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Abstract
High harmonic sources can provide ultrashort pulses of coherent radiation in the XUV and X-ray spectral region. In this paper we utilize a sub-two-cycle femtosecond fiber laser to efficiently generate a broadband continuum of high-order harmonics between 70 eV and 120 eV. The average power delivered by this source ranges from > 0.2 µW/eV at 80 eV to >0.03 µW/eV at 120 eV. At 92 eV (13.5 nm wavelength), we measured a coherent record-high average power of 0.1 µW/eV, which corresponds to 7 · 109 ph/s/eV, with a long-term stability of 0.8% rms deviation over a 20 min time period. The presented approach is average power scalable and promises up to 1011 ph/s/eV in the near future. With additional carrier-envelop phase control even isolated attosecond pulses can be expected from such sources. The combination of high flux, high photon energy and ultrashort (sub-) fs duration will enable photon-hungry time-resolved and multidimensional studies.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High harmonic generation (HHG) represents a unique method to generate coherent light with short wavelengths and ultrashort durations in a table-top setup [1,2]. High harmonic sources have thus enabled groundbreaking studies of matter on extremely small spatial (nanometer to angstrom) and temporal (femtosecond to attosecond) scales [3,4].
Ti:Sa lasers have been the workhorse for HHG for the last decades but are unfortunately limited in average output power. Novel laser concepts, employing Yb-based gain materials and advanced geometries of the active medium, such as disk [5], slab [6] and fiber [7], nowadays permit femtosecond lasers with average output powers beyond 1 kW [8]. Such lasers have the potential of increasing average photon flux and repetition rate of single-pass HHG sources by orders of magnitude and therefore advance photon hungry applications.
To date, high harmonic generation experiments with 100 W-class femtosecond fiber lasers have demonstrated efficient and absorption-limited XUV generation at photon energies between 21 eV and 70 eV [1]. The achieved average power per 1 eV bandwidth ranges from ∼1 mW at 21 eV [9] and ∼ 1 µW at 70 eV [10], exceeding those of established Ti:Sa-based high harmonic sources by about one order of magnitude. Moreover, the possibility of power scaling of the driving laser up to the kW-level promises a further increase of the XUV photon flux by another order of magnitude.
These sources have already proven their potential in high performance nanoscale coherent diffractive imaging experiments and coincidence detection photoionization experiments [10–13] and paved the way for time-resolved and multi-dimensional studies in future.
Clearly a significant number of applications requires higher photon energies, thus shorter wavelengths. Although few-cycle fiber lasers have already been applied for HHG in the soft X-ray region up to the water window, the achieved average power was low (< 0.05 µW/eV) and the spectral region between 70 eV and 120 eV was not covered so far [14].
However, many important elements e.g. Cr, Mn, Fe, Co, Ni, Al and Si have absorption edges in this spectral region. Ultrafast studies of their electronic, optical and magnetic properties, in atomic, molecular or solid state as well as in compound materials, desires sources with high photon flux and short pulse duration in this spectral region. Moreover, industry is urgently seeking for actinic (“at wavelength”) inspection of EUV lithography masks at 13.5 nm (92 eV). Here, high photon flux coherent sources in combination with coherent diffractive imaging could potentially provide an elegant solution [15].
Recently, HHG from multiply ionized plasmas with a state-of-the art Ti:Sa laser provided a remarkably high photon flux (>1011 ph/s) which corresponds to 1.5 µW average power at 97 eV [16]. This method provided high order harmonics with ultra-narrow bandwidth which is particularly interesting for spectroscopic applications, but did not demonstrate XUV bandwidths supporting few-femtosecond and attosecond pulses yet.
In this paper we present a series of high harmonics generation experiments addressing the photon energy range between 70 eV and 120 eV with a power-scalable fiber-based driving laser. A high conversion efficiency is achieved by maximizing the number of phase-matched emitters [17], using a dedicated high-density argon gas jet target. Moreover, the single-atom response and the cutoff energy are simultaneously maximized by nonlinear compression of the driving pulses to sub-two cycle (6.7 fs) durations.
