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

Theoretical Analysis of Integrated Nanophotonic Q‐Switched Laser Based on Gain and Saturable Absorption by Two‐Dimensional Materials

“…For designing the proposed lasing element, we develop a rigorous temporal coupled-mode theory (CMT) framework fed by linear finite-element method (FEM) simulations. [35][36][37][38][39][40][41] Both the lasing and pump transitions in the gain medium are described by induced electric polarization fields, which follow typical Lorentzian oscillator equations capable of describing homogeneously broadened transitions. [36,[42][43][44][45] The carrier dynamics of the 2D gain medium are described by semiclassical carrier rate equations, while the nonlinear response of graphene by its nonlinear surface conductivity.…”

“…The photoluminescence process of the MoS 2 =WSe 2 heterobilayer is illustrated in Figure 1a, and it is fundamentally the same for every TMD bilayer that forms a type-II band alignment heterostructure. [24,25,29,30] MoS 2 =WSe 2 can be readily modeled as a three-level gain medium, [41] with levels 1, 2, and 3 being the valence band of WSe 2 , the conduction band of MoS 2 , and the conduction band of WSe 2 , respectively. The surface carrier density in each level is marked as N i ðr, tÞ, i ¼ f1, 2, 3g.…”

“…The 2D nature of the TMD hetero-bilayer dictates that the polari- where the relative permittivity tensor ε r ðrÞ describes the isotropic or uniaxially anisotropic dielectric properties of the underlying bulk materials of the cavity. Note that the polarization fields describe only the resonant nonlinear response due to the respective transition in the gain medium, [45] while its nonresonant (background) linear dielectric properties are expressed by appropriate imaginary surface conductivity tensors, σ, which can be thought of as contributing to the relative permittivity tensor through the relation ε r ¼ I 3 þ jσ=ðωε 0 dÞ, where d is the thickness of the 2D material [41,46] and I 3 is the 3 Â 3 identity matrix. Throughout this work, the surface conductivity tensors are used for the 2D materials, respecting their two-dimensional nature.…”

“…The thorough mathematical evaluation of Δ ωðmÞ and a comprehensive discussion on the choice of ω ðmÞ ref is presented in our recent work, [41] while for the extraction of Δ ωðpÞ a similar process has to be followed. Here, we omit the rather long mathematical procedure and present the final result which reads Δ e ω ðmÞ ¼ jξ…”

“…The framework can be exploited to assess the response of a general "class C" laser, where the carrier dynamics and the polarization response of the gain medium are considered to determine the overall response of the laser. In comparison with our recent work, [41] here we have expanded the CMT framework to incorporate the case where the optical pumping is conducted with a tightly confined cavity mode excited by guided light rather than a uniform free-space beam. In addition, the SA effect has been introduced in the framework enabling the study of pulsed nanophotonic lasing structures.…”