Surface second harmonic generation

Abstract: We have measured optical second-harmonic generation (SHG) from atomically thin samples of MoS2 and h-BN with one to five layers. We observe strong SHG from materials with odd layer thickness, for which a noncentrosymmetric structure is expected, while the centrosymmetric materials with even layer thickness do not yield appreciable SHG. SHG for materials with odd layer thickness was measured as a function of crystal orientation. This dependence reveals the rotational symmetry of the lattice and is shown to provide a purely optical method of determining the orientation of crystallographic axes. We report values for the nonlinearity of monolayers and odd-layers of MoS2 and h-BN and compare the variation as a function of layer thickness with a model that accounts for wave propagation effects.

Abstract: 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${}^{\ensuremath{-}7}$ 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.