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.
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