Breakdown of the dipole approximation in strong-field ionization.

  title={Breakdown of the dipole approximation in strong-field ionization.},
  author={Andr{\'e} Ludwig and Jochen Maurer and Benedikt W. Mayer and Christopher R. Phillips and Lukas Gallmann and Ursula Keller},
  journal={Physical review letters},
  volume={113 24},
We report the breakdown of the electric dipole approximation in the long-wavelength limit in strong-field ionization with linearly polarized few-cycle mid-infrared laser pulses at intensities on the order of 10¹³ W/cm². Photoelectron momentum distributions were recorded by velocity map imaging and projected onto the beam propagation axis. We observe an increasing shift of the peak of this projection opposite to the beam propagation direction with increasing laser intensities. From a comparison… 

Figures from this paper

Nondipole photoelectron momentum shifts in strong-field ionization with mid-infrared laser pulses of long duration

We consider atomic strong-field ionization in the long-pulse limit for linearly polarized infrared laser fields. We show how nondipole effects in the plane formed by the propagation and polarization

High-order above-threshold ionization beyond the electric dipole approximation

Photoelectron momentum distributions from strong-field ionization are calculated by numerical solution of the one-electron time-dependent Schrödinger equation for a model atom including effects

Relativistic Nondipole Effects in Strong-Field Atomic Ionization at Moderate Intensities.

Observe counterintuitive peak shifts of the transverse electron momentum distribution in the direction opposite to that of laser propagation as a function of laser intensity and demonstrate an excellent agreement between the experimental results and theoretical predictions.

Interplay between Coulomb-focusing and non-dipole effects in strong-field ionization with elliptical polarization

We study strong-field ionization and rescattering beyond the long-wavelength limit of the dipole approximation with elliptically polarized mid-IR laser pulses. Full three-dimensional photoelectron

Ionization in intense laser fields beyond the electric dipole approximation: concepts, methods, achievements and future directions

  • J. MaurerU. Keller
  • Physics
    Journal of Physics B: Atomic, Molecular and Optical Physics
  • 2021
The electric dipole approximation is widely used in atomic, molecular and optical physics and is typically related to a regime for which the wavelength is much larger than the atomic structure.

Nondipole modification of the ac Stark effect in above-threshold ionization

Above-threshold ionization (ATI) of atoms in intense laser pulses produces photoelectron momentum distributions that exhibit discrete concentric circles related to the absorption of more photons than

Time-dependent perturbation theory beyond the dipole approximation for two-photon ionization of atoms

We develop a time-dependent perturbation theory beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization.

Non-dipole recollision-gated double ionization and observable effects

Using a three-dimensional semiclassical model, we study double ionization for strongly driven He fully accounting for magnetic field effects during the propagation in time. For linearly and slightly

Kramers–Henneberger Form of Strong Field Theory with the Correction of Dipole Approximation

We show that the breakdown of dipole approximation can be adopted to explain the asymmetry structure in the photoelectron momentum distributions along the beam propagation direction, which is defined

Transverse electron momentum distributions in strong-field ionization: nondipole and Coulomb focusing effects

In strong-field ionization, the combined influence of nondipole and Coulomb focusing effects leave a unique signature on the photoelectron momentum distributions, which may have direct implications



The tunnelling model of laser-induced ionization and its failure at low frequencies

The tunnelling model of ionization applies only to longitudinal fields: quasistatic electric fields that do not propagate. Laser fields are transverse: plane wave fields that possess the ability to

Super-Intense Laser-Atom Physics

Preface. SILAP 2000: an overview. Part I: Double Ionization of Complex Atoms. Energy distribution of two-electron ionization of helium in an intense field R. Lafon, et al. Double ionization in strong

Sub-four-cycle laser pulses directly from a high-repetition-rate optical parametric chirped-pulse amplifier at 3.4 μm.

Apodized aperiodically poled MgO:LiNbO3 crystals with a negative chirp rate are employed as gain media to achieve ultrabroadband phase-matching while minimizing optical parametric generation.


  • Rev. Lett. 106, 193002
  • 2011

Above-threshold ionization by few-cycle pulses

The theoretical description and the experimental methods and results for above-threshold ionization (ATI) by few-cycle pulses are reviewed. A pulse is referred to as a few-cycle pulse if its detailed


  • Rev. Lett. 110, 203002
  • 2013


  • Rev. A 87, 033421
  • 2013

9 J

  • Phys. B: At., Mol. Opt. Phys. 39, R203
  • 2006


  • Rev. A 85, 023428
  • 2012


  • Rev. Lett. 85, 5082
  • 2000