The Ultimate Energy Limit of HHG and Strong Field Rescattering

Recollision for a laser driven atomic system is investigated in the non-relativistic to relativistic regime via a strong field quantum description and Monte Carlo semi-classical approach. We find the relativistic recollision energy cutoff is independent of the ponderomotive potential $U_p$, in contrast to the well-known 3.2~$U_p$ scaling. The relativistic recollision energy cutoff is determined by the ionization potential of the atomic system and achievable with non-negligible recollision flux before entering a ``rescattering free'' interaction. The ultimate energy cutoff is limited by the available intensities of short wavelength lasers and cannot exceed a few thousand Hartree. This end to rescattering physics, which begins at 1,000 Hartree (27,000 eV,) sets the energy boundary for HHG and recollision based attosecond physics.