High-order harmonic generation with μJ laser pulses at high repetition rates

Abstract

We investigate the generation of high-order harmonics using laser pulse energies in the few-μJ range at high repetition rates. We analyse how the conversion efficiency is influenced by the tight focusing geometry required for the generation of high-order harmonics under these conditions. A generalized phase-matching model allows us to discuss macroscopic phase effects independent of focal length. We present experimental results using the example of a 100 kHz laser system to generate harmonics up to the 27th order in Ar with a photon flux up to 3 × 10 9 photons s −1 into one harmonic order. High-repetition-rate femtosecond or even attosecond light sources open new possibilities for a broad range of applications such as time-resolved photoelectron spectroscopy and microscopy in the extreme ultraviolet regime.

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 .…”

Macroscopic scaling of high-order harmonics generated by two-color optimized waveforms in a hollow waveguide

“…However, their designed scaling was not achieved due to the limitation in pulse energy. Recently, a general scaling rule has been proposed [14,27,28], * Corresponding author: cjin@njust.edu.cn which identifies the invariance of HHG processes from the μJ-level multi-MHz high-repetition-rate lasers with tightly focused geometry to the loosely focused 100 mJ or Joule level pulses [29]. To obtain such scaling for nonlinear optical phenomena in gases [30], several macroscopic parameters, such as the medium length, beam diameter, focal length, and gas density, need to be appropriately scaled with input pulse energy.…”