We present numerical simulations of the propagation of intense spatio-temporal fields propagating in air. Characteristic parameters of the propagation like peak intensities, plasma densities and diameters of the plasma channels are obtained. The evolution of the spectral content of the pulses is investigated and, in agreement with recent experiments, white-light supercontinuum generation is observed. We show in which areas of the pulse the supercontinuum is generated and conclude that self-phase modulation is responsible for the spectral broadening. Furthermore we investigate azimuthal instabilities of intense rotationally symmetric pulsed beams propagating in air. Although the spatial-temporal evolution of the field is strongly influenced by the onset of plasma generation, the instabilities are basically caused by the Kerr effect. We conclude that calculations assuming rotational symmetry become unrealistic due to the fast growth of azimuthal instabilities in the focal region. References: 16
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