Third-order Nonlinearity of MoS$_{\mathrm{2}}$ and WS$_{\mathrm{2}}$ atomic Layers

The third-order optical nonlinearity of 2D transition metal dichalcogenide atomic layers is of great interest for the prospective applications in optical modulators and photonic devices. The third-order nonlinearity includes the nonlinear absorption and nonlinear refraction which can be characterized through either resonant or non-resonant excitation. The atomic layers for this presentation include tungsten disulfide (WS$_{\mathrm{2}})$ and molybdenum disulfide (MoS$_{\mathrm{2}})$ nanoflakes of 1-4 layers in deionized water. The excitation wavelength was 532 nm which was located above A and B exciton absorptions of MoS$_{\mathrm{2}}$ and between A and B exciton spectra of WS$_{\mathrm{2}}$. The excitation at 2.33 eV is resonant for A and B excitons of MoS$_{\mathrm{2}}$ and A exciton of WS$_{\mathrm{2}}$, and the non-resonant for B exciton of WS$_{\mathrm{2}}$. The nonlinear absorption coefficients for WS$_{\mathrm{2}}$ and MoS$_{\mathrm{2}}$ nanoflakes were analyzed to be \textasciitilde 6.7 x 10$^{\mathrm{4}}$ cm/GW and \textasciitilde -1.0x 10$^{\mathrm{5}}$ cm/GW with open Z-scan, respectively. The nonlinear refraction of WS$_{\mathrm{2}}$ and MoS$_{\mathrm{2}}$ were estimated to be \textasciitilde - 6.7 x 10$^{\mathrm{-10}}$ cm$^{\mathrm{2}}$/W and \textasciitilde -1.3 x 10$^{\mathrm{-10}}$ cm$^{\mathrm{2}}$/W, respectively, with peak-valley nonlinear transmittance trace.