| Using a generalized Gaussian beam decomposition method we determine the propagation of a Laguerre-Gaussian (LG) beam after it has passed through a thin nonlinear optical Kerr medium. The orbital angular momentum per photon of the beam is found to be conserved while the component beams change. We apply our theory to using LG10 beams to measure the nonlinear refractive index coefficient of the medium with high sensitivity, such as the Z-scan and I-scan techniques, and to a new optical limiting geometry.;We test the validity of the theory and demonstrate the applications experimentally using a dye-doped polymer, disperse red 1 (DR1) doped poly(methyl methacrylate) (PMMA) (DR1/PMMA). In order to do that, we investigate the mechanisms of the nonlinear refractive index change in DR1/PMMA (trans-cis-trans photoisomerization and photoreorientation) by a three-state model and a holographic volume index gratings recording experiment, and determine the conditions under which DR1/PMMA acts as an optical Kerr medium. |
