Generation and optimization of high order harmonics carrying an orbital angular momentum to seed a soft X-Ray Plasma

This document presents the CIFRE/Amplitude Laser thesis work carried out to set up on the LASERIX XUV line an experiment of high harmonic generation by a pump infrared beam carrying a non-zero orbital angular momentum produced by adding a phase plate on the beam path. The originality of our approach was to generate the harmonics in a relatively long gas cell (around 10 mm) and to characterize the optical vortices of harmonic 25 by a Extreme Ultraviolet Hartmann. We demonstrated that the sensitivity of the detector and the reliability of the software processing of the data made it possible to verify that harmonic 25 typically carries an orbital angular momentum of 25, as theoretically predicted. Further analysis of the experimental data allowed us to quantitatively demonstrate the intrinsically multimode nature of the produced beams. I have therefore detailed the different methods of analysis proposed in the literature, I could compare their reliability and their relevance to describe the physical phenomenon at work. I also studied in detail the robustness and convergence of the analytical methods applied to beams with typical orbital angular momenta as high as l = 25. The analysis of the data allowed me to show the role of even very weak residual astigmatism contained in the pump infrared beam to produce the bilobal shape of the vortices. This characteristic shape was also obtained by other teams. One way to regain a truly annular shape is to set up an active optimization loop of the pump laser wavefront. I have also developed propagation and diffraction calculations of beams carrying non-zero orbital angular momenta, whether in EUV or infrared. This allowed me to quantify the multimode character, in terms of LG modes, of the infrared beams passing through a phase plate that was first assumed to be perfect, then real. Then I showed using the single atom model for harmonic generation that this non-linear, non-perturbative process intrinsically induced new radial LG modes. Finally, the objective of all this work for the LASERIX team was to demonstrate the ability of an X-ray laser amplifier plasma pumped from a solid target to amplify a harmonic vortex at the right wavelength, while maintaining its modal structure and in any case the charge carried by the beam. A collaboration with Eduardo Oliva from Madrid, who carries out Maxwell Bloch simulations, shows that this is possible from the point of view of the fundamental physics of the amplification in this wavelength range. (author)