Retrieval of target photorecombination cross sections from high-order harmonics generated in a macroscopic medium

We investigate high-order harmonic generation (HHG) in a thin macroscopic medium by solving Maxwell’s equation using microscopic single-atom induced dipole moment calculated from the recently developed quantitative rescattering (QRS) theory. We show that macroscopic HHG yields calculated from QRS compared well with those obtained from solving the single-atom time-dependent Schrödinger equation but with great saving of computer time. We also show that macroscopic HHG can be expressed as a product of a “macroscopic wave packet” and the photorecombination cross section of the target gas. The latter enables us to extract target structure from the experimentally measured HHG spectra, thus paves the way to use few-cycle infrared lasers for time-resolved chemical imaging of transient molecules with few-femtosecond temporal resolution.

Figure 1

(Color online) Photorecombination cross sections of (a) Ar, (b) Xe, and (c) Ne, obtained by using scattering wave (solid lines) and within plane wave approximation using real atom (dashed lines) and hydrogenlike atom (dotted lines).

Figure 2

(Color online) (a) Single atom and (b) macroscopic harmonic spectra of Ar from the TDSE (dot dashed lines), QRS (solid lines), and SFA (dashed lines). Spatial distribution of macroscopic harmonic emission at the exit face of gas jet from the (c) TDSE, (d) QRS, and (e) SFA.

Figure 3

(Color online) Phase difference $\Delta \varphi$ of single-atom response for Ar from the TDSE (solid squares) and QRS (open circles).

Figure 4

(Color online) Phase difference $\Delta \varphi$ of macroscopic response for Ar from the TDSE and the QRS, which is calculated for $r=0\mu \text{m}$ (solid circles) or $r=9.2\mu \text{m}$ (open triangles) at the exit of gas jet. [(a) and (b)] Gas jet is put 2 mm after the focus. [(c) and (d)] Gas jet is put at the focus. The laser intensity in the center of gas jet is always kept as $1.5\times {10}^{14}\text{W}/{\text{cm}}^2$; laser duration and wavelength are the same as in Fig. 2.

Figure 5

(Color online) Macroscopic wave packet extracted from macroscopic harmonic spectrum based on QRS using real atom (solid lines) and hydrogenlike atom (dotted lines). [(a)–(c)] Ar gas jet is 2, 2, and 1.5 mm after the focus, respectively. Laser intensities are $1.5\times {10}^{14}$, $1.25\times {10}^{14}$, and $1.5\times {10}^{14}\text{W}/{\text{cm}}^2$, respectively. (d) Xe gas jet is 2 mm after the focus; laser intensity is $5\times {10}^{13}\text{W}/{\text{cm}}^2$. (e) Ne gas jet is 2.5 mm after the focus; laser intensity is $2.5\times {10}^{14}\text{W}/{\text{cm}}^2$. The arrows indicate the cutoff energy determined by $I_P+3.2U_P$ [18, 38]; laser intensity means one in the center of gas jet.

Figure 6

(Color online) Spatially harmonic emission of (a) H15, (b) H17, (c) H25, and (d) H27 for Ar under the QRS.

Figure 7

(Color online) Intensity averaged harmonic spectra (solid lines) vs propagated one when gas jet is put 2 mm after (dotted lines) or before (dashed lines) the focus for Ar. (a) and (b) are shown the TDSE calculations; (c) and (d) are shown the QRS calculations. Harmonic yields of H20–H28 in (b) and (d) are multiplied by 6.