Phase of harmonics from strongly driven two-level atoms

Harmonic generation is studied in an idealized model medium in which the laser field essentially interacts only with a single atomic transition and where ionization can be neglected. Such two-level models are known to generate high harmonics with a plateau and a cutoff. We put forward a quantitative rule for the cutoff frequency in the harmonic spectrum in this model which we relate to the ``${\mathrm{I}}_{\mathrm{P}}$+${3\mathrm{U}}_{\mathrm{P}}$ rule'' in real systems with ionization. We examine the phase properties of the emitted harmonics and show that their coherence and thus phase matching is more favorable in the cutoff regime than in the plateau of the harmonic spectrum. This behavior is known to occur in realistic models of neon, and that this occurs also for the simple idealized two-level model strongly suggests that the sudden change of phase coherence from the cutoff to the plateau regime is as intrinsic a property of nonlinear systems as are the plateau and the cutoff.