  We show that the lack of inversion symmetry in monolayer MoS2 allows strong
optical second harmonic generation. Second harmonic of an 810-nm pulse is
generated in a mechanically exfoliated monolayer, with a nonlinear
susceptibility on the order of 1E-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 fast and non-invasive detection of crystalline
orientation, thickness uniformity, layer stacking, and single-crystal domain
size of atomically thin films of MoS2 and similar materials.
