  We demonstrate optical limiting using the self-lensing effect of a
higher-order Laguerre-Gaussian beam in a thin dye-doped polymer sample, which
we find is consistent with our model using Gaussian decomposition. The peak
phase shift in the sample required for limiting is smaller than for a
fundamental Gaussian beam with the added flexibility that the nonlinear medium
can be placed either in front of or behind the beam focus.
