Pulse splitting during self-focusing in normally dispersive media

The self-focusing of femtosecond optical pulses in a normally dispersive medium is studied numerically. This situation represents a general problem that may be modeled by a 3 + 1-dimensional nonlinear Schrödinger equation, where two dimensions are self-focusing and the third is self-defocusing. The numerical simulations show that the dispersion causes the splitting of a pulse before it self-focuses into two temporally separated pulses, which then continue to self-focus and compress rapidly. The calculated behavior results in periodic modulation of the generated continuum spectrum, as was recently observed in continuum generation by focused femtosecond pulses in gases.