Harmonic generation and phase matching in the tunnelling limit

Numerical calculations are presented of harmonic generation and phase matching in a rare-gas-like plasma. A simple model for the atomic dynamics is used, in which tunnelling ionization is assumed to be the dominant process. The nonlinear tunnelling current generates a series of odd harmonics of the fundamental radiation, which then propagate through the ionizing plasma. The use of a simple model for the atom makes it possible to solve the full time-dependent wave equation, and this allows direct investigation of phase matching effects due to free electrons. Such a treatment is necessary in the high-intensity, short-pulse limit, where conventional slowly-varying-envelope calculations are not valid. The authors investigate the pressure dependence of the generation efficiencies, and also observe blueshifting of the higher-order harmonics.