The influence of the power variation on the evolution of an arbitrary beam in strongly nonlocal nonlinear media is investigated on the basis of the mode-decomposition method. The variation of the power changes the longitudinal positions of the beam patterns and induces the longitudinal scaling. Although there is a one-to-one correspondence between the patterns before and after the power variation, the pattern sizes in the two cases differ from each other; therefore the transverse scaling occurs. The effect of the three-dimensional nonuniform scaling effect can be represented with a simple formula, with which the analytical solution for the beam after the power variation can be readily obtained from its counterpart before the power variation.

• Received 9 January 2013

DOI:https://doi.org/10.1103/PhysRevA.87.023815