On the measurement of high-order refractive nonlinearities through the Z-scan technique

High-order refractive nonlinearities play an increasingly important role for the characterization of new materials in relation to applications as optical switching, optical limiting, optical data processing, etc. In this work a novel more accurate method for determining the coefficients related to the higher-order refractive nonlinearities through the Z-scan technique is presented. The general case of an elliptic Gaussian incident beam is considered. The theoretical analysis is based on the Gaussian decomposition method, appropriately extended to higher-order nonlinearities, which are treated as a perturbation. An analytic expression for the electric field pattern of the beam at any distance D from the exit plane of the sample is obtained. This allows the analysis and simulation of Z-scan experiments based on either the measurement of the transmittance through an aperture or the direct measurement of the beam dimensions in the far-field, which has considerable advantages, especially in the case of elliptic beams. For both cases, an experimental procedure for measuring the high-order refractive nonlinearities is suggested