Cut-off scaling of high-harmonic generation driven by

Home

Search

Collections

Journals

About

Contact us

My IOPscience

Cut-off scaling of high-harmonic generation driven by a femtosecond visible optical parametric amplifier

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2012 J. Phys. B: At. Mol. Opt. Phys. 45 205601 (http://iopscience.iop.org/0953-4075/45/20/205601) View the table of contents for this issue, or go to the journal homepage for more

Download details: IP Address: 180.250.82.188 This content was downloaded on 15/10/2013 at 23:22

Please note that terms and conditions apply.

OPEN ACCESS IOP PUBLISHING

JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS

doi:10.1088/0953-4075/45/20/205601

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 205601 (10pp)

Cut-off scaling of high-harmonic generation driven by a femtosecond visible optical parametric amplifier Giovanni Cirmi 1,2 , Chien-Jen Lai 1 , Eduardo Granados 1,3 , Shu-Wei Huang 1 , Alexander Sell 1 , Kyung-Han Hong 1 , Jeffrey Moses 1 , Phillip Keathley 1 and Franz X K¨artner 1,2 1

Department of Electrical Engineering and Computer Science and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 2 Center for Free-Electron Laser Science, DESY and University of Hamburg, Notkestraße 85, D-22607 Hamburg, Germany 3 IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain E-mail: [email protected]

Received 30 May 2012, in final form 24 July 2012 Published 12 September 2012 Online at stacks.iop.org/JPhysB/45/205601 Abstract We studied high-harmonic generation (HHG) in Ar, Ne and He gas jets using a broadly tunable, high-energy optical parametric amplifier (OPA) in the visible wavelength range. We optimized the noncollinear OPA to deliver tunable, femtosecond pulses with 200–500 μJ energy at the 1 kHz repetition rate with excellent spatiotemporal properties, suitable for HHG experiments. By tuning the central wavelength of the OPA while keeping other parameters (energy, duration and beam size) constant, we experimentally studied the scaling law of cut-off energy with the driver wavelength in helium. Our measurements show a λ1.7 + 0.2 dependence of the HHG cut-off photon energy over the full visible range in agreement with previous experiments of near- and mid-IR wavelengths. By tuning the central wavelength of the driver source, the high-order harmonic spectra in the extreme ultraviolet cover the full range of photon energy between ∼25 and ∼100 eV. Due to the high coherence intrinsic in HHG, as well as the broad and continuous tunability in the extreme UV range, a high energy, high repetition rate version of this source might be an ideal seed for free electron lasers. (Some figures may appear in colour only in the online journal)

1. Introduction

and imaging experiments. FELs typically operate by selfamplified spontaneous emission, which inevitably contributes to the poor coherence, pulse-to-pulse timing jitter and poor electric field reproducibility of the output pulses, limiting the time resolution in pump-probe experiments to around 100 fs [11]. In order to improve their coherence and stability, there has been much recent interest [12–17] in the direct seeding of high photon flux EUV sources with high-harmonic generation (HHG) in noble gases, due to their excellent temporal and spatial coherence. Pulse energies in the nJ range [18] are required to effectively seed FELs in the tens of eV photon energy range to overcome spontaneous emission and transfer the beneficial HHG coherence properties to the FEL output light. In addition, x-ray FELs can be seeded in the

Coherent extreme ultraviolet (EUV) sources are of increasing importance in the scientific community because of their numerous scientific [1–5] and industrial [6] applications. Several types of laser-like sources have been developed in the EUV spectral range, such as plasma-based EUV sources [7], using both gas [8] and solid targets [9], and free electron lasers (FELs) [10]. FELs in particular are revolutionary light sources due to their very high photon flux allowing for pump-probe Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 0953-4075/12/205601+10$33.00

