Interferometric autocorrelation of an attosecond pulse train calculated using feasible formulae

The autocorrelation trace of an attosecond pulse train (APT) directly revealed the pulse envelope in our recent experiment on measuring the two-photon Coulomb explosion of a nitrogen molecule as a correlation signal. Although the spatial overlap of the two replicas of the APT in the correlation measurement was only achieved near the focal region owing to the spatial split of the measured APT field, which is a situation quite different from that of the correlation measurement using a Michelson interferometer, the interference fringes clearly appeared on the correlation envelope and provedthe odd symmetry of the electric field to the time translation with a half-period of the driving laser field. In this paper, we show a simple and practical analysis for the propagation and the nonlinear interaction of an APT to simulate the experimental result of the interferometric autocorrelation of the spatially split APT. The spatial convolution of the focused electric field is essential for obtaining the fringes. We also discuss how the autocorrelation should be described in the context of the second-order perturbation theory within a dipole approximation.