Extraction of the species-dependent dipole amplitude and phase from high-order harmonic spectra in rare-gas atoms

Abstract

Based on high-order harmonic generation (HHG) spectra obtained from solving the timedependent Schrödinger equation for atoms, we established quantitatively that the HHG yield can be expressed as the product of a returning electron wave packet and the photo-recombination cross sections, and the shape of the returning wave packet is shown to be largely independent of the species. By comparing the HHG spectra generated from different targets under identical laser pulses, accurate structural information, including the phase of the recombination amplitude, can be retrieved. This result opens up the possibility of studying the target structure of complex systems, including their time evolution, from the HHG spectra generated by short laser pulses.PACS numbers: 42.65. Ky, 33.80.Rv When an atom is subjected to a strong driving laser field, one of the most important nonlinear response processes is the generation of high-order harmonics. In the past decade, high-order harmonic generation (HHG) has been used for the production of single attosecond pulses [1,2,3] and attosecond pulse trains [4], thus opening up new opportunities for attosecond time-resolved spectroscopy. HHG is understood using the three-step model (TSM) [5,6,7] -first the electron is released by tunnel ionization; second, it is accelerated by the oscillating electric field of the laser and later driven back to the target ion; and third, the electron recombines with the ion to emit a high energy photon. A semiclassical formulation of the TSM based on the strong-field approximation (SFA) is given by Lewenstein et al [7]. In this model (often called Lewenstein model), the liberated continuum electron experiences the full effect from the laser field, but not from the ion that it has left behind. In spite of this limitation, the SFA model has been used quite successfully, in particular, for analysis of the attosecond synchronization of high harmonics, see Mairesse et al [8] and references therein. However, since the continuum electron recombines when it is near the parent ion, the neglect of electron-ion interaction in the SFA model is rather questionable.According to the TSM, the last step of HHG is analogous to the radiative recombination process in electronion collisions. Thus one may write the HHG signal aswhere d(ω) is the photo-recombination (PR) transition dipole and W (E) is the returning "electron wave packet". Electron energy E is related to the emitted photon energy ω by E = ω − I p , with I p being the ionization potential of the target. Clearly the HHG signal S(ω) and W (E) depend on the laser properties. On the other hand, d (ω) is the property of the target only. The factorization in Eq. (1) is most useful when one compares the HHG spectra from two different targets in the identical laser field. Assuming that the shape of W (E) is species independent, by measuring the relative HHG yields, one can deduce the PR cross section of one species if the PR cross section of the other is known. The validity of Eq. (1) has been shown recently in Morishit...

Scaling laws for high-order-harmonic generation with midinfrared laser pulses

“…Within the quantitative rescattering theory (QRS), which is based on the phenomenological factorization of the HHG yield in terms of the EWP and the field-free photorecombination cross section [27][28][29] [as confirmed by numerical solutions of the time-dependent Schrödinger equation (TDSE)], several scaling properties have been suggested in Ref. [26] for the EWP considered as a function of the electron energy E, the U p -scaled energỹ E = E/U p , and the carrier wavelength λ of the laser pulse:…”

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

“…It has been well documented that QRS results are nearly as accurate as those obtained from TDSE whenever accurate results from the latter can be obtained, i.e., including the atom in the SAE approximation [96] and the H + 2 molecular ion [101]. Applications of the QRS for HHG from single molecules have been investigated in Refs.…”

“…According to the QRS, the induced dipole moment D(ω) can be written as [96] In practical applications, the QRS obtains the induced dipole moment by …”

“…In the present calculation, we use QRS in the propagation calculation. For singleatom response, QRS has been tested against TDSE, both for the magnitude and phase, as documented in Le et al [96], for example. In QRS, the wave packet is obtained from SFA, including the phase.…”

“…This method is based on the recently developed quantitative rescattering (QRS) theory [26,94,95], which allows us to calculate laser induced dipole of an atom with accuracy comparable to that obtained from solving TDSE, yet with computing time comparable to that by using the SFA. The validity of the QRS, at the single-atom level has been carefully calibrated against TDSE results for oneelectron model atoms [96]. Clearly such comparison is incomplete without considering the macroscopic propagation effects.…”