Free-space propagation of ultrashort pulses: Space-time couplings in Gaussian pulse beams

The importance of space-time couplings and the validity of the paraxial approximation are discussed for the case of ultrashort freely-propagating Gaussian pulses whose spectral components all have the same frequency-independent Rayleigh length. Simple closed-form expressions describing the electric field of such pulses are derived for model spectral distributions. Space-time couplings are found to be significant only for subcycle pulses or far from the focus.