Molecular potential anisotropy probed by electron rescattering in strong-field ionization of molecules

One of the main differences between rescattering following laser-induced ionization of atoms and molecules and electron-ion collisions performed with electron beams is the quivering dynamics of the electron around the ionic site in laser experiments. This report is aimed at probing the effect of the anisotropic potential of linear and symmetric molecular ions on the departing electron following tunnel ionization and rescattering by an intense femtosecond laser field at $0.8\mu \mathrm{m}$ and ${10}^{14}{\mathrm{Wcm}}^{-2}$. The laser excitation conditions are chosen so that the maximum collision energy remains of the order of 20 eV. In the energy range where rescattering is significant, the angular widths of the photoelectron angle-resolved energy spectra are found to be significantly larger for ${\mathrm{N}}_2$ and ${\mathrm{C}}_2{\mathrm{H}}_2$ molecules aligned perpendicularly to the laser polarization than the angular widths of angle-resolved energy spectra recorded in parallel alignment, although ${\mathrm{N}}_2$ and ${\mathrm{C}}_2{\mathrm{H}}_2$ obey opposite tunnel ionization dynamics with respect to alignment. In the associated collision energy and angle ranges where this effect is observed, the lowest values of the impact parameter are less than one atomic unit. It is conjectured that the approach of the quivering departing electron may be sufficient for its trajectories to be dependent on the molecular ion core alignment, i.e., the anisotropic molecular potential.

Figure 1

Collision kinetic energy (red dotted line) and final kinetic energies (blue solid lines) as a function of the collision-ionization phase difference for different collision polar angles ${\mathrm{\Theta }}_{\mathrm{c}}\in [0^{\circ },{60}^{\circ }]$. The angle step of ${\mathrm{\Theta }}_{\mathrm{c}}$ is $\mathrm{\Delta }{\mathrm{\Theta }}_{\mathrm{c}}=6^{\circ }$. The kinetic energies are multiplied by the sign of the associated momentum component $p_z=\mathbf{p}·{\mathbf{e}}_z$ where the unit vector ${\mathbf{e}}_z$ points in the direction of the laser field at the ionization phase.

Figure 2

Collision kinetic energy, final kinetic energies, final angle, and final experimental angle as a function of the collision-ionization phase difference for different collision polar angles ${\mathrm{\Theta }}_{\mathrm{c}}\in [{60}^{\circ },{90}^{\circ }]$. The angle step of ${\mathrm{\Theta }}_{\mathrm{c}}$ is $\mathrm{\Delta }{\mathrm{\Theta }}_{\mathrm{c}}=3^{\circ }$. (a) Collision kinetic energy (red dotted line), final kinetic energies (blue solid lines). The kinetic energies are multiplied by the sign of the associated momentum component $p_z=\mathbf{p}·{\mathbf{e}}_z$ where the unit vector ${\mathbf{e}}_z$ points in the direction of the laser field at the ionization phase. (b) Final angle ${\mathrm{\Theta }}_{\mathrm{f}}=\left(\widehat{{\mathbf{e}}_z,{\mathbf{p}}_{\mathrm{f}}}\right)$ (blue solid lines) where ${\mathbf{p}}_{\mathrm{f}}$ is the final momentum. (c) Final experimental angle ${\theta }_{\mathrm{f}}$ (green solid lines) defined in the text and taking into account the indistinguishable positive and negative oscillations of the laser field and the molecular symmetries.

Figure 3

Collision kinetic energy, final kinetic energies, final angle, and final experimental angle as a function of the collision-ionization phase difference for different collision polar angles ${\mathrm{\Theta }}_{\mathrm{c}}\in [{90}^{\circ },{120}^{\circ }]$. The angle step of ${\mathrm{\Theta }}_{\mathrm{c}}$ is $\mathrm{\Delta }{\mathrm{\Theta }}_{\mathrm{c}}=3^{\circ }$. (a) Collision kinetic energy (red dotted line), final kinetic energies (blue solid lines). The kinetic energies are multiplied by the sign of the associated momentum component $p_z=\mathbf{p}·{\mathbf{e}}_z$ where the unit vector ${\mathbf{e}}_z$ points in the direction of the laser field at the ionization phase. (b) Final angle ${\mathrm{\Theta }}_{\mathrm{f}}=\left(\widehat{{\mathbf{e}}_z,{\mathbf{p}}_{\mathrm{f}}}\right)$ (blue solid lines) where ${\mathbf{p}}_{\mathrm{f}}$ is the final momentum. (c) Final experimental angle ${\theta }_{\mathrm{f}}$ (green solid lines) defined in the text and taking into account the indistinguishable positive and negative oscillations of the laser field and the molecular symmetries.

