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

Based on high-order harmonic generation (HHG) spectra obtained from solving the time-dependent Schrödinger equation for atoms, we established quantitatively that the HHG yield can be expressed as the product of a returning electron wave packet and photorecombination 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.

Figure 1

(Color online) Photorecombination cross sections of Ar (a), Xe (b), and Ne (c), obtained by using exact scattering wave functions (solid black curves) and within the plane-wave approximation (dashed red curves) for the continuum electrons.

Figure 2

(Color online) Comparison of the returning electron “wave packets” extracted from the HHG spectra of Ne, obtained by solving the TDSE (solid black line) and from the SFA model (dashed blue line). Also shown is the TDSE result for the wave packet from scaled H (dotted red line). For laser parameters, see text.

Figure 3

(Color online) Comparison of the HHG yields obtained from numerical solution of the TDSE (solid red lines), the SFA (dotted blue lines), and the SW-SFA model (solid black lines) for Ar (a), Xe (b), and Ne (c). Data for Ar have been shifted vertically to show the detailed structures. For laser parameters, see text.

Figure 4

(Color online) Extracted harmonic phase difference $\Delta \varphi$ between Ar and scaled hydrogen obtained with different lasers as function of emitted photon energy. The PR dipole phase difference $\Delta \delta$ is given as solid black line. (a) Ar, (b) Xe, and (c) Ne. $I_0={10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$.

Figure 5

(Color online) HHG spectra for Ar from the “simulated” macroscopic propagation. Shown are results from the exact TDSE (solid red line) and SW-SFA(dotted black line), and by using the wave packet extracted from TDSE solution for scaled $\mathrm{H}\left(1s\right)$ (dashed blue line). For laser parameters, see text.