Scaling of the generation of high-order harmonics in large gas media with focal length

We present theoretical and experimental results on high-order harmonic generation in a low-density few-centimeter-long gas medium (Lmed≤ 10 cm). We study the dependence with focal length of harmonic efficiency. Theoretically, we consider in detail the generation of the 25th harmonic of a short pulse Ti:sapphire laser in argon. Within the strong-field approximation for the atomic dipole, and a complete account of the macroscopic propagation, we compute the number of photons produced as a function of the medium parameters and the focusing conditions. The simulations show that, at constant intensity, the emission of the 25th harmonic scales with the focal length as ∼f4 at low pressure (P=2 Torr) and as ∼f6 at higher pressure (P=5 Torr). At constant laser energy, we find that the harmonic signal scales approximately as f2 at low pressure and as f4 at higher pressure. Those numerical results are compared with experimental data.