Statistical study of the spectrum of a partially coherent subpicosecond pulse undergoing self-modulation in a gas

We investigate the changes in the frequency spectrum of a partially coherent pulse brought on by a Kerr nonlinearity and by multiphoton ionization in a gas. We find that fluctuations in the parameters of the laser light cause the average spectrum of a pulse in a medium with a Kerr nonlinearity to be symmetric, with a single maximum at the center frequency. In the case of free-carrier generation, a long wing forms in the average spectrum that extends into the anti-Stokes region. We show that the ionization-induced nonlinearity gives rise to two time scales in the correlation function of the light.