Quantum orbits in atomic ionization beyond the dipole approximation

Using the strong-field-approximation theory beyond the dipole approximation we investigate above-threshold ionization induced by the monochromatic and bichromatic laser fields. Particular emphasis is on the approach based on the saddle-point method and the quantum-orbit theory which provides an intuitive picture of the underlying process. In particular, we investigate how the solutions of the saddle-point equations and the corresponding quantum orbits and velocities are affected by the nondipole effects. The photoelectron trajectories are two dimensional for linearly polarized field and three dimensional for two-component tailored fields, and the electron motion in the propagation direction appears due to the nondipole corrections. We show that the influence of these corrections is not the same for all contributions of different saddle-point solutions. For a linearly polarized driving field, we focus our attention only on the rescattered electrons. On the other hand, for the tailored driving field, exemplified by the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>ω</a:mi></a:math>–<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>2</b:mn><b:mi>ω</b:mi></b:mrow></b:math> orthogonally polarized two-color field, which is of the current interest in the strong-field community, we devote our attention to both the direct and the rescattered electrons. In this case, we quantitatively investigate the shift which appears in the photoelectron momentum distribution due to the nondipole effects and explain how these corrections affect the quantum orbits and velocities which correspond to the saddle-point solutions. Published by the American Physical Society 2024