We apply a finite-difference algorithm that combines the local one-dimensional approximation and the Crank-Nicolson algorithms to solve the three-dimensional nonlinear Schrödinger 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 of the closed-aperture and open-aperture Z scan are demonstrated.
© 2004 Optical Society of America
(000.4430) General : Numerical approximation and analysis
(190.3270) Nonlinear optics : Kerr effect
(190.4180) Nonlinear optics : Multiphoton processes
(190.5940) Nonlinear optics : Self-action effects
Wei-Ping Zang, Jian-Guo Tian, Zhi-Bo Liu, Wen-Yuan Zhou, Feng Song, and Chun-Ping Zhang, "Local One-Dimensional Approximation for Fast Simulation of Z-Scan Measurements with an Arbitrary Beam," Appl. Opt. 43, 4408-4414 (2004)