Optical harmonic generation in monolayer group-VI transition metal dichalcogenides

Monolayer transition metal dichalcogenides (TMDs) exhibit high nonlinear optical (NLO) susceptibilities. Experiments on ${\mathrm{MoS}}_2$ have indeed revealed very large second-order (${\chi }^{\left(2\right)}$) and third-order (${\chi }^{\left(3\right)}$) optical susceptibilities. However, third-harmonic generation results of other layered TMDs have not been reported. Furthermore, the reported ${\chi }^{\left(2\right)}$ and ${\chi }^{\left(3\right)}$ of ${\mathrm{MoS}}_2$ vary by several orders of magnitude, and a reliable quantitative comparison of optical nonlinearities across different TMDs has remained elusive. Here, we investigate second- and third-harmonic generation, and three-photon photoluminescence in TMDs. Specifically, we present an experimental study of ${\chi }^{\left(2\right)}$ and ${\chi }^{\left(3\right)}$ of four common TMD materials (${\mathrm{MoS}}_2$, ${\mathrm{MoSe}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$) by placing different TMD flakes in close proximity to each other on a common substrate, allowing their NLO properties to be accurately obtained from a single measurement. ${\chi }^{\left(2\right)}$ and ${\chi }^{\left(3\right)}$ of the four monolayer TMDs have been compared, indicating that they exhibit distinct NLO responses. We further present theoretical simulations of these susceptibilities in qualitative agreement with the measurements. Our comparative studies of the NLO responses of different two-dimensional layered materials allow us to select the best candidates for atomic-scale nonlinear photonic applications, such as frequency conversion and all-optical signal processing.

Figure 1

(a) Optical image of four different TMDs positioned close to each other. Zoomed optical images of areas marked in (a) with colored rectangles for (b) ${\mathrm{MoS}}_2$, (c) ${\mathrm{WSe}}_2$, (d) ${\mathrm{MoSe}}_2$, and (e) ${\mathrm{WS}}_2$. White dashed contours in (b)–(e) indicate the monolayer areas.

Figure 2

SHG (top) and THG (bottom) images from the areas marked with colored dashed rectangles in the optical image of Fig. 1. Blue, ${\mathrm{MoS}}_2$; purple, ${\mathrm{WSe}}_2$; orange, ${\mathrm{MoSe}}_2$; yellow, ${\mathrm{WS}}_2$. The scale bar for ${\mathrm{MoS}}_2$, ${\mathrm{WSe}}_2$, and ${\mathrm{MoSe}}_2$ is 10 $\mu \mathrm{m}$, and that for ${\mathrm{WS}}_2$ is 5 $\mu \mathrm{m}$.

Figure 3

Measured average powers of (a) THG and (b) SHG from monolayers of all four materials with 20 mW pump power ($\sim 2.7$ kW peak power). Comparison between one-photon and multiphoton excited spectrum of (c) ${\mathrm{WS}}_2$ and (d) ${\mathrm{MoSe}}_2$. Note that the intensities of one-photon and multiphoton spectra in (c) and (d) are not to scale.

Figure 4

Comparison of experimental and theoretical (a) $|{\chi }^{\left(2\right)}|$ and (b) $|{\chi }^{\left(3\right)}|$ of four TMDs at 1560 nm excitation.

Figure 5

Polar plots of normalized SHG and THG signals as a function of the quarter-wave plate (QWP) angle. The angle is defined between the polarization of the incident laser and the fast axis of the QWP.