Complete classification and additional saddle-point solutions for high-order above-threshold ionization induced by a strong laser field. II. Classical considerations

The saddle-point solutions for strong-laser-field-induced high-order above-threshold ionization, the complete classification of which was recently presented in Phys. Rev. A 111, 023103 (2025), are considered classically. In the limit of vanishing ionization potential the system of saddle-point equations simplifies, allowing a semi-analytical treatment. For a monochromatic field, the analytical nonlinear equations obtained this way allow one to determine the maximum (cutoff) photoelectron energies for the backward-and forward-scattering saddle-point solutions for all values of the multi-indices introduced by our classification scheme. These cutoffs are determined for all photoelectron momenta and it is shown how the backward-scattering solutions from one half of the momentum plane are related to the forward-scattering solutions from the other. The case of abichromatic linearly polarized field is analyzed in detail. The results are rederived with the help of a simple graphical method, which can be used to qualitatively discuss the effect of varying the field parameters.