Small-scale self-focusing of divergent beam in nonlinear media with loss

Bespalov-Talanov theory on small-scale self-focusing is extended to include medium loss for a divergent beam.Gain spectrum of small-scale perturbation is presented in integral form,and based on the derived equations we find that the cutoff spatial frequency for perturbation keeps a constant value.The larger the medium loss is,the smaller the fastest growing frequency and the maximum gain of perturbation with defined propagation distance are.For a given medium loss the maximum gain of perturbation becomes la...