Analysis of spatial scanning with thick optically nonlinear media

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Abstract
The refractive and absorptive response of a nonlinear material can be assessed by the use of a spatial scanning technique to characterize the material. This technique generally involves monitoring the normalized trans-mittance of an optical beam focused into a sample of the material. In this paper an analytic solution of the beam propagation equation correct to the first nonlinear order has been obtained for the situation in which the sample has a thickness greater than the depth of focus. In this context simple exact formulas have been obtained for the cumulative phase and the normalized transmittance of a focused beam at any position along the optic axis, and the expressions have been used to investigate the various possible scanning techniques.