Propagation effects in resonant high-harmonic generation and high-order frequency mixing in laser plasma

We study the phase matching of resonant high-harmonic generation (HHG) and high-order frequency mixing (HFM) in plasma. We solve numerically the propagation equations coupled with the time-dependent Schr\"odinger equation for the nonlinear polarisation. The macroscopic harmonic signal is enhanced in the vicinity of a multiphoton resonance with the transition between the ground and autoionising states of the generating ion. We show that narrow and strong resonances (as for gallium and indium ions) provide compensation of the plasma dispersion in a spectral region above the exact resonance improving the phase matching and leading to a high macroscopic signal. The compensation does not take place for a wider resonance (as for manganese ions), instead the phase matching is achieved in the HFM process. Comparing the XUV generated in manganese plasma and in neon gas, we show that the resonant HHG in plasma is an order of magnitude more effective than in the gas, moreover another order of magnitude can be gained from the propagation using HFM in plasma.