7-fs-pulses with 0.3 mJ are obtained after filamentation in argon and compression by double-chirped-mirrors. These pulses are used to generate high-order harmonics in a semi-infinite gas cell in different noble gases. Spectral broadening of high-order harmonics in xenon and argon is observed. In neon, an extended continuous cut-off region down to 10 nm (124 eV) is observed which is to the best of our knowledge the highest cut-off energy obtained by filamented pulses. Our result suggests the feasibility of single attosecond-pulse-generation at both high photon flux and high cut-off energy.
© 2009 Optical Society of America
The emergence of isolated attosecond pulses opened up very new perspectives for the study of electron dynamics in atoms and molecules. While a train of attosecond pulses is emitted from multi-cycle pulses during high-order harmonic generation (HHG), isolated attosecond pulses are generated by few or single-cycle pulses . Different setups have been realized to produce few-cycle infrared pulses, as for example spectral broadening and pulse re-compression in a gas filled hollow fiber . However, hollow fibers are limited by a maximal through-put pulse energy. An alternative technique with promising energy scaling potential is based on non-linear effects during the filamentation process in a cell filled with noble gases . The realization is straightforward, but at the output the spectral broadening behind the filament is not homogeneous across the spatial beam profile. Due to conical emission and non-filamented parts of the beam , the shortest pulse durations along the beam profile are only found in the white light core in the center of the beam profile, and care has to be taken to screen the outer parts. Based on simulations [5, 6], it is then possible to generate isolated attosecond pulses by HHG. In  the generation of high-order harmonics up to 50 eV from filamented pulses was demonstrated. To the best of our knowledge, however, with few-cycle pulses from filaments HHG has never reached the spectral regime beyond 90 eV where the generation of isolated attosecond pulses has been demonstrated .
In the present paper, we report on HHG in a semi-infinite gas cell in different noble gases using compressed ultra-short pulses from a filament. High-order harmonics are generated in neon with a cut-off in the 10 nm-range, reproducible on a day-to-day basis. The spectral broadening of the harmonics and the spectral position of the cut-off is investigated by controlling the dispersion. Due to the potential energy scaling of the filamentation process by using gas with low non-linear refractive index or more advanced techniques , this approach opens up new possibilities for cut-off extension and high-energy single attosecond pulses.
2. Experimental setup
For HHG with pulses from filaments we use a chirped-pulse-amplification system (Dragon, KMLabs Inc.) delivering 30-fs-pulses centered at 776 nm with energies of 1.2 mJ at a repetition rate of 3 kHz. The system is not stabilized regarding the carrier-envelope phase. These pulses are spectrally broadened and subsequently compressed in a filamentation-setup shown in Fig. 1 . With a curved silver mirror (R=-4000 mm) the pulses are focused into a 2 m long gas cell filled with 450 mbar argon. Entrance and exit windows are 1 mm-CaF2-plates in Brewsters angle arrangements. In order to generate a stable single filament, an aperture (7 mm of diameter) is placed before the focusing-mirror transmitting about 0.85 mJ.
A second aperture (3 mm of diameter) is used behind the exit to select the white light core, and discriminate the non-filamented radiation and conical emission . After the filament the pulses are focused via a 4 mm-thick (quartz)-lens with 500 mm focal length through a 2 mm-CaF2-window into the high-harmonic chamber. A pair of double-chirped mirrors (DCM)  compensating the influence of the lens and the entrance window allows for adjustment to zero chirp in the HHG-chamber. Zero chirp is realized by eight reflections at the DCM’s which corresponds to a group delay dispersion (GDD) of about -560 fs2. Our high-harmonic chamber is designed in a semi-infinite gas cell geometry (see inset in Fig. 1) [12, 13], where the entrance window is far away from the interaction region defined by the focal area. The gas cell is filled with noble gases for HHG. Due to the large interaction range and the straight-forward setup, the semi-infinite gas cell is a promising tool for HHG with a high photon flux  without the need for accurate alignment. An abrupt transition to vacuum for absorption-less propagation of the generated radiation is assured by a pinhole in a metal-plate used as a differential pumping stage which is self-drilled by the laser before the experiment. We place the focus within the gas cell about 1 cm in front of the pinhole for phase-matching of the cut-off-harmonics . The generated harmonic signal is spectrally resolved in a grazing incidence spectrometer (LHT 30, Horiba-Jobin-Yvon, 500 lines/mm).
