Analysis of small-scale self-focusing of intense laser in media with gain and loss

The differential equation followed by increase of smallscale instability in both of gain and loss media is obtained from the nonlinear wave equation based on Bespalov-Talanov theory. A comparison of different properties of small-scale self-focusing intense laser in two media is analyzed. Variations of cutoff spatial frequency, the fastest growing frequency, integral exponential gain of perturbation with different parameters are specified. Two expressions of maximal and minimal distance of ripple increase are obtained and effect of gain and loss on filamentsforming distance is deduced.