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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 20242–20250
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High harmonic generation by novel fiber amplifier based sources

S. Hädrich, J. Rothhardt, M. Krebs, F. Tavella, A. Willner, J. Limpert, and A. Tünnermann  »View Author Affiliations


Optics Express, Vol. 18, Issue 19, pp. 20242-20250 (2010)
http://dx.doi.org/10.1364/OE.18.020242


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Abstract

Significant progress in high repetition rate ultrashort pulse sources based on fiber technology is presented. These systems enable operation at a high repetition rate of up to 500 kHz and high average power in the extreme ultraviolet wavelength range via high harmonic generation in a gas jet. High average power few-cycle pulses of a fiber amplifier pumped optical parametric chirped pulse amplifier are used to produce µW level average power for the strongest harmonic at 42.9 nm at a repetition rate of 96 kHz.

© 2010 OSA

1. Introduction

High harmonic generation has emerged as a key process to enable table-top sources of spatially and temporally coherent radiation in the extreme ultraviolet or soft x-ray region as an alternative to large scale facilities. A number of applications have been made possible due to the outstanding properties of this radiation, such as the study of molecular motion [1

1. E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317(5843), 1374–1378 (2007). [CrossRef] [PubMed]

], new imaging techniques [2

2. R. L. Sandberg, D. A. Raymondson, C. La-O-Vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34(11), 1618–1620 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-11-1618. [CrossRef] [PubMed]

4

4. R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi, “Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams,” Phys. Rev. Lett. 99(9), 098103 (2007). [CrossRef] [PubMed]

], investigation of surface processes [5

5. T. Haarlammert and H. Zacharias, “Application of high harmonic radiation in surface science,” Curr. Opin. Solid State Mater. Sci. 13(1-2), 13–27 (2009). [CrossRef]

] and attosecond physics [6

6. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]

,7

7. A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B 39(1), R1–R37 (2006). [CrossRef]

]. A major limitation in high harmonic generation, so far, is the small number of photons per second (average power) due to low conversion efficiency (typically lower than 10−6) [8

8. J. Eden, “High-order harmonic generation and other intense optical field-matter interactions: review of recent experimental and theoretical advances,” Prog. Quantum Electron. 28(3-4), 197–246 (2004). [CrossRef]

].

In recent years there has been a growing interest in high repetition rate laser sources for use in high harmonic generation (HHG), e.g. for spectroscopic purposes [9

9. C. Winterfeldt, C. Spielmann, and G. Gerber, “Colloquium: Optimal control of high-harmonic generation,” Rev. Mod. Phys. 80(1), 117–140 (2008). [CrossRef]

]. Another application is seeding of free electron lasers to enhance spectral and temporal characteristics and the stability [10

10. G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, S. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M.-E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4(4), 296–300 (2008). [CrossRef]

]. Due to high intensities (1013-1015 W/cm2) required to initiate this process, mainly low repetition rate (~kHz) high energy systems have been used to date. Achieving HHG at repetition rates of hundreds of kHz and above has largely been characterized by two approaches, even though others are emerging [11

11. O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97(2), 369–373 (2009). [CrossRef]

,12

12. S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008). [CrossRef] [PubMed]

].

The first uses field enhancement inside a cavity. This has proven µW level harmonics for 60 nm generated in xenon at 10.8 MHz [13

13. A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and Th. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100(25), 253901 (2008). [CrossRef] [PubMed]

] or 250 nW at 82.3 nm also generated in xenon at even higher repetition rates of 136 MHz [14

14. D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett. 33(10), 1099–1101 (2008), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-10-1099. [CrossRef] [PubMed]

]. The main challenge is the required active stabilization of the cavity that adds experimental complexity and sensitivity and the need to couple out the harmonics, especially at higher average power [15

15. I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett. 35(12), 2052–2054 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-12-2052. [CrossRef] [PubMed]

].

