Analytical solution of on-axis beam propagation for Z-scan technique

An analytical solution of on-axis beam propagation is presented for determining the nonlinear refraction and nonlinear absorption of a thin nonlinear medium accurately, efficiently, and simultaneously by a single Z-scan method. This result is based on the general Huygens-Fresnel principle. When applying our theoretical solution to the case without nonlinear absorption, it converges to the current formula based on the Huygens-Fresnel principle. For the first-order approximation, it agrees with the expression obtained by the Gaussian decomposition method. Because of the nonlinear absorption, the peaks of the Z-scan shape are suppressed, while the variation in the valleys depends on the nonlinear phase parameters. (C) 2009 Optical Society of America