Third-order Optical Nonlinearity in Two-dimensional Transition Metal Dichalcogenides

Abstract

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer Two-Dimensional (2D) Transition-Metal Dichalcogenides (TMDCs), having the formula ${\text{MX}}_2$ with M=Mo,W and X=S,Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semiclassical perturbation analysis of response functions. We numerically calculate the linear ${\chi }_{\mu \nu }^{(1)}(-\omega ;\omega )$ and nonlinear surface susceptibility tensors ${\chi }_{\mu \nu \zeta \eta }^{(3)}(-{\omega }_{\Sigma };{\omega }_r,{\omega }_s,{\omega }_t)$ with ${\omega }_{\Sigma }={\omega }_r+{\omega }_s+{\omega }_t$. Both non-degenerate and degenerate cases are studied for third-harmonic generation and nonlinear refractive index, respectively. Computational results obtained \textit{with no external fitting parameters} are discussed regarding two recent reported experiments on ${\mathrm{MoS}}_2$, and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a $\frac{\pi }{4}-$rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and high-harmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.

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• Second- and third-order optical susceptibilities in bidimensional semiconductors near excitons states
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• Analysis of Side-band Inequivalence