A more robust approach is to use high repetition rate laser systems with the required peak intensities. Recently, high harmonic generation at a repetition rate of 100 kHz has been presented for a pulse energy of 7 µJ [16

16. F. Lindner, W. Stremme, M. G. Schätzel, F. Grasbon, G. G. Paulus, H. Walther, R. Hartmann, and L. Strüder, “High-order harmonic generation at a repetition rate of 100 kHz,” Phys. Rev. A 68(1), 013814 (2003). [CrossRef]

]. Due to the low pulse energy the conversion efficiency was lower than 10−9 resulting in rather low average power (<0.7 nW) [16

16. F. Lindner, W. Stremme, M. G. Schätzel, F. Grasbon, G. G. Paulus, H. Walther, R. Hartmann, and L. Strüder, “High-order harmonic generation at a repetition rate of 100 kHz,” Phys. Rev. A 68(1), 013814 (2003). [CrossRef]

]. More efficient harmonic generation has been achieved by phase matching in a high pressure gas cell with a Ti:Sapphire laser system operated at 50 kHz repetition rate and 25 µJ pulse energy [17

17. M.-C. Chen, M. R. Gerrity, S. Backus, T. Popmintchev, X. Zhou, P. Arpin, X. Zhang, H. C. Kapteyn, and M. M. Murnane, “Spatially coherent, phase matched, high-order harmonic EUV beams at 50 kHz,” Opt. Express 17(20), 17376–17383 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-17376. [CrossRef] [PubMed]

]. Spatial coherence together with about 10 nW of average power are demonstrated in this publication. The authors also mention that high harmonic generation in waveguide geometries can yield an average power of 1 µW for a 1 kHz system (Table 1

Table 1. Overview of the laser systems used for high harmonic generation (FCPA – fiber chirped pulse amplifcation system, NC-FCPA – nonlinear compressed fiber chirped pulse amplification system, OPCPA – optical parametric chirped pulse amplification system).

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in [17

17. M.-C. Chen, M. R. Gerrity, S. Backus, T. Popmintchev, X. Zhou, P. Arpin, X. Zhang, H. C. Kapteyn, and M. M. Murnane, “Spatially coherent, phase matched, high-order harmonic EUV beams at 50 kHz,” Opt. Express 17(20), 17376–17383 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-17376. [CrossRef] [PubMed]

]). For spectroscopic purposes higher repetition rates are favourable. In this regard MHz high harmonic generation with a fiber chirped pulse amplification system, as presented lately, becomes an interesting alternative [18

18. J. Boullet, Y. Zaouter, J. Limpert, S. Petit, Y. Mairesse, B. Fabre, J. Higuet, E. Mével, E. Constant, and E. Cormier, “High-order harmonic generation at a megahertz-level repetition rate directly driven by an ytterbium-doped-fiber chirped-pulse amplification system,” Opt. Lett. 34(9), 1489–1491 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-9-1489. [CrossRef] [PubMed]

]. When assuming a conversion efficiency of 10−6 the authors calculate an achievable average power of 30 µW at 1 MHz even though no further details nor measurements or estimations of the actual achieved average power are given. Over the last years there has also been substantial progress in optimizing the output of high harmonic generation by high energy laser systems. This resulted in µJ pulse energy in a single harmonic with an average power ≥100 µW [19

19. E. Takahashi, Y. Nabekawa, and K. Midorikawa, “Generation of 10- microJ coherent extreme-ultraviolet light by use of high-order harmonics,” Opt. Lett. 27(21), 1920–1922 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-21-1920. [CrossRef]

,20

20. I. J. Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92(2), 021125 (2008). [CrossRef]

]. However, for spectroscopic purposes a high average power in combination with a higher repetition rate is required rather than high pulse energy.

In this work we present experimental results on high repetition rate HHG with three different fiber amplifier based laser systems. In comparison to [16

16. F. Lindner, W. Stremme, M. G. Schätzel, F. Grasbon, G. G. Paulus, H. Walther, R. Hartmann, and L. Strüder, “High-order harmonic generation at a repetition rate of 100 kHz,” Phys. Rev. A 68(1), 013814 (2003). [CrossRef]

18

18. J. Boullet, Y. Zaouter, J. Limpert, S. Petit, Y. Mairesse, B. Fabre, J. Higuet, E. Mével, E. Constant, and E. Cormier, “High-order harmonic generation at a megahertz-level repetition rate directly driven by an ytterbium-doped-fiber chirped-pulse amplification system,” Opt. Lett. 34(9), 1489–1491 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-9-1489. [CrossRef] [PubMed]

] we are able to use higher average power and shorter pulse durations. This enables shorter wavelength generation in comparison to [18

18. J. Boullet, Y. Zaouter, J. Limpert, S. Petit, Y. Mairesse, B. Fabre, J. Higuet, E. Mével, E. Constant, and E. Cormier, “High-order harmonic generation at a megahertz-level repetition rate directly driven by an ytterbium-doped-fiber chirped-pulse amplification system,” Opt. Lett. 34(9), 1489–1491 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-9-1489. [CrossRef] [PubMed]

