing enabled by the enhanced coupling between the optical and matter (exciton) states. The metasurface comprises silicon-rich nitride meta-atoms periodically arrayed in a subdiffractive lattice and overlaid with MoS$_2$/WSe$_2$, which provides optically-pumped gain around $1130~\mathrm{nm}$. Light emission is enabled by exploiting a quasi-bound state in the continuum in the form of a perturbed vertical magnetic dipole resonance. Following a meticulous design process guided by full-wave simulations and multipole expansion analysis, an ultralow lasing threshold of $\sim 6~\mathrm{kW/cm^2}$ is achieved. Moreover, the thermal stability of the lasing structure is examined through heat transfer simulations; stable operation with pump power densities up to a few MW/cm$^2$ (three orders of magnitude above the threshold) is predicted. These results demonstrate that MoS$_2$/WSe$_2$-based metasurface lasers can exhibit robust operation, paving the way for highly-performing ultrathin light-emitting surfaces. The lasing response is rigorously assessed through a highly-efficient temporal coupled-mode theory framework, verified by time-domain FEM simulations showing excellent agreement. Thus, an efficient and accurate approach to design and study metasurface lasers with arbitrary geometries and surface or bulk gain media is introduced, exhibiting significant advantages over cumbersome full-wave simulations.

Figures (5)

• Figure 1: (a) Illustration of the considered metasurface laser consisting of symmetry-broken SRN stripes periodically arrayed on a SiO2 substrate. The structure is planarized with a low-index cladding and is overlaid with the MoS2/WSe2 hetero-bilayer. The metasurface laser is optically pumped by a normally-incident plane wave at $\lambda_p$ and emits vertically in both $\pm\hat{\mathbf{z}}$ directions at $\lambda_L$. The geometric parameters are annotated in the unit cell cross-section (right part). (b) Energy diagram of MoS2/WSe2 showing the lasing process due to the radiative recombination of interlayer excitons.
• Figure 2: (a) Transmission and reflection spectra of the examined metasurface under vertical plane-wave illumination when $d=20~\mathrm{nm}$ (solid lines) and $d=0$ (dashed lines). Inset: Field profile of the qBIC excited near $\sim1128$ nm when $d=20~\mathrm{nm}$. Color denotes $\mathrm{Re}\{ E_x\}$, whereas arrows the magnetic field. (b) $\mathrm{MD}_z$ mode: Radiative quality factor $Q_\mathrm{rad}$ and magnitude of the residual in-plane magnetic dipole moment $m_y$ (normalized to the dominant vertical component) as a function of the defect size $d$.
• Figure 3: (a) Total emitted power density $I_\mathrm{out}$, and (b) spatially-averaged surface carrier densities $\bar{N}_i$ in the three levels of the gain medium as a function of the pump power density $I_p$, obtained by both CMT (solid lines) and TD-FEM (circular markers). Inset in (b) Carrier density $\bar{N}_3$ versus $I_p$ in logarithmic scale.
• Figure 4: Temporal evolution of (a, b) the output power density in air, $I_\mathrm{out}^\mathrm{up}$, and (c, d) the spatially-averaged surface carrier densities $\bar{N}_1$ and $\bar{N}_2$ evaluated through both CMT and TD-FEM. The pump power density is smoothly switched-on until reaching the constant value of $I_p=1~\mathrm{MW/cm^2}$ [gray curve in (b)]. In (a, c) the defect size is $d=20~\mathrm{nm}$, while in (b, d) $d=30~\mathrm{nm}$. Inset in (a) normalized optical spectrum of the electric field in air comprising the reflected pump wave at $\lambda_p$ and the upwards emitted wave at $\lambda_L$.
• Figure 5: (a) Temperature increase in MoS2/WSe2 (spatially averaged) as a function of the generated heat rate density $I_h$ for the two different configurations shown in the insets. Dashed lines indicate operation below the lasing threshold. (b, c) Spatial distribution of the temperature variation in the metasurface unit cell for $I_h=10~\mathrm{kW/cm^2}$ ($I_p \approx 170~\mathrm{kW/cm^2}$) when the metasurface resides on top of a (a) standard silicon-on-insulator, and (b) silicon-on-sapphire substrate.