Influence of initial tunneling step on the return energy of high-order harmonic generation

To investigate high-order harmonic generation in a monochromatic laser field, we derive an analytical expression for the return energy of an electron as a function of the time interval between ionization and return. We then expand the expression for kinetic energy to second order with respect to the Keldysh parameter.. In this expansion, the zero-order term is the return energy in the simple man model and the second-order term corresponds to corrections to this model. The origin of this additional kinetic energy is frequently attributed to the nonzero exit of the initial tunneling step. Here, we show that this commonly used picture is incomplete. We present a framework to fully understand the additional kinetic energy as resulting from additive contributions of zero-order and second-order velocities. Our results show that the nonzero velocity of the initial tunneling step has a quantifiable effect on the cutoff energy measured in high harmonic generation (HHG). This opens the door to experimentally addressing the question of the initial electron velocity at the tunnel exit, with important implications for the correct calibration of the attoclock, as well as our interpretation of the strong field-ionization process more broadly.