Second harmonic microscopy of monolayer MoS${}_2$

We show that the lack of inversion symmetry in monolayer MoS${}_2$ allows strong optical second harmonic generation. The second harmonic of an 810-nm pulse is generated in a mechanically exfoliated monolayer, with a nonlinear susceptibility on the order of 10${}^{-7}$ m/V. The susceptibility reduces by a factor of seven in trilayers, and by about two orders of magnitude in even layers. A proof-of-principle second harmonic microscopy measurement is performed on samples grown by chemical vapor deposition, which illustrates potential applications of this effect in the fast and noninvasive detection of crystalline orientation, thickness uniformity, layer stacking, and single-crystal domain size of atomically thin films of MoS${}_2$ and similar materials.

Figure 1

(a) Schematics of the experimental setup. (b) Microscope image of a mechanically exfoliated MoS${}_2$ flake. (c) Lattice structure of monolayer MoS${}_2$.

Figure 2

Second harmonic generation from the mechanically exfoliated MoS${}_2$ sample: The upper inset of (a) shows the spectra of the second harmonic from the monolayer MoS${}_2$ (blue) and from the bare substrate (gray, multiplied by a factor of 100), as well as the fundamental beams (red). The lower inset shows the second harmonic power measured from regions with different atomic layers. The main panel of (a) shows the power dependence of second harmonic generation, with the solid line indicating the expected quadratic dependence. (b) The power of parallel (blue squares) and perpendicular (black circles) components of the second harmonic as a function of $\theta$, the angle between the laboratory and the crystalline coordinates. The blue (black) solid line indicates the expected ${\sin }^{2}3\theta$ (${\cos }^{2}3\theta$) dependence.

Figure 3

Second harmonic generation from a triangular monolayer MoS${}_2$ flake grown by CVD, as shown in the lower inset of (a). The main panel of (a) shows the power dependence of second harmonic generation. The solid line indicates the expected quadratic dependence. (b) shows angular dependence of the parallel (blue squares) and perpendicular (black circles) components of the second harmonic, along with the expected dependence (solid lines). The upper inset of (a) shows a separate measurement of the parallel component with a finer step size near $\theta =0^{\circ }$.

Figure 4

(a) Optical microscopy photograph of a region of a substrate containing flakes grown by CVD. (b) and (c) Maps of $P_x$ and $P_y$ over the region indicated by the box in (a). (d) Map of the total power, $P_x+P_y$. (e) Map of $\theta$ calculated from (b) and (c).