Self-focusing, self-phase modulation, and diffraction in bulk homogeneous material

The simultaneous effects of self-focusing, self-phase modulation, and diffraction on the propagation of an ultrafast pulse in a homogeneous Kerr medium are described. The competing effects of self-focusing and diffraction are shown to modify the shape and magnitude of the pulse amplitude and phase. These modifications are shown to affect the spectral distribution of the supercontinuum from that predicted by the conventional self-phase-modulation theory.