Atoms interacting with intense laser fields can emit electrons and photons of very high energies. An intuitive and quantitative explanation of these highly nonlinear processes can be found in terms of a generalization of classical Newtonian particle trajectories, the so-called quantum orbits. Very few quantum orbits are necessary to reproduce the experimental results. These orbits are clearly identified, thus opening the way for an efficient control as well as previously unknown applications of these processes.

We demonstrate that frequency-domain interferometry can be performed in the extreme ultraviolet range using high-order harmonics. We first show that two phase-locked harmonic sources delayed in time can be generated in the same medium despite ionization. This gives insight into the dynamics of the generation and ionization processes. We then apply the technique to the study of the temporal evolution of an ultrashort laser-produced plasma at the femtosecond time scale. PACS numbers: 42.65.Ky, 32.80.Rm Recently, high-order harmonic generation (HHG) has attracted considerable interest, not only as an intriguing and spectacular phenomenon, but also as a potential source presenting unique properties in the extreme ultraviolet (XUV) range. The two main characteristics of this radiation are the ultrashort pulse duration and the good coherence that are both unprecedented in this spectral region. The short pulse duration (down to a few tens of femtosecond) has been characterized [1-3] and is already used in atomic and molecular spectroscopy [4]. On the other hand, a number of experiments in the last few years have shown that good coherence properties could be obtained in some generating conditions [5][6][7][8] but no applications of this coherence have been performed yet. XUV interferometry, developed so far with x-ray lasers [9-12], would benefit a lot from the HHG properties. First, the tunability of the radiation allows one to adapt the wavelength to the probed medium, for example, far from resonances. In plasmas, different electron densities can be probed by changing the harmonic order, leading to a precise density mapping. Note that beside this coarse tunability, a fine adjustment of the wavelength can be obtained by generating the harmonics with a chirped laser [13] or with a laser mixed with an optical parametric amplifier [14]. Second, the ultrashort harmonic pulse duration is well adapted to the study of ultrafast processes, and could prevent, for example, the blurring of the fringes due to fast evolution of the density profile of a plasma close to the critical surface, as is the case when using x-ray lasers [9]. Finally, HHG is a tabletop XUV source, naturally synchronized with the generating laser at the same repetition rate (10 Hz to 1 kHz) allowing systematic experiments. In this work, we perform frequency-domain interferometry with high-order harmonics. We first demonstrate that the technique can be transposed to harmonics, and then apply it to probe the electron density of a laser-produced plasma in a high density gas jet with a femtosecond temporal resolution.Frequency-domain interferometry is now a widely used technique in the infrared for femtosecond time-resolved studies in solid-state and plasma physics [15][16][17]. It can be described as the temporal analog of the Young two-slit experiment [18]. In the latter, two spatially separated phase-locked sources lead to interferences in the far field after the beams have diffracted. In the former, two temporally separated phase-locked pulses interfere in ...

We have studied in detail the spatial coherence of the far field of the 13th harmonic from a Ti:sapphire laser generated in xenon, as a function of the generation parameters. Experimentally, we use Fresnel mirrors to produce two-dimensional interferograms. This technique allows us to probe the coherence at different scales dϭ1 -3 mm between the interfering rays, i.e., throughout the full section of the incident beam. A high uniform degree of mutual coherence ␥ d , larger than 0.5 in most cases, is measured as a function of the position of the jet relative to the focus, and pressure in the jet. It confirms the high intrinsic spatial coherence already reported for the extreme-ultraviolet harmonics, which is much larger than the one produced from x-ray lasers. Spatial coherence decreases when the laser focus is moved toward the jet, and when the pressure is increased: the onset of ionization, as well as the intensity-dependent phase of the nonlinear polarization, are rapidly varying factors in time and space which degrade the correlation between the fields at two different points. Simulation of the coherence degree emphasizes the role of the intensity-dependent phase in the evolution of the coherence degree.