Correlation-enhanced high-order-harmonic-generation spectra of Mn and ${\mathrm{Mn}}^{+}$

We examine giant resonant enhancement of high-order harmonics generation (HHG) in the Mn atom and its singly charged ${\mathrm{Mn}}^{+}$ ion. Our theoretical model combines single active electron tunneling and propagation with correlation-enhanced recombination. Previously, this approach demonstrated its useability for the Xe atom [Phys. Rev. A 100, 013404 (2019)]. Spin-polarized Hartree-Fock and random-phase approximation with exchange calculations are carried out to evaluate the correlation enhancement factor in Mn and ${\mathrm{Mn}}^{+}$, which is then compared with other reported calculations and the experiment.

Figure 1

Top: absolute photoionization cross sections of the $4s$ shell of Mn calculated in the SP-HF and SP-RPAE approximations for various final ionic states. Comparison is made with relative experimental cross sections from Ref. [24], which are internormalized and fitted to the calculated cross section corresponding to the final ${}^{7}S_3$ ionic state. Bottom: the correlation enhancement factor $R_{4s}={\sigma }_{4s}^{\mathrm{SP}-\mathrm{RPAE}}/{\sigma }_{4s}^{\mathrm{SP}-\mathrm{HF}}$ for the ${}^{7}S_3$ and ${}^{5}S_2$ ionic states. Also shown is the CEF extracted from the HHG spectra of Ref. [20].

Figure 2

Same as Fig. 1 but for the ${\mathrm{Mn}}^{+}$ ion in the ${}^{7}S_3$ and ${}^{5}S_2$ initial states.

Figure 3

Same as Fig. 2 but for the $3d$ shell. The top panel displays the total absolute experimental cross section of ${\mathrm{Mn}}^{+}$ [32]. The bottom panel shows the CEF $R_{3d}$ and the $\beta$ modified factor in the polarization direction $R_{3d,z}$

Figure 4

HHG spectra of Mn generated from SAE TDSE solutions. The driving pulse parameters are as follows: the wavelength $\lambda =1.8\mu \mathrm{m}$ and the pulse durations (from bottom to top) 12 fs, 30 fs (both at $4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$), and 50 fs (at $5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$). The 30- and 50-fs HHG spectra are scaled up for better clarity. All the spectra are calculated for the $4s$ shell except for the 12-fs driving pulse, for which the $3d$ spectrum is also shown without additional scaling.

Figure 5

Top: The experimental HHG spectra [5] recorded with pulse durations of 30 fs (purple spectra) and 50 fs (plum spectra), wavelength of 1.82 $\mu \mathrm{m}$, and laser intensities of $4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and $5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, respectively. The present correlation enhanced TDSE calculation at 30 fs is shown with a solid green line. Bottom: the same set of data for 12-fs pulse duration. Additionally, a TDSE calculation from Ref. [5] is shown.

Figure 6

HHG spectra of ${\mathrm{Mn}}^{+}$ generated from the $4s$ and $3d_{m=0}$ initial states. Top: A 35-fs driving pulse at $\lambda =400$ nm and $I=1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ as in Ref. [7]. The arrows indicate the cutoff energy. Bottom: The driving pulse is 115 fs at $\lambda =800$ nm, $I=8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ as in the experiment [8].

Figure 7

The $3d$ HHG spectrum of Fig. 6 is enlarged for the GAR region of ${\mathrm{Mn}}^{+}$. The top panel displays the raw HHG spectrum, its Gaussian convolution, and multiplicative enhancement with CEF of Fig. 3. The smoothed and enhanced spectra are scaled up for better clarity. Comparison is made with the experiment [8]. In the bottom panel, the enhanced HHG spectrum is compared with the experiment on the linear intensity scale.

Figure 8

Same as Fig. 7 for $\lambda =400$ nm and 35-fs driving pulse. Comparison is made with the experiment [7].