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We apply a finite-difference algorithm that combines the local one-dimensional approximation and the Crank-Nicolson algorithms to solve the three-dimensional nonlinear Schrodinger equation. This scheme is unconditionally stable and accurate to second order. Therefore it offers a simple and accurate means to study a two-dimensional Z scan for arbitrary beam shape and medium length. As an example, we analyze the characteristics of a Z scan by utilizing an elliptic Gaussian beam for a thick nonlinear medium. The effects of ellipticity and waist separation of the elliptic beam on the normalized transmittance the closed-aperture and open-aperture Z scan are demonstrated. OCIS codes: 190.3270, 190.4180, 190.5940, 000.4430.

Optical nonlinearities of five new organophosphorus fullerene derivatives with similar structures were determined by the Z-scan method by use of a nanosecond-pulse laser at 532 nm. The experimental results demonstrate that the five derivatives have much larger excited-state absorption and nonlinear refraction than [C.sub.60]. The excited-state absorption cross sections are nearly two to three times that of [C.sub.60]. Using a five-level model to fit the experimental data, we obtained some parameters such as excited-state absorption and refraction cross sections. A simple analysis of correlations between molecular structure and nonlinear properties is given. Optical nonlinearities of the five new organophosphorus fullerene derivatives were compared with those of some other kinds of fullerene derivatives, and the results show that the nonlinearities of the new derivatives are the larger. OCIS codes: 190.0190, 190.4710, 190.5330, 160.4330.

By variational approach, we analyze the characteristics of beam propagation through a cubic optical nonlinear medium using a laser beam that has a transverse elliptic Gaussian profile. The analytic solution to the normalized transmittance at the center of the far field as a function of medium position and the beam characteristics is obtained and compared with the numerical simulation, which is realized by a combination of algorithms. We also analyze the peak-valley transmittance difference as a function of medium length, ellipticity, and astigmatism. The relationship between peak-valley normalized transmittance difference of the z-scan trace and aperture size or the slit width are obtained. Meanwhile, the comparison of z-scan characteristics with an elliptic Gaussian beam with those using a circular symmetric Gaussian beam is made.