The Z-scan method proposed by Sheik-Bahae et al [1] has been widely used to determine the nonlinear characteristics, especially nonlinear refraction and nonlinear absorption, of a medium. Recently Boudebs pointed out that in a case with large nonlinear absorption and small nonlinear refraction the relative error of nonlinear refraction obtained by the above method can reach as high as 50% [2]. Yin et al. presented a method to obtain nonlinear refraction and nonlinear absorption simultaneously by a pinhole Z-scan curve [3], but it is suitable only for a case with a small nonlinearity. Liu et al. also analyzed Z-scan characteristics of a nonlinear medium with both nonlinear refraction and nonlinear absorption, but the results obtained are accurate only for a case with a small nonlinearity, too [4]. A theoretical model based on the Gaussian decomposition method and symmetric analysis is demonstrated to determine the nonlinear refraction and nonlinear absorption of a nonlinear medium accurately and simultaneously by a single Z-scan method. More accurate values of nonlinear refraction and nonlinear absorption can be obtained simultaneously by the model, no matter how much they are, if accurate experimental data are acquired. The treatment procedure of Z-scan experimental data is demonstrated. The effect of aperture size is also considered in our analysis. It will provide a solid theoretical foundation for determination of nonlinearities by the Z-scan method. Fig. 1 (a) Group of curves of odd function To, (b) A group of curves of even function Te

The radiation forces and trajectories of Rayleigh dielectric particles induced by one-dimensional Airy beam were numerically analyzed. Results show that the Airy beam drags particles into the optical intensity peaks, and guides particles vertically along parabolic trajectories. Viscosity of surrounding medium significantly affects the trajectories. Random Brownian force affects the trajectories. Meanwhile, trapping potential depths and minimum trapping particle radii in different potential wells were also discussed. The trapping stability could be improved by increasing either the input peak intensity or the particle radius.

The possibility of enhancing the energy gain in vacuum electron acceleration by Airy beams is examined. The characteristics of transverse acceleration and non-diffraction of Airy beam can lead to the formation of a long "asymmetric field channel" along the propagation axis, where the intense asymmetric field can accelerate the injected electron to higher energy. Meanwhile, the injection energy of electron plays an important role in determining the final energy gain.

Using numerical simulation, we have studied in detail vacuum electron acceleration driven by two crossed Airy beams with identical characteristics except for opposite accelerating directions. An electron injected along the longitudinal central axis is only affected by the combined longitudinal electric field. In addition, a suitable crossed Airy beams scheme is more beneficial to the energy gain of an electron than the single Airy beam acceleration scheme [Opt. Lett. 35, 3258 (2010)]. Meanwhile, the cross angle, the injection energy of the electron, and the initial phase of the Airy beams play significant roles in the energy gain of the electron.

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