Nonlinear optical processes, such as harmonic generation, are of great interest for various applications, e.g., microscopy, therapy, and frequency conversion. However, high-order harmonic conversion is typically much less efficient than low-order, due to the weak intrinsic response of the higher-order nonlinear processes. Here we report ultra-strong optical nonlinearities in monolayer MoS2 (1L-MoS2): the third harmonic is 30 times stronger than the second, and the fourth is comparable to the second. The third harmonic generation efficiency for 1L-MoS2 is approximately three times higher than that for graphene, which was reported to have a large χ (3). We explain this by calculating the nonlinear response functions of 1L-MoS2 with a continuum-model Hamiltonian and quantum mechanical diagrammatic perturbation theory, highlighting the role of trigonal warping. A similar effect is expected in all other transition-metal dichalcogenides. Our results pave the way for efficient harmonic generation based on layered materials for applications such as microscopy and imaging.

Single- and few-layer graphene was studied with simultaneous third-harmonic and multiphoton-absorption-excited fluorescence microscopy using a compact 1.55 μm mode-locked fiber laser source. Strong third-harmonic generation (THG) and multiphoton-absorption-excited fluorescence (MAEF) signals were observed with high contrast over the signal from the substrate. High contrast was also achieved between single- and bilayer graphene. The measurement is straightforward and very fast compared to typical Raman mapping, which is the conventional method for characterization of graphene. Multiphoton microscopy is also proved to be an extremely efficient method for detecting certain structural features in few-layer graphene. The accuracy and speed of multiphoton microscopy make it a very promising characterization technique for fundamental research as well as large-scale fabrication of graphene. To our knowledge, this is the first time simultaneous THG and MAEF microscopy has been utilized in the characterization of graphene. This is also the first THG microscopy study on graphene using the excitation wavelength of 1.55 μm, which is significant in telecommunications and signal processing.

Gallium selenide (GaSe) is a layered semiconductor and a well-known nonlinear optical crystal. The discovery of graphene has created a new vast research field focusing on two-dimensional materials. We report on the nonlinear optical properties of few-layer GaSe using multiphoton microscopy. Both second- and third-harmonic generation from few-layer GaSe flakes were observed. Unexpectedly, even the peak at the wavelength of 390 nm, corresponding to the fourth-harmonic generation or the sum frequency generation from third-harmonic generation and pump light, was detected during the spectral measurements in thin GaSe flakes.