Self-focusing of chirped optical pulses in nonlinear dispersive media

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Abstract
The spatiotemporal self-focusing of chirped optical pulses propagating in a nonlinear dispersive medium has been studied analytically and numerically. The analytic theory shows that the critical power for self-focusing occurring in a dispersive media changes quadratically with the chirp parameter in both two and three dimensions. It is found that the critical wave action depends on the sign of the total chirp parameter. Analytic results show that the effect of chirp is similar to that of beam ellipticity except that ellipticity always increases the critical wave action. Numerical simulations are used to study the effect of chirp and group-velocity dispersion on self-focusing. It is shown numerically and analytically that the self-focusing process can be controlled by changing the chirp parameter.