Self-phase Modulation of MoS$_{\mathrm{2}}$ Nanoflakes

The third-order nonlinear optical property of molybdenum disulfide (MoS$_{\mathrm{2}})$ atomic layers was characterized by the spatial self-phase modulation (SSPM) which arises from an intensity-dependent refractive index change. The diffraction ring of SSPM was distorted along the vertical direction after the MoS$_{\mathrm{2}}$ nanoflakes was exited by a laser pulse at 532 nm, \textasciitilde 6 ns temporal pulse width, and 10 Hz repetition rate. The nonlinear refractive index and the third-order susceptibility was estimated a series of concentric circles of SSPM diffraction ring patterns. The nonlinear refractive index and the third-order susceptibility of MoS$_{\mathrm{2}}$ nanoflakes were estimated to be \textit{\textasciitilde }2.09 x 10$^{\mathrm{-10}}$\textit{ cm}$^{2}/W$ and \textasciitilde 1.68x10$^{\mathrm{-16}} \quad m^{2}/V^{2}$ respectively at the peak intensity \textasciitilde 0.3\textit{GW/cm}$^{2}$. Acknowledgment:~This work is supported by ARO W911NF-15-1-0535, NSF HRD-1137747, and NASA NNX15AQ03A