Phase-shift control of the Rabi sideband emission from excitation gratings in cross-beam filament wake channels in a dense argon gas*

When femtosecond laser filamentation happens in a dense gas at the crossing of two laser beams, the intensity modulation in the crossing area leads to the formation of finite density gratings of ions and excited atoms. The resulting excitation grating can be controlled by the parameters of the crossing laser pulses, specifically, by the crossing angle and the inter-beam phase delay. The variation in the latter parameter has a prominent effect on the grating structure, which is especially pronounced when the crossing angle is small. Addressing the case of high-pressure argon gas, we explore theoretically the excitation grating formation and show the quantitative relation between the positions of the grating maxima and the inter-beam phase delay. If a picosecond probe pulse is incident normally on thus produced excitation gratings, the electric field of the probe pulse couples the excited state manifolds, resulting in Rabi sideband emission at frequencies red-shifted and blue-shifted about the probe carrier frequency. This emitted radiation participates in spatial and temporal interference and generates complicated spatial-spectral interference patterns on a remote screen. We investigate how these patterns are considerably modified in response to variations in the phase delay between the grating-generating crossing beams.