Above-threshold ionization of Mg by linearly and circularly polarized laser fields: Origin of the subpeaks in the photoelectron energy spectra

We theoretically investigate above-threshold ionization of Mg by linearly and circularly polarized fs laser pulses. We find that the above-threshold ionization peaks are accompanied by small subpeaks for both linearly and circularly polarized pulses. We interpret the physical origin of the subpeaks as above-threshold ionization from the low-lying bound states which are far off-resonantly excited by the spectral wing of the pulse. This interpretation is confirmed by our comparative numerical studies. Furthermore, we provide a clear explanation of why this kind of subpeak in the photoelectron energy spectra has not been reported for smaller photon energies with Mg and other commonly used atoms such as H and rare gas atoms.

Figure 1

Relevant energy levels of Mg.

Figure 2

(a) The allowed ionization paths in multiphoton ionization from an $S(L=0)$ initial state using (a) linearly polarized light and (b) right circularly polarized light.

Figure 3

(Color online) (a) Ionization yield as a function of peak intensity for the linearly (dashed) and circularly polarized (solid) laser pulses at the photon energy of $3\mathrm{eV}$. (b) Ratio of the ionization yield by the circularly polarized pulse, $Y_{CP}$, to that by the linearly polarized pulse $Y_{LP}$. The pulse duration is $50\mathrm{fs}$ (FWHM).

Figure 4

(Color online) Photoelectron energy spectra by the linearly (dashed) and circularly polarized (solid) laser pulses at the photon energy of $3\mathrm{eV}$. The pulse duration is $50\mathrm{fs}$ (FWHM) and the peak intensity is $2\times {10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$.

Figure 5

(Color online) Comparison of the photoelectron energy spectra by the linearly polarized pulse at the photon energy of $3\mathrm{eV}$ when the $3s3p$ (dashed) and $3s5s$ (dot-dashed) bound states of Mg are removed from the atomic basis when solving the time-dependent Schrödinger equation. The pulse duration and peak intensity are the same as in Fig. 4.

Figure 6

(Color online) The height of the first four subpeaks [labeled as (1)–(4) in Fig. 4] subject to the two-color (main and auxiliary) laser pulses as a function of population of the $3s3p$ state (labeled on the bottom horizontal axis) and accordingly peak intensity of the auxiliary laser (labeled on the top horizontal axis). The peak intensity and the photon energy of the main laser are ${10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$ and $3\mathrm{eV}$, respectively. The photon energy of the auxiliary laser is $4.35\mathrm{eV}$. Both lasers are linearly polarized with the same pulse durations of $50\mathrm{fs}$ (FWHM).

Figure 7

(Color online) Comparison of the photoelectron energy spectra for the pulses with cosine-squared (solid), hyperbolic secant (dashed), and Gaussian (dot-dashed) temporal envelope functions having the same pulse duration of $50\mathrm{fs}$ (FWHM). Polarization is linear for all cases and the photon energy and peak intensity are the same as in Fig. 4.

Figure 8

Photoelectron energy spectra at the photon energy of $3\mathrm{eV}$ and the peak intensity of $2\times {10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$ for three different pulse durations, (a) 50, (b) 20, and (c) $10\mathrm{fs}$ (FWHM). Laser polarization is linear.

Figure 9

(Color online) (a) Ionization yield as a function of peak intensity for the linearly (dashed) and circularly polarized (solid) laser pulses at the photon energy of $4.65\mathrm{eV}$. (b) Ratio of the ionization yield by the circularly polarized pulse, $Y_{CP}$, to that by the linearly polarized pulse $Y_{LP}$. The pulse duration is $50\mathrm{fs}$ (FWHM).

Figure 10

(Color online) Photoelectron energy spectra by the linearly (dashed) and circularly polarized (solid) laser pulses at the photon energy of $4.65\mathrm{eV}$. The pulse duration and peak intensity are $50\mathrm{fs}$ (FWHM) and ${10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$, respectively.

Figure 11

(Color online) Comparison of the photoelectron energy spectra by the linearly polarized pulse at the photon energy of $4.65\mathrm{eV}$ when the (a) $3s3p$, (b) $3s4p$, (c) $3s5p$, and (d) $3s6p$ bound states of Mg are removed from the atomic basis when solving the time-dependent Schrödinger equation. The pulse duration and peak intensity are the same as in Fig. 10.