] and higher average powers compared to [16

16. F. Lindner, W. Stremme, M. G. Schätzel, F. Grasbon, G. G. Paulus, H. Walther, R. Hartmann, and L. Strüder, “High-order harmonic generation at a repetition rate of 100 kHz,” Phys. Rev. A 68(1), 013814 (2003). [CrossRef]

,17

17. M.-C. Chen, M. R. Gerrity, S. Backus, T. Popmintchev, X. Zhou, P. Arpin, X. Zhang, H. C. Kapteyn, and M. M. Murnane, “Spatially coherent, phase matched, high-order harmonic EUV beams at 50 kHz,” Opt. Express 17(20), 17376–17383 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-17376. [CrossRef] [PubMed]

]. We demonstrate how recent advances in fiber laser and amplifier technique can be exploited for enhancement of conversion efficiency.

2. Experimental setup and driving laser systems

The experiments have been performed in a free focusing geometry meaning that we either use lenses or mirrors to focus onto a gas jet (Fig. 1
Fig. 1 Schematic of the experimental setup. Different high repetition rate driving laser sources are focused with a focusing element (lens or mirror) onto a gas jet (Argon or Krypton) which is provided by a gas nozzle with a diameter of about 50 µm. The fundamental light is blocked by a 200 nm thick aluminium filter. Spectral analysis is performed by a grazing incidence monochromator (McPherson 248/310G) and a channel electron multiplier (Photonics CEM 5900 SL Magnum).
.). A 50 µm gas nozzle enables high particle densities of either argon or krypton gas in the focal region while keeping the overall gas load minimal. This is necessary, since the operation at high repetition rates does not allow for a pulsed gas jet. Note that the confocal parameter for all of the used laser systems is expected to be larger than the interaction length with the gas (Table 1).

The high harmonic radiation has been separated from the fundamental by a 200 nm aluminium filter and spectral analysis has been carried out with a grazing incidence monochromator (McPherson Inc., 248/310G) and a channel electron multiplier (Photonics CEM 5900 SL Magnum). The CEM is operated in analog modus and is expected to have a linear response and no saturation effects for the measurements presented in this work.

A first laser system that has been used for high harmonic generation is a fiber chirped pulse amplification system (FCPA) that has been presented elsewhere [21

21. F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32(24), 3495–3497 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-24-3495. [CrossRef] [PubMed]

]. It can be operated at different repetition rates and pulse energies and has a typical pulse duration of 800 fs at a center wavelength of 1030 nm. The output beam has been focused to a 45 µm diameter (1/e2 intensity diameter) onto an argon and krypton gas jet with a f = 100 mm lens.

To shorten the pulses and increase their peak power we use nonlinear compression of the FCPA (NC-FCPA) system with improved performance compared to [22

22. S. Hädrich, J. Rothhardt, T. Eidam, J. Limpert, and A. Tünnermann, “High energy ultrashort pulses via hollow fiber compression of a fiber chirped pulse amplification system,” Opt. Express 17(5), 3913–3922 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3913. [CrossRef] [PubMed]

]. The technique is based on spectral broadening in noble gas filled hollow fibers with subsequent chirp removal. This allows compressing the pulses to 51 fs with a pulse energy of 200 µJ while increasing the peak power to 2.5 GW at a repetition rate of 50 kHz and a center wavelength of 1030 nm. An estimation of the peak power can be performed by Fourier transforming the spectrum and adding third order dispersion to match the autocorrelation width, since second order dispersion is mostly compensated by the chirped mirrors. The overall efficiency of this compression technique is 50% meaning that we start with 400 µJ, 800 fs pulses. The output of the compressor has been focused to a 50 µm diameter (1/e2 intensity diameter) onto a krypton gas jet with the same f = 100 mm lens.

A third driving laser source that is used for HHG is a few-cycle optical parametric chirped pulse amplification system (OPCPA). Amplification of the ultrashort pulses of a Ti:Sapphire oscillator at a high repetition rate and average power is achieved by pumping the parametric amplifier with the frequency doubled output of the FCPA system. The system is operated at 96 kHz with pulses of 8 fs duration, 53 µJ pulse energy and a peak power of ~6 GW at a center wavelength of 730 nm [23

23. J. Rothhardt, S. Hädrich, E. Seise, M. Krebs, F. Tavella, A. Willner, S. Düsterer, H. Schlarb, J. Feldhaus, J. Limpert, J. Rossbach, and A. Tünnermann, “High average and peak power few-cycle laser pulses delivered by fiber pumped OPCPA system,” Opt. Express 18(12), 12719–12726 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-12-12719. [CrossRef] [PubMed]

]. The pulses are focused to a focal spot size of 69 µm x 91 µm (1/e2 intensity diameter) onto a krypton gas jet with a f = 200 mm lens.

