Multiphoton ionization distributions beyond the dipole approximation: Retardation versus recoil corrections
Phys. Rev. A 112, 023105 – Published 4 August, 2025
DOI: https://doi.org/10.1103/df6g-tpt9
Abstract
We study nondipole effects in multiphoton ionization of a two-dimensional hydrogen-like atom by a flat-top laser pulse of varied intensity. For this purpose, we solve numerically a two-dimensional Schrödinger equation treating a propagating laser pulse exactly. The resulting distributions are then compared to those calculated in the dipole approximation. By investigating the energy-angular photoelectron distributions, we demonstrate that the multiphoton peaks shift toward either smaller or larger energies depending on the photoelectron emission angle. This is analytically interpreted based on the leading-order relativistic expansion of the electron Volkov state, showing a significant contribution of the electron recoil to that behavior. In contrast, the retardation correction originating from the space- and time dependence of the laser field leads to a tiny redshift of the photoelectron energy spectra. Other features of ionization distributions are also analyzed, including the sidelobes and the double-hump structures of multiphoton peaks, or their disappearance for intense propagating laser pulses.
