Nonlinear self-defocusing in doped silica sono-gels

Experiments with nonlinear self-refraction of Gaussian laser beams in silica sono-gels doped with copper tetrasulfonated phthalocyanine are reported. The propagation of laser beams inside nonlinear sol-gel samples with different Cu-phthalocyanine concentrations has been monitored by measuring the spatial beam profile in the near field and in the far field behind the sample. The experimental results are analyzed by a new simple theoretical approach, in which we assume that the incident Gaussian beam induces a phase shift that varies as a Gaussian function of the beam radius. The beam propagation behind the sample is determined by the Huygens–Fresnel integral formalism. By solving the Huygens–Fresnel integral, analytical expressions for the spatial beam profile in both the near field and the far field after the nonlinear sample are obtained. Experiments are carried out with a diode pumped frequency doubled Nd–YAG laser at 532 nm. We obtain very large third-order nonlinearities in these doped sol-gel samples at temperatures just above room temperature. When we compare the predictions of the theory with the experimental data, we find experimental values of the nonlinear third-order susceptibility up to −2.3×10−4 esu.