Cubic Nonlinearity of WS$_{\mathrm{2}}$ Nanoflakes

The cubic nonlinearity of tungsten disulfide atomic layers is of great interest for optical power limiting and saturable Q-switching. The nonlinear optical properties of tungsten disulfide nanoflakes in aqueous solution was characterized with Z-scan technique with resonant at 532 nm with 6 ns pulse width and 10 Hz repetition rate. The absorption spectrum of WS$_{\mathrm{2}}$ nanoflake mixtures of one to four atomic layers in aqueous solution shows the characteristic A, B, and C peaks. The A and B absorption bands are due to the large band spitting of conduction band with strong coupling between electron spin and d-electron orbital coupling, and the C band is due to the band nesting by the singularity of joint density of state. The nonlinear absorption and nonlinear refraction coefficients of WS$_{\mathrm{2}}$ nanoflakes were estimated to be \textasciitilde 6.2 x 10$^{\mathrm{4}}$ cm/GW with open Z-scan, and \textasciitilde -0.9 x 10$^{\mathrm{-10}}$ cm$^{\mathrm{2}}$/W with closed Z-scan. Acknowledgment: This work is supported by ARO W911NF-15-1-0535, NSF HRD-1137747, and NASA NNX15AQ03A.