Transverse Electromagnetic Mode Conversion for High-Harmonic Self-Probing Spectroscopy

We report on high-order harmonic (HHG) two-source interferometry (TSI) in molecular gases. We used a 0-\(\pi\) phase plate to create two bright spots at the focus of a lens by converting a Gaussian laser beam into a TEM please define \(_{01}\) Transverse Electromagnetic Mode. The two bright foci produce two synchronized HHG sources. One of them is used to probe on-going dynamics in the generating medium, while the other serves to heterodyne the signal. The interference of the emissions in the far-field gives access to the phase difference between the two sources. In self-probing HHG phase spectroscopy, one of the two sources is used as a reference while the other one probes some on goin dynamics in the generating medium. We first compute overlap integrals to investigate the mode conversion efficiency. We then establish a clear relation between the laser phase-front curvature and the far-field overlap of the two HHG beams. Both Fresnel diffraction calculations and an experimental lens position scan are used to reveal variations of the phase front inclination in each source. We show that this arrangement offers \(\frac{\lambda_{XUV}}{100}\) precision, enabling extremely sensitive phase measurements. Finally, we use this compact setup for TSI and measure phase variations across the molecular alignment revival of nitrogen and in vibrating sulfur hexafluoride. In both gases, the phase variations change sign around the ionization threshold of the investigated molecule.