On the feasibility of performing non-linear autocorrelation with attosecond pulse trains

We present experimental results in which a second-order effect, namely two-photon ionization of atomic He induced by a superposition of harmonics, is observed. The harmonics are generated in a Xe gas-jet using a 790-nm 10-Hz femtosecond Ti:sapphire laser and are subsequently focused into a He gas-jet with a Kirkpatrick–Baez arrangement. The superposition is formed by using a thin In filter and it comprises the 7th to 13th harmonics. Solving the time-dependent Schrödinger equation for He in a polychromatic laser field, the He ⁺ ion yield is calculated as a function of the total XUV intensity. Using the calculated yield and taking into account the focusing and transmission properties of the arrangement, the number of He ⁺ ions produced per laser pulse is estimated and is found to be in reasonable agreement with its measured value. The total number of ions produced non-resonantly follows a nearly quadratic dependence on the harmonic intensity, thus establishing the feasibility of a second-order auto-correlation measurement of the superposition of harmonics, i.e., of a direct temporal characterization of attosecond pulse trains.