Analysis of The Thick Medium Z-Scan

An analytic solution of the propagation equation for a symmetrical optical beam has been obtained, in the situation where the beam is focused within an optically nonlinear medium having a thickness greater than the depth of focus. Previous related work by the author has concentrated upon finding solutions, in continued-fraction format, within the strongly self-focusing/defocusing limit [1]. In the present work, an expression is derived for the transmitted electric field envelope in the weakly nonlinear case. The result is described in terms of a linear superposition of Gaussian-Laguerre modes, the coefficients of which depend only upon the linear component of the accumulated optical phase on the optic axis. The medium that has been explored possesses a Kerr-type susceptibility with refractive and absorptive components.