Z-scan with arbitrary aperture transmittance: the strongly nonlinear regime

We consider theoretical models of nonlinear optical propagation suitable for describing optical Z-scan measurements within the strongly nonlinear regime. In particular, we demonstrate the equivalence of two alternative descriptions of beam propagation from a thin nonlinear refractor, in which the transmission measurements are modelled using a receiving aperture of arbitrary size. If nonlinear absorption is the dominant process, then we predict that a localized peak within the normalized transmittance will appear at the waist position and should be observable if the nonlinear interaction is sufficiently strong.