3. Experimental results
The pulses after filament and DCM’s contain about 0.3 mJ of energy and are characterized with a SPIDER-setup  supporting the measurement of few-cycle pulses. The pulse spectrum with a Fourier limit of 5.2 fs and the measured phase are shown in Fig. 2(a). From this data we reconstruct an upper limit of 7.0 fs for the compressed pulse duration (Fig. 2(b)). Note that dispersion compensation by the DCM’s is limited to wavelengths from 550 to 1200 nm exploiting not the full spectral range of the filamented pulse. Mirrors with advanced multi-layer optics designs  covering the full spectral bandwidth after the filament from 400 to 900 nm  would provide potential for future optimization.
Using the characterized filament pulses, high-order harmonics are generated in different noble gases with different ionization potentials. Fig. 3(a) shows the harmonic spectrum in 5 mbar xenon for compressed filamented pulses. For comparison, a harmonic spectrum from non-filamented 30-fs-pulses directly from the amplifier at comparable intensity is illustrated. Using 7.0-fs-pulses from the filament, spectral broadening of the harmonics is clearly visible, whereas a discrete structure of the harmonics is observed with non-filamented pulses.
The harmonic spectra produced in argon are shown in Fig. 3(b). The spectral broadening of the harmonics is observable as well. Due to the higher ionization potential the cut-off extends to smaller wavelengths.
We observed the broadest continuum at high cut-off energies in harmonic spectra generated in neon. Fig. 4 shows the measured spectra obtained in 40 mbar neon. The high ionization potential of neon allows for a cut-off around 10 nm. Our pulses from the filamentation are short enough to generate broadband continuum radiation. Modifying the re-compression setup we can demonstrate the effect of longer pulses on the cut-off and the discrete nature of the harmonic emission. In order to elongate the pulses, we decrease the number of reflections at the DCM’s by two for positive chirp with +140 fs2. Analogous, the number of reflections are increased by two to achieve negatively chirped pulses. The spectra from longer pulses exhibit a discrete peak structure with reduced cut-off and are shown in green and blue in Fig. 4. The decrease in the cut-off energy can be explained by a lower peak power for elongated pulses at constant pulse energy.
In conclusion, we have shown high-order harmonics generated with ultra-short pulses from a filament. The results are well reproducible and stable. The observed pulse energy and duration results in high-order harmonic generation in neon with a cut-off up to 10 nm corresponding to 124 eV. This represents an extension of the HHG cut-off energy of more than 70 eV compared to previous results  via filaments and proves the suitability of this scheme for the generation of high energy few-cycle pulses. The present setup is limited by the bandwidth of the DCM’s. Thus, optimizing the spectral properties of the DCM’s would allow for even shorter-pulses in the single-cycle regime.
Single attosecond pulses via few-cycle-pulses from filamentation are now in reach employing multi-layer mirrors available in the EUV-spectral region filtering only the continuous part of the cut-off region. Due to to the promising energy scaling properties of the filamentation process higher photon and pulse energies in isolated attosecond pulses become feasible. Assuming a mirror covering 28 eV of bandwidth , our spectrum would correspond to an isolated attosecond pulse with Fourier-limit below 80 as.
The authors like to thank Manfred Lein, and Thorsten Uphues for fruitful discussions. This work was funded by Deutsche Forschungsgemeinschaft within the Cluster of Excellence QUEST, Centre for Quantum Engineering and Space-Time Research.
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