Short-pulse splitting and pulse collisions in dispersive nonlinear media

We have developed a method to precisely propagate short optical pulses through dispersive media with a self-focusing chi((3)) Kerr-type nonlinear polarization. Above the critical cw self-focusing power, onset of pulse splitting into pulselets separated in time occurs, and for a certain regime of parameters a cyclic series of pulse splitting (into pulselets separated in time) and pulse recombination occurs for diffraction length smaller than dispersion length. At higher power, another threshold for non-cyclic temporal and spatial pulse splitting is manifest. Self-steepening and self-frequency shifting affect pulse propagation too. We use our formulation to calculate the dynamics of collisions of two pulses in nonlinear optical media, and show how the collision can give rise to pulse splitting. We also investigate the effects of saturation of the nonlinearity on the phenomenon of pulse splitting and pulse collision dynamics.