1

© 2012 IOP Publishing Ltd

Printed in the UK & the USA

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 205601

G Cirmi et al

hard x-ray range by a coherent EUV source via cascade upconversion processes in undulators based on high-gain harmonic generation [19]. In recent years, the wavelength scaling of cut-off energy and conversion efficiency of HHG has been extensively studied with long-wavelength pulses in the infrared region [20–23], mainly because it is beneficial to extend the cut-off energy of the produced harmonics. However, the HHG efficiency dramatically decreases for longer driver wavelengths. The single-atom efficiency scales with the driver wavelengths as λ−(5–6) [24–26], and the total efficiency that takes propagation and phase matching into account decreases even more rapidly as λ−(8–10) [27] because phase matching becomes more difficult for longer driver wavelengths. Therefore, the long-wavelength IR drivers are not a good choice for HHG in the range of low photon energy, i.e. the EUV range (25%. A 30% fraction of the energy though is lost in the second compressor, mainly due to the multiple bounces on folding mirrors. The second scheme consists of only a single SF10 prism pair after the first stage (6.9 cm of prism separation), and no further compressor at the output. With the last scheme we produced less OPA output energy, but had no additional losses in the following beam path. As a result, the second scheme was overall more efficient, except for the shortest wavelength pulses. The OPA output spectra for the two aforementioned cases are shown in figure 3 (panel (a): S1–S4 for FS compressor, panel (b): S5–S9 for SF10 compressor) together with the final energies after compression, and the measured and transformlimited pulse durations. We also show the normalized WLC spectrum as a dashed line. SF10, the prism material used in the compressor scheme 2 (S5–S9), has higher third-order dispersion (TOD) compared to the FS used in the compressor scheme 1 based on two prism pairs (S1–S4). For pulse durations of >30 fs TOD does not play an important role.

We measured the pulse duration with a background free autocorrelator based on self-diffraction using a 150 μmlong BBO crystal [44]. When we employed two compressors (compressor scheme 1, FS, with spectra in figure 3(a)), we had large variations in the pulse duration between 26 and 71 fs due to difficulties in the compressor alignment. For the compression scheme 2 based on one SF10 prism pair, we were more successful in keeping a constant duration between 34 and 46 fs. In most cases, we were able to compress the pulses close to their transform limit. Figure 4 shows an autocorrelation trace (dots: experimental points, line: Gaussian fit) of the pulse at 470 nm using the compression scheme 1 (FS) and another at 590 nm using compression scheme 2 (SF10). The corresponding spectra from figure 3 are shown in the two insets, and the corresponding pulse durations are indicated in full-width at half-maximum (FWHM). Note that the decorrelation factor for a self-diffraction autocorrelation is 1.22 because of the third-order nonlinear process involved. By blocking the WLC seed, the OPA signal energy drops to 1% of its seeded value, showing excellent superfluorescence suppression. This measurement gives the upper limit of the superfluorescence power. The rms fluctuations of the OPA signal energy are less than 2.5% measured over 9 min. The quality of the beam is also good, as shown in figure 5, where we measured an M2 parameter of 1.9. Good beam quality is mandatory to reach a laser intensity necessary for HHG experiments. We did not observe a significant angular chirp in the beam, which would be deleterious for the HHG experiments. 4

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 205601

G Cirmi et al

(a)

(b)

Figure 4. Self-diffraction background-free autocorrelation of: (a) the pulse at 470 nm (spectrum S1 from figure 3(a), repeated in the inset), corresponding to a 44 fs FWHM pulse duration; (b) the pulse at 590 nm (spectrum S7 from figure 3(b), repeated in the inset), corresponding to a 34 fs FWHM pulse duration. Lines: Gaussian fits; circles: experimental points.

