Z-scan and eclipsing Z-scan analytical expressions for third-order optical nonlinearities

Analytical expressions for Gaussian-beam Z-scan and eclipsing Z-scan signals are obtained in a unified format in the case of third-order optical nonlinearities. Considering optically thin media in the presence of both nonlinear refraction and nonlinear absorption, the Gaussian decomposition method is applied to express the normalized transmittance through an aperture or a disk in terms of a sum of heterodyne and homodyne contributions. The expressions presented are also valid for arbitrary circularly symmetric real ABCD post-sample optical systems.