Laser-Induced Interference, Focusing, and Diffraction of Rescattering Molecular Photoelectrons

We solve the time-dependent Schrödinger equation in three dimensions for ${\mathrm{H}}_2^{+}$ in a one-cycle laser pulse of moderate intensity. We consider fixed nuclear positions and Coulomb electron-nuclear interaction potentials. We analyze the field-induced electron interference and diffraction patterns. To extract the ionization dynamics we subtract the excitations to low-lying bound states explicitly. We follow the time evolution of a well-defined wave packet that is formed near the first peak of the laser field. We observe the fragmentation of the wave packet due to molecular focusing. We show how to retrieve a diffraction molecular image by taking the ratio of the momentum distributions in the two lateral directions. The positions of the diffraction peaks are well described by the classical double slit diffraction rule.

Figure 1

The time evolution of the ionized part of the spatial electron density distributions at $I=3\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. The density slices are in the $xz$ plane. $\mathbf{A}$ and $\mathbf{B}$ label directly detached wave packets. $\mathbf{C}$, $\mathbf{D}$, and $\mathbf{E}$ label the focused wave packets; see text. The electron density is plotted using a $\mathrm{l}\mathrm{o}{\mathrm{g}}_{10}$ scale.

Figure 2

The reduced one-dimensional momentum distribution ${\chi }_z(p,t)$ after the first half cycle (dashed lines) and after one cycle (solid lines) at $I={10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ (left) and $3\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ (right).

Figure 3

The 3D electron density distributions (top) and the ratios of momentum distributions $\mu (p,t)$ (bottom). Left column shows the diffraction of a Gaussian wave packet with its initial momentum matching the effective cutoff momentum at $I=3\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$; see details in text. Right column shows laser-induced diffraction at the same intensity and time $t=55.2$. The labels $\mathbf{B}$, $\mathbf{C}$, and $\mathbf{D}$ in top right panel refer to the same wave packets as in Fig. 1. The image in the top right panel is clipped at $y=0$. The electron density is plotted using a $\mathrm{l}\mathrm{o}{\mathrm{g}}_{10}$ scale.

Figure 4

The ratios of momentum distributions $\mu (p,t)$. The positions of the peaks are unchanged after the first half cycle ($1/2$ collision, dashed lines) and after one full cycle ($1^1{/}_2$ collision, solid lines) at $I={10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ (left) and $3\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ (right).