Estimation of conversion efficiency

The conversion efficiency can be estimated by accounting for all losses of the harmonic beam emerging from the interaction region and considering all signal manipulation that has to be made for data acquisition. The harmonic photons are detected via a channel electron multiplier with subsequent current amplifier. The detected signal A in Volts can then be used to calculate the number of photons/s Nph at the entrance of the spectrometer:
Nph=AGCEMgηeηgtAl,
(1)
where A [V] is the recorded value, GCEM = 107 is the gain of the CEM, g [V/A] the gain of the voltage amplifier, η = 0.2 the detection efficiency [Electrons/Photon] of the CEM, e [C] is the elementary charge, ηg = 0.1 the grating efficiency and tAl the aluminium filter transmission [24]. We did not account for losses of oxidation of the aluminium foil that could lead to a decrease in signal, e.g. of a factor of 5 for a 20 nm Al2O3 layer [24]. The gain of the voltage amplifier is 105 or 106 depending on the measurement. Please note that for the estimation of the conversion efficiency the signal A has been obtained by integrating over the strongest harmonic.

Major losses occur at the entrance slit of the spectrometer, so that the number of photons/s impinging on the spectrometer is higher than estimated by Eq. (1). They depend on the divergence of the generated harmonic beam. Since we do not have the possibility to monitor the spatial profile of the harmonic beam an upper and lower boundary for the divergence, and consequently, for the conversion efficiency has been defined. It has been reported that the intensity of the plateau harmonics can be approximated by an I6 power law [25

25. E. Constant, D. Garzella, P. Breger, E. Mével, Ch. 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]

]. By measuring the intensity distribution of the fundamental in the focal region, the focal spot size of the harmonics is then ωHHG=ω0/6, where ωHHG and ω0 are the 1/e2 intensity radii for the harmonic and fundamental radiation, respectively. The lowest divergence can be expected for diffraction limited propagation resulting in
θHHGmin=arctan(λHHGπωHHG),
(2)
where λHHG is the wavelength of the considered harmonic. Typically, using Eq. (2) results in divergence angles of ~1 mrad for wavelengths of about 45 nm and a focal spot diameter of less than 100 µm (Table 2

Table 2. Experimental results of high harmonic generation with the laser systems presented in Table 1. Note that the shortest harmonic with the FCPA system has been obtained with argon gas. The estimation of conversion efficiency has been carried out based upon the method described in section 2 and Krypton is used for all three laser systems.

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). However, there are two contributions to each harmonic resulting from a short and a long trajectory of the freed electron. This imposes a phase that has consequences for spatial and spectral characteristics. Most importantly, the long trajectories lead to higher divergence angles of the harmonics and can be described as [26

26. X. He, M. Miranda, J. Schwenke, O. Guilbaud, T. Ruchon, C. Heyl, E. Georgadiou, R. Rakowski, A. Persson, M. B. Gaarde, and A. L’Huillier, “Spatial and spectral properties of the high-order harmonic emission in argon for seeding applications,” Phys. Rev. A 79(6), 063829 (2009). [CrossRef]

]
θHHGmax=λHHGπωHHG1+4α2I02ωHHG4ω04,
(3)
where λHHG and ωHHG are the wavelength and 1/e2 intensity radius of the harmonic beam and I0 and ω0 are the peak intensity and 1/e2 intensity radius of the fundamental. The quantity α describes the intensity dependent phase Φ = α·I that is accumulated by the free electron. Typical α values for the long trajectory of plateau harmonics and intensity >1014 W/cm2 are 22 [26

26. X. He, M. Miranda, J. Schwenke, O. Guilbaud, T. Ruchon, C. Heyl, E. Georgadiou, R. Rakowski, A. Persson, M. B. Gaarde, and A. L’Huillier, “Spatial and spectral properties of the high-order harmonic emission in argon for seeding applications,” Phys. Rev. A 79(6), 063829 (2009). [CrossRef]

]. Using Eq. (3) leads to divergence angles >10 mrad for the considered harmonics and defines the upper boundary for the estimation (Table 2). The fraction Te transmitted through the rectangular entrance slit with width we can then be calculated using
Temin/max=2Φ0(wezϑmin/max),
(4)
where erf(x)=2Φ0(2x), z = 26 cm is the distance of gas jet and slit and ϑmin/max is the divergence of the harmonics beam (Eq. (2) and 3). Equation (4) enables the calculation of Photons/s generated in the interaction region.

