ABCD Matrix formalism to Determine Nonlinear Refraction Coefficient by Z-Scan Technique

In this study, we revisit the popular method of measuring the nonlinear susceptibility of a material through Z-scan technique, introduced in 1990 by Sheik-Bahae and co-workers through a simple ray optics defined by the ABCD matrix formulation. The work therefore looks at the Z-scan measurement curves analysed through ray propagation in the medium and analysed through an aperture. The transmittance of a sample in the Z-scan technique is measured through a finite aperture in the far field, as the sample is scanned along the propagation direction (Z) of a focussed Gaussian beam. The sign and magnitude of nonlinear refractive index are easily deduced from the transmittance curve (Z-scan) using the theoretical model based on ABCD matrix formalism.