Nonlinear refractive index of a glass plate used for beam transformation and its application to Z scans

We present a simple theory based on the method of moments for fitting experimental measurements of optical nonlinearities obtained by the Z-scan technique. Our method provides a simple and intuitive image for Gaussian beam propagation through a nonlinear optical plate: a linear transformation that consists of a displacement and a contraction of the beam waist. We study cubic nonlinearities of samples of arbitrary thickness. We also consider, for thin samples, higher-order nonlinearities such as cubic-quintic nonlinearities and the effect of nonlinear absorption. (C) 2003 Optical Society of America.