Observation of four-photon absorption and determination of corresponding   nonlinearities in CdS quantum dots
  Bound- and excited-state electronic nonlinearities in CdS quantum dots have been investigated by Degenerate Four-Wave Mixing (DFWM) and Z-scan techniques in the femtosecond time regime. This QD sample shows Kerr-type nonlinearity for incident beam intensity below 0.18 TW/cm$^2$. However, further increment in intensity results in four-photon absorption (4PA) indicated by open- and closed-aperture Z-scan experiments. Comparing open-aperture Z-scan experimental results with theoretical models, the 4PA coefficient $\alpha_4$ has been deduced. Furthermore, third-order nonlinear index $\gamma$ and refractive-index change coefficient $\sigma_r$ corresponding to excited-state electrons due to 4PA have been calculated from the closed-aperture Z-scan results. UV-visible absorption and photoluminescence experimental results are analyzed towards estimating band gap energy and defect state energy. Time Correlated Single Photon Counting (TCSPC) was employed to determine the decay time corresponding to band-edge and defect states. The linear and nonlinear optical techniques have allowed the direct observation of lower and higher-order electronic states in CdS quantum dots. 
P. Ghosh, E. Ramya, P. K. Mohapatra, D. Kushavah, D. N. Rao, P. Vasa,   K. C. Rustagi, and B. P. Singh
cond-mat.mtrl-sci cond-mat.mes-hall