Small-scale self-focusing of laser radiation in amplifier systems

A matrix method is developed for the calculation of the evolution of small-scale self-focusing as applied to laser amplifier systems, i.e., active elements with a nonlinear refractive index, separated by air gaps or lens systems. Calculations made for collimated and diverging laser beams indicate that in amplifier systems it is preferable to use spatial filters with beam expansion. These calculations can be used to optimize their parameters.