Quantum-mechanical model for ultrahigh-order harmonic generation in the moderately relativistic regime

A quantum theory of ultrahigh-order harmonic generation is presented that generalizes the Lewenstein model into the relativistic regime. Various effects appear in the harmonic spectrum: a multiplateau structure in the weakly relativistic case; for stronger fields, the interference pattern familiar from the nonrelativistic case disappears, the height of the plateau decreases towards high harmonic orders, and the cutoff is lower compared to the nonrelativistic case. All of these features are explained in terms of relativistic quantum trajectories.