First-order strong field approximation for high-order harmonic generation

Recently it was shown [A. Gordon and F. X. Kaertner, Phys. Rev. Lett. 95, 223901 (2005)] that the strong field approximation (SFA) for high-order harmonic generation (HHG) is significantly improved when the SFA wave function is used with the acceleration rather than the length form of the dipole operator. In this work it is shown that using the acceleration form upgrades the SFA from zeroth-order to first-order accuracy in the binding potential. The first-order correct three-step model (1st-order TSM) obtained thereby is systematically compared to its standard zeroth-order counterpart (0th-order TSM) and it is found that they differ significantly even for energetic electrons. For molecules (in the single-electron approximation), the 0th-order and the 1st-order TSMs in general disagree about the connection between the orbital symmetry and the positions of the minima in the HHG spectrum. At last, we briefly comment on gauge and translation invariance issues of the SFA.