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 as the photoelectron longitudinal momentum distributions (PLMD), in tunneling regime (\gamma_\rm K\ll 1), based on the strong field approximation theory. The nondipole Hamiltonian for photoelectrons interacting with laser fields from a hydrogen-like atom is transformed into the Kramers–Henneberger frame in our model. To introduce the correction of dipole approximation, the spatial variable is kept in a vector potential \boldsymbol A(\boldsymbol r,t), demonstrating that the breakdown of dipole approximation is the major reason for the shift of the peak in PLMD. The nondipole effects are apparent when circularly polarized lasers are adopted to ionize the atoms, and clear tendency to increase offsets is found for increasing laser intensities.