Controlled excitation gratings in cross-beam filament wake channels in a dense argon gas and their manifestation in hyperspectral Rabi sideband patterns

When two intense femtosecond laser beams intersect at a small angle, the resulting intensity modulation in the crossing region results in a structured filament channel with transverse periodic density modulation of ions and excited atoms. The formation of these finite gratings is strongly influenced by the beam profile, the crossing angle, and the inter-beam phase delay of the two pump beans. Specifically, the crossing angle controls the fringe width and spacing, the spatial and temporal beam profile mainly determines the total number of fringes, and inter-beam phase delay affects the symmetry of the grating structure through the shift of the periodic pattern with respect to the grating axis. The details of the transient grating formation can be probed by means of sideband Rabi emission induced by a picosecond probe pulse. This pulse, incident normally on the grating, couples to the excited state manifolds in the gas atoms, generating Rabi emission at the frequencies that are red- and blue-shifted around the carrier frequency. The emitted broadband radiation undergoes spatial and temporal interference, producing intricate spatial-spectral patterns on a distant screen. These hyperspectral patterns provide a powerful tool for characterizing complex beams in experiments. We explore how variations in the crossing angle and the pump beam profile influence the characteristics of the finite excitation gratings and the resulting Rabi sideband patterns, offering new insights into the control and optimization of laser-induced transient gratings for ultrafast optical applications.