| Z-scan technique is a very important method for characterizing the optical nonlinearities for materials, which has some advantages such as the simple experiment setup and the high sensitivity. It can not only measure the magnitudes of the third-order nonlinear refractivity (NLR) and the nonlinear absorption (NLA) coefficient, but also determine their signs. Generally, both the closed-aperture (S→0) Z-scan and the open-aperture (S=1) Z-scan processing are required to separate NLR effect and NLA effect. In this paper, a numerical method is introduced, which can separate NLA effect from the normalized transmittance curve without open-aperture experiment. This method is discussed detailedly in allusion to the self-focusing saturated absorption material. Then two important parameters, the distance between the aperture and the lens focus, and the aperture radius, were analyzed to improve the sensitivity.Surface-modification can extremely enhance the optical nonlinearities of semiconductor nanoparticles. Almost all explanations about this phenomenon may be due to the quantum size effect, the dielectric confinement effect, the surface pole effect or the bleaching of exciton absorption. The investigations with the local field enhancement theory nearly are all qualitative, and existing quantitative numeration with the theory is applicable for the analysis of semiconductor nanoparticles. This article tries to find the relation between the dielectric constant of modifying medium and the third-order nonlinearities enhancement of the semiconductor nanoparticles, and defined the relative local field enhancement factor, which might quantitatively explain that the enhancement phenomenon. Then the two samples, coated Fe2O3 nanoparticles and bare ones were measured with the single beam closed-aperture Z-scan. The enhancement ratio of their NLR coefficients obtained by the experiment is in agreement with the relative local field enhancement theory.
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