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Monolayer transition metal dichalcogenides (TMDs) exhibit high nonlinearoptical (NLO) susceptibilities. Experiments on MoS$_2$ have indeed revealedvery large second-order ($\chi^{(2)}$) and third-order ($\chi^{(3)}$) opticalsusceptibilities. However, third harmonic generation results of other layeredTMDs has not been reported. Furthermore, the reported $\chi^{(2)}$ and$\chi^{(3)}$ of MoS$_2$ vary by several orders of magnitude, and a reliablequantitative comparison of optical nonlinearities across different TMDs hasremained elusive. Here, we investigate second- and third-harmonic generation,and three-photon photoluminescence in TMDs. Specifically, we present anexperimental study of $\chi^{(2)}$, and $\chi^{(3)}$ of four common TMDmaterials (\ce{MoS2}, \ce{MoSe2}, \ce{WS2} and \ce{WSe2}) by placing differentTMD flakes in close proximity to each other on a common substrate, allowingtheir NLO properties to be accurately obtained from a single measurement.$\chi^{(2)}$ and $\chi^{(3)}$ of the four monolayer TMDs have been compared,indicating that they exhibit distinct NLO responses. We further presenttheoretical simulations of these susceptibilities in qualitative agreement withthe measurements. Our comparative studies of the NLO responses of differenttwo-dimensional layered materials allow us to select the best candidates foratomic-scale nonlinear photonic applications, such as frequency conversion andall-optical signal processing.

Optical harmonic generation in monolayer group-VI transition metal dichalcogenides