Dependence of transition probabilities for non-linear photo-ionization of He atoms on the structure of the exciting radiation pulses

We discuss the expected dependence of the probability transitions for 2-photon and 3-photon absorption in Helium gas on the spatial and temporal structure of the exciting radiation pulses. Regarding spatial structure, we assumed a Gaussian radial intensity distribution; we find, as expected, that the 2-photon and 3-photon processes become negligible at distances D away from the focus, where D is of the order of the beam waist FWHM. Regarding temporal structure, we compared transition probabilities for square, Gaussian and cosine squared temporal profiles; we find that for the same FWHM, Gaussian and cosine squared pulses give essentially the same transition probabilities, but the square pulses are about twice as efficient. We finally studied the effect of sharp versus smooth rise and fall edges in the light pulse; we find negligible correlation with the shape of the pulse edges, and strong correlation with the pulse FWHM, i.e., with pulse total energy, as might be expected.