Analytical approach to Coulomb focusing in strong-field ionization. II. Multiple recollisions

Abstract

The role of the Coulomb potential of the atomic core for creation of caustics in the photoelectron momentum distribution for tunneling ionization in a linearly polarized strong laser field, usually termed as Coulomb focusing, is investigated within classical theory beyond the dipole approximation. Coulomb focusing is addressed by analytical calculation of Coulomb momentum transfer to the tunneled electron due to rescatterings, while applying perturbation theory and classifying the recollisions either as fast or as slow. The accuracy of the obtained analytical formulas for the Coulomb momentum transfer is investigated by analytical derivation of asymptotic photoelectron momentum distribution and its comparison to exact numerical calculations. With the help of the applied analytical treatment, we analyze the origin of the counterintuitive energy-dependent bend of the Coulomb focusing cusp in the photoelectron momentum distribution in a linearly polarized laser field in the non-dipole regime, and its scaling with the field parameters. The importance of high-order recollisions is also investigated and they are shown to be responsible for a decrease of the bend of the cusp at very low energies in this regime. In general, the momentum transfer caused by high-order rescattering events, while being a perturbation with respect to the instantaneous electron momentum at the rescattering, is shown to induce a significant non-perturbative contribution to the total momentum transfer.

Holographic interference in atomic photoionization from a semiclassical standpoint

“…One can see very clearly the weak effect of the ionic potential on the escaping trajectories slowing down the electron in the perpendicular direction, i.e., k ⊥ < v ⊥0 . In our case of the hydrogen atom, this effect is called Coulomb focusing, although this name is commonly extended to other atoms with non-Coulombic potentials [11,21,22]. We see that 1HCNT must have an initial transversal momentum higher than…”

“…According to Eq. (22) in Sec. II, due to an interference process of glory trajectories, the angular distribution (for a fix energy) can be described by the square of a Bessel function of the first type of the angular momentum times the angle, i.e., J 2 0 (L θ) (see Ref.…”

“…Rescattering processes are responsible for different high energy structures such as a plateau in the photoelectron energy spectrum [13][14][15][16][17][18][19][20][21][22] and the so-called rescattering rings in the momentum distributions [20,23]. Although classical mechanics explains many features of electron distributions in atomic photoionization [24], electron dynamics can only be fully described by quantum mechanics as quantum interference effects.…”

Classical theory of laser-assisted spontaneous bremsstrahlung

“…In contrast, we are mostly concerned with the effect of the Coulomb interaction in the continuum, particularly the Coulomb focusing effect, which can be described classically, as follows, for example, from Refs. [18][19][20][21][22][23][24][25]. It would be unphysical to apply our approach to a short-range potential, since quantum effects play a crucial role in scattering of low-energy electrons by a short-range potential.…”

“…Here we investigate another feature of the process relevant to low-energy electron scattering when the Coulomb interaction cannot be treated perturbatively. It is known that the laser-induced atomic ionization processes can be enhanced by the Coulomb focusing [18][19][20][21][22][23][24][25]. The action of the Coulomb potential, in combination with multiple electron returns due to the laser field, focuses parts of the electron wave function, increasing the efficiency of such processes as multiphoton ionization.…”