Numerical analysis of Z-scan experiments by use of a mode expansion

Abstract

The Z-scan analysis technique has been developed to permit characterization of nonlinear refractive indices and nonlinear absorption of non-Gaussian laser beams by a numerical approach. The new approach is based on a mode expansion of the electric field of the laser beam into Gaussian–Laguerre or Gaussian–Hermite modes. The individual modes are propagated within the nonlinear sample under the influence of the intensity-dependent phase shifts. The resulting electric field at the exit plane is expanded as a new sum of Gaussian–Laguerre or Gaussian–Hermite modes. From the final mode expansion the field distribution at the detector plane is calculated. The method also makes it possible to simulate a variety of complex optical limiting devices, such as stacks of samples with different material parameters and thick samples with a variation of material parameters along the z axis. A series of test simulations is presented and compared with experimental Z-scan data of solutions of substituted phthalocyanine molecules.