CEP stabilization of the driving laser is feasible [18] and isolated attosecond pulses can thus be expected from this HHG source. The average power delivered by this source ranges from > 0.2 µW/eV at 80 eV to > 0.03 µW/eV at 120 eV, which is among the most powerful coherent sources in this spectral region to date. At 92 eV (13.5 nm wavelength) we measured a record-high average power of 0.1 µW/eV which corresponds to $7 \cdot {10^9}\; \textrm{ph}/\textrm{s}/\textrm{eV}$. Since femtosecond fiber lasers have demonstrated average power up to kW recently [8] and the components for nonlinear pulse compression have proven to handle kW-level average powers [19], we are confident that the demonstrated harmonic source can be scaled up to 1011 ph/s/eV in the near future.
The paper is structured as follows: The first part of the paper briefly reviews how the single-atom response and the cutoff energy are simultaneously maximized with few-cycle driving pulses. In the second part, the experimental setup for the generation of the required sub-two-cycle laser pulses at high average power is described. The characterization of the implemented high harmonic source is shown in the third part followed by a summary and outlook.
2. High-harmonic generation – increasing the single-atom response and the cutoff energy with few-cycle pulses
The process of HHG can be explained with the simple and well-known three-step model [20]: (1) ionization of an atom, (2) acceleration of the free electron and (3) recombination of the free electron with the parent ion. This simple model explains some fundamental properties of the HHG process, e.g. the typical $2\; \omega $ spacing of the harmonics and the cutoff rule with the cutoff photon energy ${E_{cutoff}}$ [21]:
where ${I_p}$ is the ionization potential, I the intensity, $\lambda $ the central wavelength of the driving laser field and a is a constant. At a given wavelength, the cutoff can be increased in two ways according to the cutoff formula: (1) Use different gases with a higher ${I_p}$. Nevertheless, the HHG yield typically decreases with lighter gases. (2) Use higher intensities. However, the intensity is no arbitrary parameter since phase matching is crucial for the efficient generation of EUV light via HHG. For true phase-matched HHG the ionization at the peak of the pulse should not exceed the so-called critical ionization, which typically is smaller 5% [22]. Figure 1(a) shows the ionization fraction of argon, using the Yudin-Ivanov ionization model [23]. For the calculation, different pulse lengths at a central wavelength of 1030 nm are used. For each pulse length the intensity is adjusted for a < 3.5% ionization at the peak of the laser pulse ($t = 0\; \textrm{fs}$). This shows that the same ionization level can be reached with shorter pulses, while applying a significantly higher intensity. Furthermore, the single atom yield of HHG (${S_{HHG}}$) in the plateau region scales with the intensity I as [24]:
Fig. 1. (a) Calculated ionization fraction. Using Yudin-Ivanov rates for different pulse lengths and intensities to reach ∼10% ionization at the peak of the laser in argon. (b) Phase-matching cutoff with different pulse lengths at. The central wavelength is 1030 nm [1].
Therefore, the use of shorter driving pulses for HHG and the resultant higher usable intensity increases the cutoff (see Fig. 1(b)), as well as the conversion efficiency of phase-matched emitters.
For HHG in argon and pulses with a central wavelength of 1030, these simple considerations yield the same ionization level at the peak of the laser pulse at an intensity of $1.8 \cdot {10^{14}}\; \textrm{W/c}{\textrm{m}^2}$ at 30 fs pulses and $2.5 \cdot {10^{14}}\; \textrm{W/c}{\textrm{m}^2}$ at 7 fs (Fig. 1(a)). Using these intensities in the formulas above, the cutoff scales from 72 eV at 30 fs pulses to 94 eV at 7 fs (Fig. 1(b)), with an order of magnitude higher efficiency. Therefore, the typically more efficient argon can be used to generate radiation up to ∼ 90 eV, using ultrashort pulses with a pulse duration of 7 fs.
