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11Complex Systems of Charged Particles and their Interactions with Electromagnetic Radiation 2018
RESONANT METHOD OF XUV ATTOSECOND PULSE MEASUREMENT
V. V. Strelkov, A. I. Magunov
A.M. Prokhorov General Physics Institute of RAS, Moscow, Russia, e-mail: strelkov.v@gmail.com
We suggest and study theoretically the method of an attosecond XUV pulse train characterization. Our approach is based on the attosecond pulse autocorrelation measurement using two-photon interaction of the XUV with a gas. Using of the resonant two-photon process allows obtaining reasonable signal in spite of low intensity of the attosecond pulses.
The idea of the method is illustrated by the inset in the Fig. 1. We consider an interaction of an atom with a number of odd high harmonics having frequencies q<0 where a0 is the fundamental frequency. The attosecond pulse train is obtained using a group of these harmonics. The energy difference of the excited and the ground atomic states is equal to the even number of laser photon energy: E2-E1=Aqa0. This resonant condition can be satisfied by choosing the gas medium and tuning the fundamental frequency: having in mind that Aq is rather high number, small tuning of <30 allows satisfying the condition. Note that much wider tuning of the fundamental frequency is utilized in the high harmonic generation experiments using mid-IR OPA laser systems. We suppose that the parity of the states is so that the two-photon transition from the ground to the excited state is aloud. Transitions to the other bound states are assumed to be non-resonant and that is why they can be neglected. The atom is initially in the ground state and under exposure to XUV some population appears in the excited state due to two-photon Raman-type transitions via continuum. The complex amplitude of the excited state is a sum of contributions due to different pairs of harmonics. The phases of these contributions are determined in particular by the phase difference between the harmonics. So the population of the excited state can be used to investigate the harmonic phase differences and thus the properties of the attosecond pulse trains obtained using these harmonics.
We consider two identical attosecond pulse trains with a controllable delay between them and show that the upper state population after the XUV irradiation can be linked to the attosecond pulse autocorrelation function (see Fig. 1). Thus the attosecond pulse autocorrelation can be found experimentally measuring this population. The analytical results are compared with the numerical ones based on the solution of 3D time-dependent Schrodinger equation (TDSE). Our calculations show that the moderate harmonic intensities (namely, orders of magnitude lower than the maximal ones obtained experimentally) are required for the measurable upper state population.
1.0 1.5 2.0 2.5 delay (carrier cycles)
Fig. 1. The upper atomic state population after the XUV irradiation as a function of the delay between the two replicas of the attosecond pulse train; the analytical calculation (lines) and the numerical one based on the TDSE solution (squares). The attosecond pulse autocorrelation can be reconstructed from this dependence. The inset shows the Raman-type resonance transitions in the atomic system irradiated by a multiple-harmonic field.