(20–70 eV), or a 500 nm-thick Be filter allowing ∼20% transmission between 50 and 110 eV. We magnified the photodiode signal with a low-noise amplifier to significantly improve the detection sensitivity. To acquire the HHG spectra, we collected the high-harmonic beam with a toroidal mirror, and imaged it onto the slit of the EUV spectrometer [23]. We recorded the spectra with a microchannel plate backed by a phosphor screen followed by a thermo-electrically cooled visible charge-coupled device (CCD). For the experimental study on the cut-off energy, we changed the central wavelength of the OPA while keeping other characteristics as constant as possible, and measured the cut-off energy versus driver wavelength. We kept roughly constant energies, intensities and spot sizes (measured with the knife edge method at the gas jet position) for all four drivers. We focused the study on helium gas because its high ionization potential allows the highest cut-off energy among all gases. We drove HHG with the OPA tuned at three different central wavelengths, obtained with the SF10-based compression scheme (figure 3(b)), and drove HHG also with the light at 400 nm from the second harmonic of the Ti:sapphire laser. We controlled the spot size with an iris at fixed aperture before the vacuum chamber and focused the pulses into the gas jet (gas pressure: 50 mbar, backing pressure: 3 bar), with the parameters summarized in table 1. Figure 7 shows the experimental data as green squares, while the blue dashed line showing the linear fitting curve in logarithmic scale (λ1.7 ± 0.2), which stays within the range of the phase-matched cut-off relation (λ1.4–1.7) observed in the infrared region [33]. The absolute value of the cut-off energy is not optimized due to the low energy of the OPA driver pulses. The pulse energy available at the gas jet was about 120 μJ, and we needed to focus the OPA pulses tightly ( f = 100 mm) to reach an intensity high enough to observe an HHG signal. Such a tight focus has the drawback of poor phase matching due to the Gouy phase and limited interaction volume with the medium. To show the cut-off energy improvement with higher pulse energies [45, 46], we numerically studied HHG by solving

Figure 5. CCD image of OPA output beam focused with an f = 250 mm lens indicating the FWHM beam diameters in x and y direction, and the M2 value.

3. HHG cut-off energy scaling The visible OPA described in section 2 allowed studying the impact of drive wavelength on the cut-off energy extension of HHG. This study is necessary for building an optimized seed source for FELs. As previously discussed, driving HHG with visible pulses is beneficial to the conversion efficiency at the expense of the cut-off energy extension. The cut-off scaling law in the visible range was never explored experimentally, as we pursue in this work. In the HHG experiments, we focused the OPA beam into gas jets of different gases (Ar, Ne and He), and measured the total HHG output signal and its spectrum. Figure 6 shows the photographs of the HHG setup illuminated by each colour from the tunable visible OPA system. The schematic of the setup is shown in figure 1. We measured the HHG signal and efficiency with a highly sensitive Al-coated EUV calibrated photodiode (AXUV100, IRD, Inc.). We used different EUV filters to separate the driver pulse from the harmonics: a 500 nm-thick Al filter allowing ∼20% transmission over the Al transmission window 5

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 205601

G Cirmi et al

(a)

(b)

(c)

(d)

Figure 6. Pictures of the OPA setup when operated at the different OPA colours in the HHG chamber ((a) S1, 470 nm; (b) S2, 530 nm; (c) S3, 590 nm; (d) S4, 620 nm; colour online only); vis: visible OPA driver. Table 1. Driver pulse characteristics for cut-off scaling study. Driver wavelength (nm)

Duration FWHM (fs)

Size at focus (μm × μm)

400 524 (S6) 589 (S7) 618 (S8)

26 39 34 46

26 23 24 20

× × × ×

26 16 12 13

the 3D propagation of the driver pulse [47] with the threestep model HHG [24]. Figure 7 shows also a simulation of the cut-off energy under the experimental conditions (black triangles and connecting line) and one with the saturation of the cut-off energy, occurring with a few mJ driver energies (red circles and connecting line). Both in the experiments and in the simulations we considered as cut-off energy the photon energy at which the signal drops by one order of magnitude with respect to the plateau region. The simulations show that with more pulse energy than possible with the current OPA, one could reach higher cut-off energies. This happens because one could use higher peak intensities without focusing the driver pulses tightly. Phase matching, which is particularly critical for higher energy photons, also becomes easier with looser focusing due to a lower Guoy phase. In our earlier measurement with higher pulse energy (1 mJ) of 400 nm driver [31], we were able to reach experimentally a cut-off at 71 eV. In this work, we investigated the cut-off scaling of HHG driven by a continuously tunable OPA at low pump energy. Due to the low driver energy, we observed only a 10−9 visible-to-EUV conversion efficiency per harmonic order in the plateau region, corresponding to ∼104 photons/shot at 100 eV, from the 589 nm driver wavelength. To show the improvement in efficiency with higher pulse energies, we simulated the efficiency for three different He gas jet

