Predicting the filamentation of high-power beams and pulses without numerical integration: A nonlinear geometrical optics method

We present an analytic method for predicting the initial self-focusing dynamics of high-power beams and pulses. Using this method we study the filamentation pattern of a variety of input profiles, without solving partial differential equations. In particular, this method shows that in the anomalous regime, high-power pulses with temporal super-Gaussian profiles will split in time into two shorter pulses, and spherically symmetric pulses with super-Gaussian spatiotemporal profiles will evolve into a spatiotemporal shell.