Fig. 1. Differential ionization rates of Ar for the angle θ=0° as functions of the electron energy in units of Up for a linearly polarized laser field with intensity 2×1014  W/cm2 and wavelength 2000 nm (Up=74.7  eV) for various approximations as explained in the text. The FS LFA spectra obtained using the FS saddle-point solutions within the low-frequency approximation are smooth for energies above 0.1Up. Below this energy they rise strongly and display the peaks of the classical LES series^[18,22].

Fig. 2. Classical solutions for the electron energies in units of Up as a function of the electron travel time (expressed as ωτ) for backward- (upper panel) and forward- (lower panel) scattered electrons for the final electron emission angle θ between 0° and 90° in steps of 10°, as denoted in the legend.

Fig. 3. Logarithm of the differential ionization rate of Xe presented in false colors (the color map covers more than 4 orders of magnitude in arbitrary units) in the electron momentum plane for ionization by a linearly polarized laser field with intensity 5.217×1013  W/cm2 and wavelength 2000 nm (Up=19.49  eV). Results are obtained using the coherent sum of forward-like scattering solutions with μ≥1 (upper panel) and both of the forward-like and backward-like scattering solutions (lower panel).

Fig. 4. Logarithm of the differential ionization rate of Xe presented in false colors in the electron momentum plane for ionization by a linearly polarized laser field having the intensity 4.5×1013  W/cm2 and the wavelength 1800 nm (Up=13.6  eV). The upper (lower) panel exhibits the results obtained for the FS contribution μ=0 (μ=8). Rescattering matrix element is taken in the LFA (ISFA) for the right (left) part of each panel.

Fig. 5. Logarithm of the differential ionization rate of Xe, for the same laser parameters as in Fig. 4, presented in false colors in the electron momentum plane with the momentum expressed in units of the laser field vector potential amplitude A0. Results are obtained using the ISFA with only the rescattering amplitude and numerical integration. Classical cutoffs of the electron drift energy, calculated by the method used in Ref. [25], for some characteristic orbits are represented by black lines. They can be compared with the cutoffs inferred from Fig. 2.