| Abstract: | The Bespalov Talanov theory on small scale self focusing (SSSF) extended to include loss of medium. An exact analytical expression for gain spectrum of the small scale perturbations is obtained and it reveals two new properties of SSSF. The first one is that the cutoff spatial frequency for perturbation growth in a lossy medium becomes smaller than in a lossless one, and the longer the propagation distance, the smaller the cutoff spatial frequency. The second one is that the fastest growing frequency decreases with the propagation distance increases. Thus the nonlinear phase accumulation or the value of B integral no longer characterizes the gain of a single most unstable spatial frequency. |
