Z-scan nonlinear refraction model with elliptical Gaussian beam

This paper presents a theoretical model for an arbitrary [Formula: see text]-order nonlinear refraction using an elliptical Gaussian beam propagating in a thin nonlinear medium. In contrast to circular Gaussian beams, elliptical Gaussian beams better represent real laser beams and distortions. The model derives an analytical expression for the optical normalized transmittance in [Formula: see text]-scan experiments. This is achieved by using the Gaussian decomposition method and weak phase approximation. The transmittance depends on the on-axis nonlinear phase shift, elliptical beam sizes along transverse axes, and the nonlinear refractive index. Fitting the expression to [Formula: see text]-scan data extracts these parameters.