3. Experimental setup
The first experimental challenge is to generate the shortest possible pulses with enough peak power for HHG in a power scalable architecture. Therefore, the experimental setup, similar to the one presented in [14] (shown in Fig. 2) is used. A home-built fiber-based chirped pulsed amplifier using two coherently combined fibers is delivering 75 W, 1 mJ, 75 kHz and 250 fs pulses. In a first step the pulses are coupled into a 250 µm inner diameter hollow core fiber with a length of 1 m and filled with 2 bar of argon. Subsequently, the pulses are compressed using a chirped mirror compressor with a dispersion of -2100 fs2. This results in 30 fs pulses with an energy of 600 µJ at 45 W average power. Afterwards, a second hollow core fiber compression stage (inner diameter 250 µm, length 70 cm), filled with 11 bar of helium to reduce ionization effects, is used. The ultrabroadened spectrum is shown as the blue line in Fig. 3(a). The pulses are finally compressed by ultrabroadband chirped mirrors (total group velocity dispersion -163 fs2) in combination with 5 mm of bulk fused silica. The pulses are characterized using a SPIDER device (Venteon), revealing a pulse duration of 6.7 fs (Fig. 3(b)). In addition, interferometric autocorrelation measurements confirm the reliability of the pulse duration. The overall transmission through the two stage compression setup is as high as 40%, resulting in a compressed pulse energy of 400 µJ at an average power of 30 W. Simulations considering self phase modulation, self steepening and losses in the fibers confirm the measurements and show a peak power of > 35 GW, which corresponds to ∼ 60% of energy in the central pulse after a propagating in two hollow core compression stages.
Fig. 2. Experimental setup for a few-cycle laser driven 13.5 nm EUV source (HFC: hollow core fiber compression, ID: inner diameter, L: length, GIPs: gracing incidence plates).
Fig. 3. Measured and simulated spectrum as well as the retrieved SPIDER phase (a), and the corresponding reconstructed pulse (b) after the second hollow core compression stage.
Subsequently, the few-cycle pulses are sent into a vacuum chamber and focussed via a spherical mirror with a custom design ultrabroad-bandwidth multilayer coating into a gas jet, where the higher order harmonics are generated. The spot size of the focussed beam is 75 µm (1/e2).
The separation of the generated high harmonics from the driving laser is a second experimental challenge. Usually, thin Zr foils are employed for this purpose, since they provide a a high transmission between 70 eV and 120 eV and block the fundamental driving laser. Unfortunately these Zr foils cannot withstand high average powers and we observed damage repeatedly at > 100 mW average power. Thus, additional gracing incidence plates (GIPs) are employed beforehand [25]. These are plan parallel plates with an custom design ultrabroad-bandwidth AR coating (R < 10%) for the driving laser and a high refractive index top layer at an gracing incidence configuration for a high XUV reflectivity, placed ∼ 200 mm behind the laser focus. This results in less than 10 mW of IR average power after four GIPs. Afterwards two 200 nm thick Zr foils are used to fully block the residual IR light. Finally, the XUV light is characterized spectrally and spatially with a flat field spectrometer with a 1200 lines/mm imaging grating.
An experimental optimization of the EUV flux at a given nozzle size is done by iteratively optimizing the nozzle position via a xyz-translation stage, the iris size at the entrance of the vacuum chamber, the amount of glass inserted into the laser beam and by varying the backing pressure. This procedure is repeated for different nozzle diameters. However, choosing the correct nozzle diameter is a trade-off between a sufficient medium length for efficient HHG and a low residual pressure in the chamber. The latter will reduce the usable flux due to reabsorption of the XUV photons in the residual gas.
