Coulomb and polarization effects in sub-cycle dynamics of strong-field ionization

We discuss the sub-cycle dynamics of strong-field ionization by an intense few-cycle laser pulse. Even at high intensities when all the excited states are embedded into the continuum, the dynamics are found to be strongly dependent both on the presence or absence of excited states in the field-free potential and on the structure of the continuum. Both Coulomb effects in the continuum and polarization of the initial state are important even for qualitative description of sub-cycle ionization. We show how to consistently include effects of the binding (Coulomb) potential on the continuum part of the electron wavefunction while retaining the effects of the laser field on the bound part. We demonstrate quantitative accuracy of our approach in the barrier-suppression region of laser intensities.