The interaction of an intense laser pulse of short duration with a rare gas induces a highly non-linear polarization in the XUV spectral range: the high order harmonics. Due to the specific properties of the harmonic radiation and its applications, this issue is particularly rich and fertile. The efficient production of high order harmonics is based both on the non-linear response of the single atom and on collective behavior.The principle of the research presented in this thesis is the understanding and control of phase matching or quasi-phase matching in the presence of substantial ionization in the generating gas. In this context, we show the importance of the coherence length on the phase matching in High harmonic generation. We study its dependence on laser focusing, pressure but also its time dependence related to ionization. Moreover, experiments and simulations aim at extending harmonic spectra towards shorter wavelengths, a spectral range for which the X Ray Laser is emitted. This will give access to a source with complementary characteristics as regards to X-ray lasers. This source shall be developed in parallel on the LASERIX station or injected in soft X-ray laser amplifiers.
