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

Abstract

We present theoretical and experimental results on high-order harmonic generation in a low-density few-centimeter-long gas medium (${L}_{\mathrm{med}}\ensuremath{\leqslant}$ 10 cm). We study the dependence with focal length of harmonic efficiency. Theoretically, we consider in detail the generation of the $25\mathrm{th}$ 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 $25\mathrm{th}$ harmonic scales with the focal length as $\ensuremath{\sim}$$f$${}^{4}$ at low pressure ($P=2$ Torr) and as $\ensuremath{\sim}$$f$${}^{6}$ at higher pressure ($P=5$ Torr). At constant laser energy, we find that the harmonic signal scales approximately as $f$${}^{2}$ at low pressure and as $f$${}^{4}$ at higher pressure. Those numerical results are compared with experimental data.