Fig. 1: Origin of the dependence of the Wigner time delay on the molecular orientation for strong-field ionization.
From: Angular dependence of the Wigner time delay upon tunnel ionization of H2
a Two-dimensional distribution \(\left| {\psi _r\left( {x,y} \right)} \right|^2\) of the molecular orbital of H2 in position space. Different tunneling directions (orange arrows, defined by the angle γ) and the corresponding perpendicular directions (black arrows, labeled with \(s_ \bot\)) are indicated. The colored Gaussian curves allude to the dependence of the projection of \(\left| {\psi _r\left( {x,y} \right)} \right|^2\) along \(s_ \bot\) as a function of γ that is discussed in (b, c). The tunnel exit position that is used in (a) is chosen unrealistically short (about a factor of 12) for illustrational purposes (see “Methods”). b One-dimensional cuts of the square of the wave function in position space along the four exemplary arrows labeled with \(s_ \bot\) from (a). The position offset \({{\Delta }}s_ \bot\) is zero for tunneling parallel or perpendicularly to the molecular axis (γ = 0° and γ = ±90°) due to the symmetry of H2. Maximally positive [negative] values of \({{\Delta }}s_ \bot\) appear for γ = 45° [γ = −45°]. c The position offset \({{\Delta }}s_ \bot (\gamma )\) of the one-dimensional cuts of the square of the wave function in position space along \(s_ \bot\). Note, that \({{\Delta }}s_ \bot\)is equivalent to \(- {{\Delta }}\phi _{{\mathrm{init}}}^\prime\) (see text and “Methods”). d The values of ΔτW,M as a function of the electron energy E and β, which is the electron emission direction with respect to the molecular axis, are obtained using the curve from (c) and \({{\Delta }}\tau _{{\mathrm{W}},{\mathrm{M}}} = \frac{{\hbar \,m_{\mathrm{e}}}}{{|{\boldsymbol{p}}_{\rm{elec}}|}}{{\Delta }}\phi _{{\mathrm{init}}}^\prime\) (see Methods). Note that \(\beta = \gamma - 90^\circ\) within the PFT model and that the width of the illustrated wave packets in (a) is not to scale.
