Analytic solutions to Z-scan characteristics of thick media with nonlinear refraction and nonlinear absorption

Using a Gaussian decomposition method and a distributed lens model, we have analyzed the Z-scan measurements of thick optical nonlinear media with nonlinear refraction and nonlinear absorption. With the introduction of correction functions that include saturation of nonlinear refraction and coupling between nonlinear refraction and nonlinear absorption, analytic solutions to closed-aperture and open-aperture Z-scan characteristics were obtained. Detailed comparisons of the analytic solutions with numerical solutions were made, and the two kinds of solution coincided well, no matter how much nonlinear refraction or nonlinear absorption there was.