  Semiconducting Transition Metal Dichalcogenides (TMDs) have significant
nonlinear optical effects. In this work we have used second-harmonic generation
(SHG) and the four-wave mixing (FWM) spectroscopy in resonance with the
excitons in MoS2, MoSe2, and WS2 monolayers to characterize the nonlinear
optical properties of these materials. We show that trions and excitons are
responsible for enhancing the nonlinear optical response, and determine the
exciton and trion energies by comparing with the photoluminescence spectra.
Moreover, we extract the second and third order optical sheet susceptibility
near exciton energies and compare with values found in the literature. We also
demonstrate the ability to generate different nonlinear effects in a wide
spectral range in the visible region for monolayer MoS2, opening the
possibility of using two-dimensional materials for nonlinear optoelectronic and
photonic applications.
