Third-harmonic generation with ultrahigh-intensity laser pulses

When an intense, plane-polarized, laser pulse interacts with a plasma, the relativistic nonlinearities induce a third-harmonic polarization. A phase-locked growth of a third-harmonic wave can take place, but the difference between the nonlinear dispersion of the pump and driven waves leads to a rapid unlocking, resulting in a saturation. What become third-harmonic amplitude oscillations are identified here, and the nonlinear phase velocity and the renormalized electron mass due to plasmon screening are calculated. A simple phase-matching scheme, based on a resonant density modulation, is then proposed and analyzed.