Absorption-limited and phase-matched high harmonic generation in the tight focusing regime

Abstract

High harmonic generation (HHG) at a high repetition rate requires tight focusing of the moderate peak power driving pulses. So far the conversion efficiencies that have been achieved in this regime are orders of magnitude behind the values that have been demonstrated with loose focusing of high energy (high peak power) lasers. In this contribution, we discuss the scaling laws for the main physical quantities of HHG and in particular analyze the limiting effects: dephasing, absorption and plasma defocusing. It turns out that phase-matched and absorption-limited HHG can be achieved even for very small focal spot sizes using a target gas provided with an adequately high density. Experimentally, we investigate HHG in a gas jet of argon, krypton and xenon. By analyzing the pressure dependence we are able to disentangle the dephasing and absorption effects and prove that the generated high order harmonics are phase-matched and absorption-limited. The obtained conversion efficiency is as high as 8 × 10 −6 for the 17th harmonic generated in xenon and 1.4 × 10 −6 for the 27th harmonic generated in argon. Our findings pave the way for highly efficient harmonic generation at megahertz repetition rates. New J. Phys. 16 (2014) 033022 J Rothhardt et al New J. Phys. 16 (2014) 033022 J Rothhardt et al 3 New J. Phys. 16 (2014) 033022 J Rothhardt et al New J. Phys. 16 (2014) 033022 J Rothhardt et al 5

Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources

“…For a better understanding of the phasematching conditions, the signal of the harmonics is studied with respect to the backing pressure, e.g., for the two strongest harmonics H21 and H23 ( Figure 3). As shown in Figure 3, the maximum signal is obtained at 1-1.2 bar, which is also in good agreement with the predictions of the scaling laws 10,11 . At these experimental conditions, well-defined harmonics with a Gaussian beam profile are generated ( Figure 4) as expected for phase-matched generation.…”

“…Further details on the calculation of the remaining terms are described elsewhere [9][10][11] . For the calculation a focal spot size radius of 11 mm (1/e 2 -intensity), an intensity of 7.4 3 10 13 W cm 22 and a Gaussian temporal envelope with a full width at half maximum duration of 30 fs are used.…”

“…The efficiency of the HHG process critically depends on the possibility of achieving phase-matching, i.e., matching the phase velocity of the driving laser field and the generated XUV field 9 . The phase-mismatch is determined by the dispersion of the neutral atoms and free electrons, the intrinsic phase due to the propagation of the free electron wave-packet as well as a geometrical term, which is caused by the Gouy phase-shift 10,11 . The dispersion terms (neutral atoms, free electrons) have opposite signs and are density dependent.…”

“…Indeed, the lack of phase-matching explains the poor efficiency of previous multi-MHz repetition rate sources that do not deliver more than a few 10 8 photons s -1 in a single harmonic 28,29 . However, investigations of the phase-matching behavior suggest that this can be overcome by properly choosing the experimental conditions, most notably a high-density gas target, to achieve the same pressure-length product as in loose focusing geometries 10,11 . Recent experiments have successfully demonstrated efficient conversion (8 3 10 26 ) in a tight focusing geometry 11 .…”

“…However, investigations of the phase-matching behavior suggest that this can be overcome by properly choosing the experimental conditions, most notably a high-density gas target, to achieve the same pressure-length product as in loose focusing geometries 10,11 . Recent experiments have successfully demonstrated efficient conversion (8 3 10 26 ) in a tight focusing geometry 11 .…”