Nonperturbative quantum electrodynamics theory of high-order harmonic generation

Using a formal scattering theoretical approach, we develop a nonperturbative quantum electrodynamics theory to describe high-order harmonic generation (HHG). This approach recovers the semiclassical interpretation that HHG results from the recombination of photoelectrons, ionized by the laser field, with the parent ions, and gives the same phenomenological cutoff law. The HHG emission rate is expressed as an analytic closed form. We also discuss the connection between HHG and the above threshold ionization from the formal scattering viewpoint.