Dynamic effects of Kerr nonlinearity and spatial diffraction on self-phase modulation of optical pulses

An investigation is made of the combined effects of nonlinearity and diffraction on self-phase modulation of optical pulses propagating in dispersionless homogeneous bulk material. It is found that the presence of transverse spatial dynamics leaves the phase characteristics qualitatively the same as for conventional self-phase modulation. In particular, this implies that, contrary to what has recently been claimed, the red always leads the blue in the supercontinuum.