Multielectron effect in the strong-field ionization of aligned nonpolar molecules

We revisit strong-field ionization of aligned ${\mathrm{O}}_2, {\mathrm{CO}}_2$, and ${\mathrm{CS}}_2$ molecules in light of recent advances in the field of strong-field physics, in particular the inclusion of multielectron polarization in the numerical solution of the time-dependent Schrödinger equation (TDSE) within the singe-active-electron approximation. Multielectron polarization is modeled by the introduction of a long-range induced dipole term based on the polarizability of the cation, and a field at short distances that counteracts the applied external field and leads to a vanishing time-dependent interaction within a certain cutoff radius. For the probed molecules, the main effect of including multielectron polarization is the reduction of the total ionization yields (TIYs), and for molecules with large polarizability of their cation (${\mathrm{CO}}_2$ and ${\mathrm{CS}}_2$), the alignment angle of maximum TIY will shift. The photoelectron momentum distributions and above-threshold ionization spectra show little imprint of the multielectron polarization associated with the long-range part of the laser-induced dipole potential. For ${\mathrm{CO}}_2$ and ${\mathrm{CS}}_2$, the inclusion of multielectron polarization and the associated induced dipole potential in the TDSE model gives alignment-resolved distributions of total ionization yields which are in better agreement with the available experimental results.

Figure 1

Illustration of the degenerate HOMOs of $\pi$ symmetry in ${\mathrm{CO}}_2$ in the molecular fixed (superscript M) (a) ${\left(xz\right)}^M$ and (b) ${\left(yz\right)}^M$ planes. In (a), the laboratory-frame $z^L$ axis and alignment angle ($\beta$) are illustrated. The $\mathrm{HOMO}\left(yz\right)$ in (b) always has a node in the polarization direction. This is not the case with the HOMO ($xz$) in (a).

Figure 2

Bound state spectrum of ${\mathrm{CO}}_2$ after the end of an 800-nm laser pulse containing five optical cycles with peak intensity of $5.6\times {10}^{13} \mathrm{W}/{\mathrm{cm}}^2$. The solid (dotted) line denotes TDSE calculations without (with) MEP correction.

Figure 3

Effect of MEP on the alignment dependence of TIYs from the HOMOs of the ${\mathrm{CO}}_2$ molecule at peak intensities of (a) $1.4\times {10}^{13}$, (b) $3.2\times {10}^{13}$, (c) $5.6\times {10}^{13}$, and (d) $8.8\times {10}^{13} \mathrm{W}/{\mathrm{cm}}^2$. The dotted lines denote no field within $r_c$, while the solid lines denote full MEP including the long-range laser-induced dipole potential.

Figure 4

Contributions from the (a)–(d) $\mathrm{HOMO}\left(xz\right)$ and (e)–(h) $\mathrm{HOMO}\left(yz\right)$ of ${\mathrm{CO}}_2$ to the TIYs shown in Fig. 3. In each panel, the TIYs are normalized to unity.

Figure 5

Effect of MEP on the alignment dependence of TIYs from the HOMOs of the ${\mathrm{CO}}_2$ molecule at peak intensity of $8.8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ for pulses containing (a) two, (b) five, and (c) eight optical cycles. The dotted lines denote no field within $r_c$, while the solid lines denote full MEP including the long-range laser-induced dipole potential.

Figure 6

Field-dressed SAE potential for ${\mathrm{CO}}_2$ along the molecular axis ($\beta =0^{\circ }$) at external field strength values (a) $E=0.04$ a.u. and (b) $E=0.075$ a.u. In (a) and (b), solid lines denote full MEP; dotted lines: no MEP; blue circles: field-free ionization potential.

Figure 7

(a) Interpolation of the theoretical distributions of TIYs from ${\mathrm{CO}}_2$ presented in Fig. 3 in order to obtain an estimate for the TIYs at a denser angular grid. In (b), the theoretical yields in (a) were convoluted with an experimental convolution function taken from Ref. [29]. Solid lines denote full MEP; dotted lines: no field within $r_c$.

Figure 8

Effect of MEP on laboratory-frame PMDs and ATI spectra from the $\mathrm{HOMO}\left(xz\right)$ of the ${\mathrm{CO}}_2$ molecule at a peak intensity of $8.8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and alignment angle $\beta ={45}^{\circ }$ for 800 nm pulses containing (a)–(c) two and (d)–(f) eight cycles. The PMDs in (a), (d) refer to TDSE calculations with no field within $r_c$, while (b), (e) refer to the full MEP account. In the ATI spectra in (c), (f), the dotted lines (solid lines) denote TDSE calculations with no field within $r_c$ (full MEP account).

Figure 9

Effect of MEP on (a) alignment dependence of TIYs for ${\mathrm{CS}}_2$ obtained as the incoherent sum of the yields from the $\mathrm{HOMO}\left(xz\right)$ and the $\mathrm{HOMO}\left(yz\right)$ and (b),(c) photoelectron momentum distributions from the $\mathrm{HOMO}\left(xz\right)$ of the ${\mathrm{CS}}_2$ molecule at peak intensity of $4.5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ for pulses containing five cycles. In (a), the dotted line denotes no field within $r_c$, while the solid line denotes full MEP; the TIYs are given on a relative scale. The PMD in (b) refers to TDSE calculations with no field within $r_c$, while (c) refers to the full MEP account.

Figure 10

Effect of MEP on the (a) alignment dependence of TIYs for ${\mathrm{O}}_2$ obtained as the incoherent sum of the yields from the $\mathrm{HOMO}\left(xz\right)$ and the $\mathrm{HOMO}\left(yz\right)$ and (b), (c) photoelectron momentum distributions from the $\mathrm{HOMO}\left(xz\right)$ of the ${\mathrm{O}}_2$ molecule at peak intensity of $8.8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ for pulses containing five cycles. In (a), the dashed line denotes no field within $r_c$, while the solid line denotes full MEP, and the TIYs are given on a relative scale. The PMD in (b) refers to TDSE calculations with no field within $r_c$, while (c) refers to the full MEP account.