In the presented experiments, a significant reduction of the residual gas pressure in the vacuum chamber is achieved by installling a gas catch with an orifice of 3 mm directly opposite the gas nozzle. Compared to no gas catch, a reduction of the residual gas pressure by more than one order of magnitude is achieved. With a propagation length of 1 m, this results in a transmission of nearly 100% in argon or neon, while not using a gas catch results in a transmission of 80% in argon and 50% in neon. Therefore, a much higher photon flux can be transferred to subsequent experiments.
Testing nozzle diameters ranging from 50 µm up to 1.5 mm results in an optimal diameter of 700 µm for argon and 150 µm for neon. Varying the backing pressure for these nozzle diameters results in a optimal backing pressure of 0.6 bar for argon and 13 bar for neon (Fig. 4). The results of a corresponding simulation with a simple one-dimensional model [24,26], shown as the dotted lines in Fig. 4 support these findings, assuming a distance of the laser to the gas nozzle opening of $2 \cdot {w_0} = 75$ µm [17]. The resultant optimal gas density for HHG is $7 \cdot {10^{18}}\; \textrm{c}{\textrm{m}^{ - 3}}$ for argon and $7 \cdot {10^{19}}\; \textrm{c}{\textrm{m}^{ - 3}}$ for neon. The resulting absorption lengths are 1 mm for argon and 32 µm for neon, showing that the absorption limited HHG (${L_{med}} > 3{L_{abs}}$) is achieved for neon, while the absorption length in argon is about equal to the medium length.
Fig. 4. Pressure scans for (a) argon and (b) neon (solid lines) at 13.5 nm, with the corresponding simulations (dashed lines).
4. Results
In order to verify the theoretical predictions, the second hollow core fiber compression stage is used passively (evacuated), resulting in 400 µJ and 30 fs pulses at a reduced repetition rate of 50 kHz and 23 W average power. In this case, the HHG in argon is optimized for the highest achievable photon energy and the result is shown as the green line in Fig. 5(a). However, no photon energies above 80 eV could be reached, which corresponds to the simulations shown in Fig. 1(b).
Fig. 5. (a) Spectra for HHG driven by 30 fs pulses at 50 kHz in argon (green line), as well as for HHG driven by 7 fs pulses at 75 kHz in argon (blue line) and neon (red line). The dashed yellow line marks 13.5 nm (92 eV). (b) Spatial lineout of HHG with 7 fs and argon at 13.5 nm (solid line) with the Gaussian fit (dashed line).
To reach higher photon energies, the second hollow core fiber compression stage is used actively at a repetition rate of 75 kHz, resulting in 400 µJ, 7 fs pulses at 30 W of average power. Optimization of HHG in argon for the highest flux at 13.5 nm (92 eV) results in the spectrum shown as the solid blue line in Fig. 5(a). The maximum detectable photon energy increases from ∼80 eV (using 30 fs pulses) to ∼120 eV (using 7 fs pulses). This 40 eV increase in generated photon energies is as expected due to the higher usable intensity for phase matched HHG. Therefore, efficient generation of radiation up to ∼ 100 eV is feasible using argon as a HHG medium.
To evaluate the generated photon flux, the measured data is corrected by the transmission through the residual gas (99%), the theoretical reflectivity of the GIPs (77% per GIP), the measured transmission of the Zr filters (23% per filter) and by spatially cutting at the grating and the detector (90%). Furthermore, the diffraction efficiency of the used grating (21%) as well as the sensitivity of the used CCD (Andor Newton, 4.7 ph/count) are calibrated at the National Metrology Institute of Germany (PTB). Note that all mentioned efficiencies are given at 13.5 nm. Resulting in a calibrated overall photon flux of $7 \cdot {10^9}\; \textrm{ph}/\textrm{s}/\textrm{eV}$. Even though, that the desired wavelength is in the cutoff region and HHG is not in the absorption limited regime, this coherent source is among the most powerful demonstrated [27,28].
A spatial lineout of the harmonics is shown in Fig. 5(b), showing a Gaussian like beam profile at 13.5 nm suitable for further experiments.