3. High average power high harmonic generation

The laser systems presented in the section above have all been used to generate high harmonics. The first measurements are carried out with the FCPA system as driving laser source. Using this system allowed for very high repetition rates of up to 500 kHz (100 µJ pulse energy). The highest harmonic observed at this repetition rate is the 27th at a wavelength of 38.1 nm (Fig. 2
Fig. 2 HHG with fiber chirped pulse amplification system. The harmonic signal intensity with respect to the wavelength is shown for 4 different repetition rates of 500 kHz, 200 kHz, 100 kHz and 50 kHz. The spectra have been obtained by focusing the output of the fiber chirped pulse amplification system onto an argon gas jet. The same pulse duration of 800 fs and focal spot size of 45 µm (1/e2 intensity diameter) was used for all repetition rates while the pulse energies were 100 µJ (500 kHz), 150 µJ (200 kHz), 300 µJ (100 kHz) and 400 µJ (50 kHz). At the highest repetition rate of 500 kHz the spectrum is an average of 4 consecutive scans and a lower spectrometer resolution has been used to improve the signal to noise ratio. The highest order harmonics observed are the 27th (38.1 nm, 500 kHz), the 33th (31.2 nm, 200 kHz), the 39th (26.4 nm, 100 kHz) and the 43rd (23.9 nm, 50 kHz).
.). By reducing the repetition rate to 200 kHz, 100 kHz and 50 kHz the pulse energy can be increased up to 400 µJ. Consequently, the intensity is increased and higher orders up to the 43rd (23.9 nm) at 50 kHz can be observed (Fig. 2). A main limitation for the generation of shorter wavelengths is ionization due to the long pulse duration. The fraction of ionized medium can be estimated by calculating ionization rates with the ADK model [27

27. M. V. Ammosov, N. B. Delone, and V. P. Kraĭnov, “Tunnel ionization of complex atoms and of atomic ions in an altering electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

]. For an 800 fs, 400 µJ Gaussian pulse with a peak intensity of 1.1·1014 W/cm2 (corresponding to H43 in argon via the cutoff law [28

28. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993). [CrossRef] [PubMed]

]) the ionization fraction at the pulse peak is 0.5%. Increasing the pulse energy leads to higher ionization levels which prevents phase matching and shorter wavelength generation as has been observed experimentally.

The above presented results have been obtained with argon as nonlinear medium. However, the results presented later used krypton as target medium. Hence, to estimate and compare conversion efficiency and number of photons per second for the three driving laser systems commensurable experimental conditions have been applied, i.e. identical interaction region, krypton gas and similar backing pressure. Therefore, measurements of the harmonic spectra generated in krypton have been repeated for 400 µJ, 800 fs pulses at a repetition rate of 50 kHz. Due to the lower ionization potential of krypton the ionization at the peak of the pulse is calculated to be 9%. Nevertheless, this experiment yields a conversion efficiency between 1.4·10−11 and 1.3·10−10 into the strongest harmonic at 44.7 nm. Due to the high repetition rate this already corresponds to an average power of 0.3 to 3 nW (6·107 photons/s - 6·108 photons/s).

The nonlinear compressed pulses of the FCPA system enable higher peak power and consequently intensity. This leads to the generation of higher harmonics up to the 47th order at a wavelength of 21.9 nm (Fig. 3
Fig. 3 HHG with post-compressed pulses. The nonlinear compression of a fiber chirped pulse amplification system is used to shorten 400 µJ, 800 fs pulses to 200 µJ, 51 fs pulses at a repetition rate of 50 kHz. They are focused to a focal spot diameter of 50 µm (1/e2 intensity diameter) onto a krypton gas jet. The left side shows the short wavelength part of the harmonic spectrum (right side). The shortest wavelength that has been observed is the 47th harmonic at 21.9 nm.
). However, this cutoff harmonic corresponds to an intensity of 1.4·1014 W/cm2, which is almost a factor of 2 below the expected intensity of 2.5·1014 W/cm2. This is mostly due to the high ionization level of 41% at the pulse peak (65% after the pulse) which leads to dephasing (phase mismatch) and prevents the generation of shorter wavelengths. Nevertheless, this helps to increase the conversion efficiency by more than a factor of 5 (1.0·10−10 - 1.0·10−9) and consequently the number of photons per second to 2.3·108 photons/s - 2.3·109 photons/s (1 nW – 10 nW) at the strongest harmonic of 44.7 nm.