Energy (μJ)

Intensity (×1014 W cm−2)

121 127 119 119

4.4 5.6 7.7 6.3

pressures, as shown in figure 8. In the simulation, we compared the total efficiency between 80 and 90 eV for a 589 nm driver pulse. The pulse duration is the same as in the experiments, 34 fs, and we fixed the peak intensity to 7.7 × 1014 W cm−2 (corresponding to the experimental value) by changing the beam size accordingly. Figure 8 shows that, as the pulse energy increases from 120 μJ to a few mJs, the simulated efficiency improves by two or three order of magnitude due to the loose focusing and the longer interaction length (up to 10−(6–7) in the example considered here). Before reaching the asymptotic value, the efficiency curves show some oscillatory behaviour due to phase matching. Further optimization of the gas jet position in the simulation may result in efficiencies higher than those shown in figure 8, but this does not affect the main conclusion that a looser focusing can help phase matching and give an improvement by a few orders of magnitude. Previous simulations [24] predicted even higher efficiencies in the range of 10−(4–6). The difference can be explained because the simulations in [24] considered 1D propagation and an ideal case with perfect phase matching and infinitely long interaction lengths, while in this paper, we consider 3D propagation and a 2 mm interaction length, which we estimate to be the same as in the experiments. Despite this increased efficiency one would still need multi-mJ driver energies to reach a nJ EUV energy in order 6

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 205601

G Cirmi et al

Figure 7. Cut-off energy versus driver wavelength in helium. Green squares: experimental data; blue dashed line: linear fit in logarithmic scale; black triangles: simulation under the experimental conditions; red circles: simulations under cut-off saturation conditions.

Figure 8. The calculated HHG efficiencies in helium for different driver pulse energies and different pressure values shows that one can improve the efficiency by 2–3 orders of magnitude by using more energetic drivers.

to seed an FEL [18]. Hundreds of μJs through mJ could be enough in the case of shorter driver wavelengths, due to the favourable efficiency scaling (λ−(5–6)), at the expense of a slightly lower cut-off energy. The necessary energy could be further reduced by using more efficient gases, like argon, again at the expense of lower cut-off energy. In addition to the energy requirements, repetition rates as high as 100 kHz–1 MHz are desired to match future FEL repetition rates [48]. These requirements would be too restrictive for an OPA scheme, and one should use an optical parametric chirped pulse amplifier (OPCPA). Scaling to mJ energies, even at higher repetition rates, seems to be possible by using Yb-pump laser technology [49, 50].

with an iris before the chamber controls the intensity at the focus in the chamber and with it the ionization level and phase matching. For the cases of neon and helium, we used the full beam to maximize the delivered pulse energy. The HHG spectra show a broad continuous tunability, allowing for the production of any photon energy between 25 and 100 eV. The tuning range of the nth-order harmonic is larger than two times the central frequency of the driver pulse, which is the spectral gap between two consecutive harmonics. For example, figure 9(a) shows that the 13th-order harmonic peak is found to be tunable up to ∼8 eV, which is > 3 × 2.5 eV (2.5 eV is the photon energy for 490 nm). Note that in the region 80–100 eV the tunability is limited to ∼2 times the driver’s central frequency because only the long wavelength OPA drivers allow for the production of these photon energies. This still allows for full tunability because the harmonic peaks are closer for longer driver wavelengths. We exploited the HHG tunability by adjusting the OPA central wavelength (i.e. by changing only the birefringent phase-matching angles and the delays of the three OPA stages), the target gases and the focusing lenses. This is similar to what has been done with an infrared driver [44, 52–54]. Compared to the continuum-like EUV generation covering broad bandwidths when using long wavelength drivers, the strong high-order harmonic structure observed here with visible drivers is more advantageous in terms of the amount of energy concentrated in one harmonic as long as the tunability is sufficiently maintained. Therefore, due to the high expected maximum efficiency achievable with higher driver pulse energies, the HHG source demonstrated here is very promising in high-energy or high-flux seeding over a narrow EUV bandwidth. The EUV laser line width is typically a few times narrower than the HHG line width, which is advantageous for robust seeding. A source similar to this, after proper scaling of the energy and of the repetition rate, can be used for seeding EUV FELs, which have typically the same spectral range as the HHG source demonstrated here, and is eventually a good candidate for seeding hard-x-ray FELs

4. Spectral tunability of the HHG pulses Tunability is a crucial characteristic for a seed source because it makes it possible to finely match the photon energy of the seed with the photon energy of the FEL. In FELs, for example, one can think of tuning the pump, or probe, wavelength to excite, or observe, certain dynamics in a pump-probe experiment which occur at those particular wavelengths, and it is necessary to have a continuously tunable seed source to follow the photon energy of the FEL [51]. Figure 9 shows several spectra measured while tuning the driver wavelength in Ar, Ne and He gases. Note that the spectra for helium are not necessarily the same as the ones used in the cut-off energy study. We focused the beams with f = 150 mm for argon, f = 100 mm for neon and argon. We estimated the driver intensities to be (0.9 ± 0.2) × 1014 W cm−2 in Ar, (6.6 ± 1.0) × 1014 W cm−2 in Ne, and (1.6 ± 0.9) × 1015 W cm−2 in He. We measured the efficiencies per harmonic (referring to the highest HHG peak) to be (0.9–4) × 10−7 for Ar, ∼1 × 10−9 for Ne, and (0.4–10) × 10−10 for He, respectively. In the case of argon, we observed the maximum EUV signal at a gas pressure of 42 mbar, corresponding to a backing pressure of 1.5 bar. Varying the aperture of the beam 7

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 205601

G Cirmi et al

(a)

(b)

(c)

Figure 9. Linear scale HHG spectra for (a) Ar (blue, driven by S1; green, S2; black, S3; red: S4); (b) Ne (green, S6; black, S7; red, S8); (c) He (blue, S1; green, S2; black, S3; red, S8). The 13th-order harmonic peak at each driver wavelength is indicated in panel (a) to show the tunability of ∼8 eV with OPA wavelength tuning.

using cascade schemes. In this way, the coherence, stability and reproducibility of FEL pulses could be greatly improved, provided that high enough seed energy is obtained as a seeding source. In addition, the photon energy at ∼92 eV (∼13.5 nm), which can be obtained with helium from long wavelength visible drivers, is of interest for applications such as mask and optics inspection for EUV lithography [30].

limiting the HHG tunability. Thus, phase-matched and absorption limited HHG driven by a tunable source like an OPCPA in the visible range pumped by a Yb amplifier gives the most for seeding FELs when fine wavelength tuning is needed. The scaling study conducted here shows the possible choices in driver wavelengths for seeding at a desired EUV FEL photon energy.

5. Conclusion

Acknowledgments

We developed a fully tunable source in the EUV range based on HHG driven by a broadly tunable visible OPA. The OPA produces pulses with hundreds of μJ energy between 450 and 650 nm, and pulse durations around 30 fs. With these pulses we drove HHG in different gases, and studied the dependence of the cut-off energy up to 100 eV on the driver wavelength. We found a λ1.7 ± 0.2 experimental scaling law, which agrees well with previous experimental works in the literature. We showed by simulations that the values of the cut-off energy and efficiency could be further optimized by scaling the output energy of the OPA to the mJ level. The EUV spectra show full spectral coverage between 25 and 100 eV with continuous tunability. All photon frequencies in this range can be produced by changing the crystal orientations and pump-seed delays of the OPA, the focusing lens, the species (Ar, Ne, He) and the pressure of gas in the HHG chamber. HHG driven by a visible OPA (or an OPCPA) provides full tunability in the proper range for EUV FEL seeding, while maximizing the conversion efficiency, in contrast to Ti:sapphire technology, which operates at a fixed wavelength,

This work was supported by the Air Force Office of Scientific Research under contract FA9550-10-1-0471, and the Center for Free-Electron Laser Science, DESY, Hamburg, and by Progetto Roberto Rocca. AS acknowledges support by the Alexander von Humboldt Foundation. PK acknowledges support by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

References [1] Miao J, Charalambous P, Kirz J and Sayre D 1999 Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens Nature 400 342–4 [2] Neutze R, Wouts R, van der Spoel D, Weckert E and Hajdu J 2000 Potential for biomolecular imaging with femtosecond x-ray pulses Nature 406 7527 [3] Wabnitz H et al 2002 Multiple ionization of atom clusters by intense soft x-rays from a free-electron laser Nature 420 482–5 [4] Young L et al 2010 Femtosecond electronic response of atoms to ultra-intense x-rays Nature 466 56–61 8

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 205601

G Cirmi et al

[26] Shiner A D, Trallero-Herrero C, Kajumba N, Bandulet H C, Comtois D, L´egar´e F, Jigu`ere M, Kieffer J C, Corkum P B and Villeneuve D M 2009 Wavelength scaling of high harmonic generation efficiency Phys. Rev. Lett. 103 073902 [27] Jin C, Le A T and Lin C D 2011 Medium propagation effects in high-order harmonic generation of Ar and N2 Phys. Rev. A 83 023411 [28] Laarmann T, Rusek M, Wabnitz H, Schulz J, de Castro A R B, G¨urtler P, Laasch W and M¨oller T 2005 Emission of thermally activated electrons from rare gas clusters irradiated with intense VUV light pulses from a free electron laser Phys. Rev. Lett. 95 063402 [29] Nagasono M et al 2007 Resonant two-photon absorption of extreme-ultraviolet free-electron-laser radiation in helium Phys. Rev. A 75 051406 [30] Tallents G, Wagenaars E and Pert G 2010 Optical lithography: lithography at EUV wavelengths Nature Photon. 4 809–11 [31] Falc˜ao-Filho E L, Lai C J, Hong K H, Gkortsas V M, Huang S W, Chen L J and K¨artner F X 2010 Scaling of high-order harmonic efficiencies with visible wavelength drivers: a route to efficient extreme ultraviolet sources Appl. Phys. Lett. 97 061107 [32] Popmintchev T, Chen M C, Bahabad A, Gerrity M, Sidorenko P, Cohen O, Christov I P, Murnane M M and Kapteyn H C 2009 Phase matching of high harmonic generation in the soft and hard x-ray regions of the spectrum PNAS 106 10516–21 [33] Chen M C, Arpin P, Popmintchev T, Gerrity M, Zhang B, Seaberg M, Popmintchev D, Murnane M M and Kapteyn H C 2010 Bright, coherent, ultrafast soft x-ray harmonics spanning the water window from a tabletop light source Phys. Rev. Lett. 105 173901 [34] Cerullo G and De Silvestri S 2003 Ultrafast optical parametric amplifiers Rev. Sci. Instrum. 74 1–18 [35] Manzoni C, Polli D and Cerullo G 2006 Two-color pump-probe system broadly tunable over the visible and the near infrared with sub-30 fs temporal resolution Rev. Sci. Instrum. 77 023103 [36] Riedle E, Beutter M, Lochbrunner S, Piel J, Schenkl S, Spoerlein S and Zinth W 2000 Generation of 10 to 50 fs pulses tunable through all of the visible and the NIR Appl. Phys. B 71 457–65 [37] Piel J, Riedle E, Gundlach L, Ernstorfer R and Eichberger R 2006 Sub-20 fs visible pulses with 750 nJ energy from a 100 kHz noncollinear optical parametric amplifier Opt. Lett. 31 1289–91 [38] Baltuˇska A, Fuji T and Kobayashi T 2002 Visible pulse compression to 4 fs by optical parametric amplification and programmable dispersion control Opt. Lett. 27 306–8 [39] Baum P, Breuer M, Riedle E and Steinmeyer G 2006 Brewster-angled chirped mirrors for broadband pulse compression without dispersion oscillations Opt. Lett. 31 2220–2 [40] Tzankov P, Zheng J, Mero M, Polli D, Manzoni C and Cerullo G 2006 300 μJ noncollinear optical parametric amplifier in the visible at 1 kHz repetition rate Opt. Lett. 31 3629–31 [41] Di Trapani P, Andreoni A, Solcia C, Foggi P, Danielius R, Dubietis A and Piskarskas A 1995 Matching of group velocities in three-wave parametric interaction with femtosecond pulses and application to traveling-wave generators J. Opt. Soc. Am. B 12 2237–44 [42] Shirakawa A, Sakane I and Kobayashi T 1998 Pulse-front-matched optical parametric amplification for sub-10 fs pulse generation tunable in the visible and near infrared Opt. Lett. 23 1292–4 [43] Bor Z and R´acz B 1985 Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation Opt. Commun. 54 165–70

[5] Gaffney K J and Chapman H N 2007 Imaging atomic structure and dynamics with ultrafast x-ray scattering Science 316 1444–8 [6] Yamanaka C 1992 Future industrial application of free electron lasers Nucl. Instrum. Methods A 318 1–8 [7] Suckewer S, Skinner C H, Milchberg H, Keane C and Voorhees D 1985 Amplification of stimulated soft x-ray emission in a confined plasma column Phys. Rev. Lett. 55 1753–6 [8] Fiedorowicz H, Bartnik A, Li Y, Lu P and Fill E 1996 Demonstration of soft x-ray lasing with neonlike argon and nickel-like xenon ions using a laser-irradiated gas puff target Phys. Rev. Lett. 76 415–8 [9] Wang Y, Granados E, Larotonda M A, Berrill M, Luther B M, Patel D, Menoni C S and Rocca J J 2006 High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target Phys. Rev. Lett. 97 123901 [10] Madey J M J 1971 Stimulated emission of bremsstrahlung in a periodic magnetic field J. Appl. Phys. 42 1906–13 [11] Willner A et al 2010 High repetition rate seeding of a free-electron laser at DESY Hamburg IPAC’10: Proc. Int. Particle Accelerator Conf. (Kyoto, Japan) pp 2158–60 [12] Zeitoun P et al 2004 A high-intensity highly coherent soft x-ray femtosecond laser seeded by a high harmonic beam Nature 431 426–9 [13] Guilbaud O et al 2010 Fourier-limited seeded soft x-ray laser pulse Opt. Lett. 35 1326–8 [14] Fiedorowicz H, Bartnik A, Dunn J, Smith R F, Hunter J, Nilsen J, Osterheld A L and Shlyaptsev V N 2001 Demonstration of a neonlike argon soft-x-ray laser with a picosecond-laser-irradiated gas puff target Opt. Lett. 26 1403–5 [15] Berrill M, Alessi D, Wang Y, Domingue S R, Martz D H, Luther B M, Liu Y and Rocca J J 2010 Improved beam characteristics of solid-target soft x-ray laser amplifiers by injection seeding with high harmonic pulses Opt. Lett. 35 2317–9 [16] McNeil B W J, Clarke J A, Dunning D J, Hirst G J, Owen H L, Thompson N R, Sheehy B and Williams P H 2007 An XUV-FEL amplifier seeded using high harmonic generation New J. Phys. 9 82 [17] Willner A et al 2011 Coherent control of high harmonic generation via dual-gas multijet arrays Phys. Rev. Lett. 107 175002 [18] Lambert G et al 2009 An optimized kHz two-colour high harmonic source for seeding free-electron lasers and plasma-based soft x-ray lasers New J. Phys. 11 083033 [19] Yu L H et al 2000 High-gain harmonic-generation free-electron laser Science 289 932–4 [20] Hong K H, Huang S W, Moses J, Fu X, Lai C J, Cirmi G, Sell A, Granados E, Keathley P and K¨artner F X 2011 High-energy, phase-stable, ultrabroadband kHz OPCPA at 2.1 μm pumped by a picosecond cryogenic Yb:YAG laser Opt. Express 19 15538–48 [21] Huang S W et al 2011 High-energy pulse synthesis with sub-cycle waveform control for strong-field physics Nature Photon. 5 475–9 [22] Shan B and Chang Z 2001 Dramatic extension of the high-order harmonic cut-off by using a long-wavelength driving field Phys. Rev. A 65 011804 [23] Gordon A and K¨artner F X 2005 Scaling of keV HHG photon yield with drive wavelength Opt. Express 13 2941–7 [24] Falc˜ao-Filho E L, Gkortsas V M, Gordon A and K¨artner F X 2009 Analytic scaling analysis of high harmonic generation conversion efficiency Opt. Express 17 11217–29 [25] Tate J, Auguste T, Muller H G, Sali`eres P, Agostini P and DiMauro L F 2007 Scaling of wave-packet dynamics in an intense midinfrared field Phys. Rev. Lett. 98 013901 9

