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Above-threshold ionization (ATI) results from strong field laser-matterinteraction and it is one of the fundamental processes that may be used toextract electron structural and dynamical information about the atomic ormolecular target. Moreover, it can also be used to characterize the laser fielditself. Here, we develop an analytical description of ATI, which extends thetheoretical Strong Field Approximation (SFA), for both the direct andre-scattering transition amplitudes in atoms. From a non-local, but separablepotential, the bound-free dipole and the re-scattering transition matrixelements are analytically computed. In comparison with the standard approachesto the ATI process, our analytical derivation of the re-scattering matrixelements allows us to study directly how the re-scattering process depends onthe atomic target and laser pulse features -we can turn on and offcontributions having different physical origins or corresponding to differentphysical mechanisms. We compare SFA results with the full numerical solutionsof the time-dependent Schroedinger equation (TDSE) within the few-cycle pulseregime. Good agreement between our SFA and TDSE model is found for the ATIspectrum. Our model captures also the strong dependence of the photoelectronspectra on the carrier envelope phase of the laser field.

Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields