The Z-scan method is one of the common methods for obtaining nonlinear optical coefficients of materials. In  Nonlinear media due to the change in the behavior of light in the matter the response of dielectric polarization to the electric field is nonlinear and some properties like coefficients of refraction and absorption will be changed. In this paper the Z-scan method for the nonlinear Kerr media is applied based on the ABCD matrix method. By using the Collins formula the field before the aperture is calculated numerically and after integration and normalization the normalized transmittance of close aperture for positive and negative nonlinear refractive index are obtained. Results show that the ABCD matrix method is a suitable method for determine the nonlinear behavior around the focal point for positive and negative nonlinear refractive index.

Keywords: Z-scan, Nonlinear refraction, Kerr media, ABCD matrix, Collins formula.

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