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 205601

G Cirmi et al

[44] Kim H T, Lee D G, Hong K H, Kim J H, Choi I W and Nam C H 2003 Continuously tunable high-order harmonics from atoms in an intense femtosecond laser field Phys. Rev. A 67 051801 [45] Balcou P, Cornaggia C, Gomes A S L, Lompr e´ L A and L’Huillier A 1992 Optimizing high-order harmonic generation in strong fields J. Phys. B: At. Mol. Opt. Phys. 25 4467–85 [46] L’Huillier A, Lewenstein M, Sali`eres, Balcou P, Ivanov M Y, Larsson J and Wahlstr¨om C G 1993 High-order harmonic generation cutoff Phys. Rev. A 48 R3433–6 [47] Lai C J and K¨artner F X 2011 The influence of plasma defocusing in high harmonic generation Opt. Express 19 22377–87 [48] Corlett J N et al 2011 A next generation light source facility at LBNL Lawrence Berkeley National Laboratory (LBNL) Paper LBNL-4391E [49] Tavella F et al 2010 Fiber-amplifier pumped high average power few-cycle pulse non-collinear OPCPA Opt. Express 18 4689–94

[50] Hong K H, Gopinath J T, Rand D, Siddiqui A M, Huang S W, Li E, Eggleton B J, Hybl J D, Fan T Y and K¨artner F X 2010 High-energy, kHz-repetition-rate, ps cryogenic Yb:YAG chirped-pulse amplifier Opt. Lett. 35 1752–4 [51] Tiedtke K et al 2009 The soft x-ray free-electron laser FLASH at DESY: beamlines, diagnostics and end-stations New J. Phys. 11 023029 [52] Schulz H, Scheuler H, Engers T and von der Linde D 1989 Measurement of intense ultraviolet subpicosecond pulses using degenerate four-wave mixing IEEE J. Quantum Electron. 25 2580–5 [53] Shan B, Cavalieri A and Chang Z 2002 Tunable high harmonic generation with an optical parametric amplifier Appl. Phys. B 74 S23–6 [54] Vozzi C, Calegari F, Frassetto F, Poletto L, Sansone G, Villoresi P, Nisoli M, De Silvestri S and Stagira S 2009 Coherent continuum generation above 100 eV driven by an IR parametric source in a two-color scheme Phys. Rev. A 79 033842

10