Optimizing the HHG conditions for the highest flux at 13.5 nm (92 eV) using neon results in the spectrum shown as the red solid line in Fig. 5(a). The cutoff scales as expected (see Fig. 1(b)). A spectral continuum extends up to ∼160 eV. However, a lower conversion efficiency compared to argon is observed. Nevertheless >0.03 µW/eV are observed up to 120 eV.
In a final experiment, the spatial coherence of the generated radiation is investigated. Therefore, narrow bandwidth mirrors are used to select a bandwidth of 0.2 nm at a central wavelength of 13.5 nm and are further employed to focus the beam with a flux of $2 \cdot {10^7}$ ph/s on a double slit (shown in the inset of Fig. 6(a)). The diffraction pattern, measured with 5 s of integration time, is depicted in Fig. 6(a) and shows a visibility of > 90% which demonstrates a high degree of spatial coherence. Further on, this setup was used to measure the long term stability of the source over a time period of 20 min. Even though, that the used wavelength is in the cutoff region, the source shows very stable photon flux with an rms deviation of 0.8%, shown in Fig. 6(b).
Fig. 6. (a) Diffraction pattern (upper panel) and lineout along the dashed white line (lower panel) after focusing a 13.5 nm EUV beam on a double slit (inset). (b) Long term stability of the source at 13.5 nm with a rms deviation of 0.8%
5. Summary and outlook
In summary, a high harmonic light source in the energy range between 70 eV and 120 eV has been presented using an average power scalable fiber laser. Using ultrashort pulses of sub 7 fs duration allows increasing the phase-matching cutoff and generating broadband harmonics up to ∼100 eV in Argon and up to ∼160 eV in Neon. The measured photon flux is as high as > 0.2 µW/eV at 80 eV up to >0.03 µW/eV at 120 eV, which is among the most powerful coherent sources in this spectral region today [27,28]. At 92 eV (13.5 nm wavelength) record-high $7 \cdot {10^9}\; \textrm{ph}/\textrm{s}/\textrm{eV}$ have been obtained. While the long term stability of the source was measured to be 0.8% rms deviation over a time period of 20 min.
This high photon flux comes along with high spatial coherence and a Gaussian like spatial beam profile. CEP stabilization of the driving laser will allow to generate isolated attosecond pulses with similar properties in the near future.
With the power scalable concept of fiber based amplifiers an average power scaling to the kW regime is possible [8]. Together with the power scalability of hollow core fiber compression [29], and high average power capable separation schemes for HHG [30], $> {10^{11}}\; \textrm{ph}/\textrm{s}/\textrm{eV}$ at 13.5 nm appear feasible in the near future, enabling ultrafast spectroscopy, nanoscale imaging and high performance EUV metrology applications.
Funding
Federal State of Thuringia (2015 FGR 0094); European Social Fund; Fraunhofer-Gesellschaft (Fraunhofer) (Advanced Photon Sources); Deutsche Forschungsgemeinschaft (IRTG 2101).
Acknowledgments
RK acknowledges support from the German Science Foundation DFG, IRTG 2101. We thank Michael Steinert from the Institute of Applied Physics at the University of Jena for the preparation of the double slit samples.
Disclosures
The authors declare no conflicts of interest.