Figure 4

Collision kinetic energy, final kinetic energies, final angle, and final experimental angle as a function of the collision-ionization phase difference for different collision polar angles ${\mathrm{\Theta }}_{\mathrm{c}}\in [{120}^{\circ },{180}^{\circ }]$. The angle step of ${\mathrm{\Theta }}_{\mathrm{c}}$ is $\mathrm{\Delta }{\mathrm{\Theta }}_{\mathrm{c}}=6^{\circ }$. (a) Collision kinetic energy (red dotted line), final kinetic energies (blue solid lines). The kinetic energies are multiplied by the sign of the associated momentum component $p_z=\mathbf{p}·{\mathbf{e}}_z$ where the unit vector ${\mathbf{e}}_z$ points in the direction of the laser field at the ionization phase. (b) Final angle ${\mathrm{\Theta }}_{\mathrm{f}}=\left(\widehat{{\mathbf{e}}_z,{\mathbf{p}}_{\mathrm{f}}}\right)$ (blue solid lines) where ${\mathbf{p}}_{\mathrm{f}}$ is the final momentum. (c) Final experimental angle ${\theta }_{\mathrm{f}}$ (green solid lines) defined in the text and taking into account the indistinguishable positive and negative oscillations of the laser field and the molecular symmetries.

Figure 5

Largest experimental angle ${\theta }_{\mathrm{f},\max }$ as a function of the final energy. (a) (red dotted line): For large collision-ionization phase differences, i.e., larger than several times $2\pi$ rad. (b) (blue solid line): For all collision-ionization phase differences.

Figure 6

Photoelectron angle-resolved energy spectra recorded at $0.8\mu \mathrm{m}$ with the laser polarization parallel to the time-of-flight axis, i.e., $\theta =0^{\circ }$. Top panel: ${\mathrm{C}}_2{\mathrm{H}}_2$ at ${10}^{14}{\mathrm{Wcm}}^{-2}$. (a) (blue dotted line): Parallel alignment. (b) (red solid line): Perpendicular alignment. Bottom panel: ${\mathrm{N}}_2$ at $1.2\times {10}^{14}{\mathrm{Wcm}}^{-2}$. (c) (blue dotted line): Parallel alignment. (d) (red solid line): Perpendicular alignment. The classical energy limits at $2U_{\mathrm{p}}$ and $10U_{\mathrm{p}}$ are indicated by vertical green dashed lines.

Figure 7

Top panel: Angular widths recorded in ${\mathrm{N}}_2$ at $1.2\times {10}^{14}{\mathrm{Wcm}}^{-2}$. (a) (blue dotted line): Parallel alignment. (b) (red solid line): Perpendicular alignment. Bottom panel: Ratios of the angular widths and angle-integrated energy spectra in ${\mathrm{N}}_2$ from angle-resolved energy spectra recorded in perpendicular and parallel alignments, respectively. (c) (navy solid line): Ratio of the angular widths. (d) (purple dotted line): Ratio of the angle-integrated energy spectra. The classical energy limit at $2U_{\mathrm{p}}$ of the direct electron signal is indicated by vertical green dashed lines.

Figure 8

Top panel: Angular widths recorded in ${\mathrm{C}}_2{\mathrm{H}}_2$ at ${10}^{14}{\mathrm{Wcm}}^{-2}$. (a) (blue dotted line): Parallel alignment. (b) (red solid line): Perpendicular alignment. Bottom panel: Ratios of the angular widths and angle-integrated energy spectra in ${\mathrm{C}}_2{\mathrm{H}}_2$ from angle-resolved energy spectra recorded in perpendicular and parallel alignments, respectively. (c) (navy solid line): Ratio of the angular widths. (d) (purple dotted line): Ratio of the angle-integrated energy spectra. The classical energy limit at $2U_{\mathrm{p}}$ of the direct electron signal is indicated by vertical green dashed lines.

Figure 9

Photoelectron normalized difference momentum spectrum $\mathrm{\Delta }{S}_{{\mathbf{p}}_{\mathrm{f}}}(p_{\mathrm{f}z},p_{\mathrm{f}x})$ defined by Eq. (21) obtained from electron momenta spectra recorded in ${\mathrm{C}}_2{\mathrm{H}}_2$ at ${10}^{14}{\mathrm{Wcm}}^{-2}$ and $0.8\mu \mathrm{m}$ in parallel and perpendicular alignments, respectively. The quarter circle (black dashed line) represents the momentum $(p_{\mathrm{f}z},p_{\mathrm{f}x})$ locations corresponding to $2U_{\mathrm{p}}=12$ eV.