Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime

We describe a very simple physical model that allows the analysis of high-order harmonic generation in gases when the pumping laser beam has an intensity profile that is not Gaussian but truncated Bessel. This is the typical experimental condition when sub-10-fs pump-laser pulses, generated by the hollow fiber compression technique, are used. This model is based on the analysis of the phase-matching conditions for the harmonic generation process revisited in view of the new spatial mode of the fundamental beam. In particular, the role of the atomic dipole phase and the geometric phase terms are evidenced both for harmonics generated in the plateau and in the cutoff spectral regions. The influence of dispersion introduced by free electrons produced by laser ionization has also been discussed in some detail. Spatial patterns of far-field harmonics are then obtained by means of a simplified algorithm which allows one to avoid the numerical integration of the harmonic beam propagation equation. Experimental spatial distributions and divergence angles of high-order harmonics generated in Ne with 7-fs titanium-sapphire pulses are compared with numerical simulations in various experimental conditions. The agreement between measurements and calculated results is found to be very satisfactory.