References
1. S. Hädrich, J. Rothhardt, M. Krebs, S. Demmler, A. Klenke, A. Tünnermann, and J. Limpert, “Single-pass high harmonic generation at high repetition rate and photon flux,” J. Phys. B: At., Mol. Opt. Phys. 49(17), 172002 (2016). [CrossRef]
2. R. Schoenlein, T. Elsaesser, K. Holldack, Z. Huang, H. Kapteyn, M. Murnane, and M. Woerner, “Recent advances in ultrafast X-ray sources,” Philos. Trans. R. Soc., A 377(2145), 20180384 (2019). [CrossRef]
3. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]
4. J. Rothhardt, G. K. Tadesse, W. Eschen, and J. Limpert, “Table-top nanoscale coherent imaging with XUV light,” J. Opt. (U. K.) 20(11), 113001 (2018). [CrossRef]
5. T. Nubbemeyer, M. Kaumanns, M. Ueffing, M. Gorjan, A. Alismail, H. Fattahi, J. Brons, O. Pronin, H. G. Barros, Z. Major, T. Metzger, D. Sutter, and F. Krausz, “1 kW, 200 mJ picosecond thin-disk laser system,” Opt. Lett. 42(7), 1381–1384 (2017). [CrossRef]
6. H. Höppner, A. Hage, T. Tanikawa, M. Schulz, R. Riedel, U. Teubner, M. J. Prandolini, B. Faatz, and F. Tavella, “An optical parametric chirped-pulse amplifier for seeding highrepetition rate free-electron lasers,”,” New J. Phys. 17(5), 053020 (2015). [CrossRef]
7. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010). [CrossRef]
8. M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41(15), 3439–3442 (2016). [CrossRef]
9. R. Klas, S. Demmler, M. Tschernajew, S. Hädrich, Y. Shamir, A. Tünnermann, J. Rothhardt, and J. Limpert, “Table-top milliwatt-class extreme ultraviolet high harmonic light source,” Optica 3(11), 1167–1170 (2016). [CrossRef]
10. J. Rothhardt, S. Hädrich, Y. Shamir, M. Tschnernajew, R. Klas, A. Hoffmann, G. K. Tadesse, A. Klenke, T. Gottschall, T. Eidam, J. Limpert, A. Tünnermann, R. Boll, C. Bomme, H. Dachraoui, B. Erk, M. Di Fraia, D. A. Horke, T. Kierspel, T. Mullins, A. Przystawik, E. Savelyev, J. Wiese, T. Laarmann, J. Küpper, and D. Rolles, “High-repetition-rate and high-photon-flux 70 eV high-harmonic source for coincidence ion imaging of gas-phase molecules,” Opt. Express 24(16), 18133–18147 (2016). [CrossRef]
11. G. K. Tadesse, R. Klas, S. Demmler, S. Hädrich, I. Wahyutama, M. Steinert, C. Spielmann, M. Zürch, T. Pertsch, A. Tünnermann, J. Limpert, and J. Rothhardt, “High speed and high resolution table-top nanoscale imaging,” Opt. Lett. 41(22), 5170–5173 (2016). [CrossRef]
12. G. K. Tadesse, W. Eschen, R. Klas, M. Tschernajew, T. Frederik, M. Steinert, M. Zilk, V. Sch, M. Zürch, T. Pertsch, C. Spiel, J. Li, and J. Rothhardt, “Wavelength-scale ptychographic coherent diffractive imaging using a high-order harmonic source,” Sci. Rep. 9(1), 1735 (2019). [CrossRef]
13. G. K. Tadesse, W. Eschen, R. Klas, V. Hilbert, D. Schelle, A. Nathanel, M. Zilk, M. Steinert, F. Schrempel, T. Pertsch, A. Tünnermann, J. Limpert, and J. Rothhardt, “High resolution XUV Fourier transform holography on a table top,” Sci. Rep. 8(1), 8677 (2018). [CrossRef]
14. J. Rothhardt, S. Hädrich, A. Klenke, S. Demmler, A. Hoffmann, T. Gotschall, T. Eidam, M. Krebs, J. Limpert, and A. Tünnermann, “53W average power few-cycle fiber laser system generating soft x rays up to the water window,” Opt. Lett. 39(17), 5224–5227 (2014). [CrossRef]
