Modified $Z$-scan method for determining third-order nonlinearity of quantum dots in the resonant excitation mode

A modified $Z$-scan method for determining the nonlinear refractive index of colloidal quantum dots in the near-IR spectral range in the resonant excitation mode is proposed. It is demonstrated that the thermal effects related to heating of the solution due to strong light absorption can be mitigated by reducing the probing pulse repetition rate. The nonlinear refractive index of colloidal lead sulfide quantum dots is found to be on the order of 10$^{-16}$ cm$^{2}$/W.