15. H. Kinoshita, T. Harada, Y. Nagata, T. Watanabe, and K. Midorikawa, “Development of EUV mask inspection system using high-order harmonic generationwith a femtosecond laser,” Jpn. J. Appl. Phys. 53(8), 086701 (2014). [CrossRef]
16. D. Popmintchev, C. Hernandez-Garcia, F. Dollar, C. Mancuso, J. A. Perez-Hernandez, M.-C. Chen, A. Hankla, X. Gao, B. Shim, A. L. Gaeta, M. Tarazkar, D. A. Romanov, R. J. Levis, J. A. Gaffney, M. Foord, S. B. Libby, A. Jaron-Becker, A. Becker, L. Plaja, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Ultraviolet surprise: Efficient soft x-ray high-harmonic generation in multiply ionized plasmas,” Science 350(6265), 1225–1231 (2015). [CrossRef]
17. J. Rothhardt, M. Krebs, S. Hädrich, S. Demmler, J. Limpert, and A. Tünnermann, “Absorption-limited and phase-matched high harmonic generation in the tight focusing regime,” New J. Phys. 16(3), 033022 (2014). [CrossRef]
18. E. Shestaev, D. Hoff, A. M. Sayler, A. Klenke, S. Hädrich, F. Just, T. Eidam, P. Jójárt, Z. Várallyay, K. Osvay, G.G. Paulus, A. Tünnermann, and J. Limpert, “High power Ytterbium-doped fiber laser delivering few-cycle, CEP-stable 100 uJ pulses at 100 kHz”, submitted to Opt. Lett. (2019).
19. S. Hädrich, J. Rothhardt, S. Demmler, M. Tschernajew, A. Hoffmann, M. Krebs, A. Liem, O. de Vries, M. Plötner, S. Fabian, T. Schreiber, J. Limpert, and A. Tünnermann, “Scalability of components for kW-level average power few-cycle lasers,” Appl. Opt. 55(7), 1636–1640 (2016). [CrossRef]
20. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993). [CrossRef]
21. J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68(24), 3535–3538 (1992). [CrossRef]
22. C. M. Heyl, C. L. Arnold, A. Couairon, and A. L’Huillier, “Introduction to macroscopic power scaling principles for high-order harmonic generation,” J. Phys. B: At., Mol. Opt. Phys. 50(1), 013001 (2017). [CrossRef]
23. G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A: At., Mol., Opt. Phys. 64(1), 013409 (2001). [CrossRef]
24. S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011). [CrossRef]
25. O. Pronin, V. Pervak, E. Fill, J. Rauschenberger, F. Krausz, and A. Apolonski, “Ultrabroadband efficient intracavity XUV output coupler,” Opt. Express 19(11), 10232–10240 (2011). [CrossRef]
26. E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999). [CrossRef]
27. C. Ding, W. Xiong, T. Fan, D. D. Hickstein, T. Popmintchev, X. Zhang, M. Walls, M. M. Murnane, and H. C. Kapteyn, “High flux coherent super-continuum soft X-ray source driven by a single-stage, 10mJ, Ti:sapphire amplifier-pumped OPA,” Opt. Express 22(5), 6194–6202 (2014). [CrossRef]
28. D. Mamezaki, T. Harada, Y. Nagata, and T. Watanabe, “Imaging performance improvement of coherent extreme-ultraviolet scatterometry microscope with high-harmonic-generation extreme-ultraviolet source,” Jpn. J. Appl. Phys. 56(6S1), 06GB01 (2017). [CrossRef]
29. S. Hädrich, M. Kienel, M. Müller, A. Klenke, J. Rothhardt, R. Klas, T. Gottschall, T. Eidam, A. Drozdy, P. Zoltán, Z. Várallyay, E. Cormier, K. Osvay, A. Tünnermann, and J. Limpert, “Energetic sub-2-cycle laser with 216 W average power,” Opt. Lett. 41(18), 4332–4335 (2016). [CrossRef]
30. R. Klas, A. Kirsche, M. Tschernajew, J. Rothhardt, and J. Limpert, “Annular beam driven high harmonic generation for high flux coherent XUV and soft X-ray radiation,” Opt. Express 26(15), 19318–19327 (2018). [CrossRef]