The few-cycle OPCPA at 730 nm central wavelength allows for even higher peak power, and therefore, the generation of the 35th harmonic at a wavelength of 20.1 nm (Fig. 4
Fig. 4 HHG with few-cycle laser pulses. An optical parametric chirped pulse amplification system generates few-cycle laser pulses with 53 µJ pulse energy, 8 fs pulse duration at a repetition rate of 96 kHz. These pulses are focused to a focal spot size of 69 µm x 91 µm (1/e2 intensity diameter) onto a krypton gas jet. The left side shows the short wavelength part of the harmonics spectrum together with the expected harmonic wavelength (dashed gray line). The shortest wavelength that has been observed is the 35th harmonic at 20.1 nm which is blueshifted.
). Due to the ultrashort pulse duration of only 8 fs the ionization level at the pulse peak is only 6% even though the peak intensity is >2.4·1014 W/cm2. We observe a blueshift for the 27th up to the 35th harmonic, attributed to self-phase modulation in the ionising medium [29

29. K. Miyazaki and H. Takada, “High-order harmonic generation in the tunneling regime,” Phys. Rev. A 52(4), 3007–3021 (1995). [CrossRef] [PubMed]

] and/or a nonadiabatic effect caused by the time-dependent phase of the freed electron in the rapidly increasing electrical field of few-cycle laser pulses [30

30. H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of Nonadiabatic Blueshift of High Harmonics in an Intense Femtosecond Laser Field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999). [CrossRef]

]. The latter one is expected to grow linearly with harmonic order. That agrees qualitatively with our experimental data indicating that the nonadiabatic blueshift is dominant for our experiments.

The shortest achievable wavelength is only a minor improvement compared to the harmonic generation with the nonlinear compressed pulses of the fiber chirped pulse amplification system, but is in good agreement with the cutoff law 1/λc~I·λ2, where λc is the cutoff wavelength, I the intensity and λ the wavelength of the driving laser system [28

28. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993). [CrossRef] [PubMed]

]. More interestingly, HHG with this system has been significantly more efficient (Table 2). This is due to reduced ionization resulting from the ultrashort pulse duration of 8 fs, and higher possible peak intensities in the focal region. Part of this enhancement can also be attributed to the single atom response that recently experimentally has been determined to scale as λ-(6.5 ± 1.1) [31

31. A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009). [CrossRef] [PubMed]

]. This scaling law leads to an increase in single atom response by a factor of ~9.4. The conversion efficiency is increased by more than 2 orders of magnitude compared to the use of nonlinear compressed pulses and 3 orders of magnitude compared to the use of fiber chirped pulse amplification system. It is estimated to be 1.8·10−8 – 3.4·10−7 (1.7·1010 Photons/s – 3.8·1011 Photons/s) at the strongest harmonic of 42.9 nm. Considering the input average power of 5 W this conversion efficiency already belongs to µW level harmonic power (Table 2). We have not investigated phase matching in particular, but expect phase mismatch to limit our output. In consequence, even higher conversion efficiency can be expected for proper phase matching.

We have also worked with xenon gas, but were limited in pressure due to gas load at the turbo molecular pump. Improved vacuum conditions and pumping will help to test xenon in the near future, since it may help to increase the conversion efficiency further.

4. Conclusion

In summary, we have presented significant experimental progress in HHG at high repetition rates. We demonstrate improvements in conversion efficiency with pulse shortening techniques. Our experimental data indicate photon numbers that are comparable with optimized high repetition rate high harmonic generation based on waveguides or cavity enhancement. With further improvements in experimental conditions (interaction region, focusing conditions, quasi-phasematching schemes) and the feasibility of increasing the average power of the few cycle optical parametric chirped pulse amplification system by at least an order of magnitude we expect the possibility to enhance the number of photons per second by 3 orders of magnitude resulting in milliwatt harmonic average power. Even though we only generate low energy harmonics (fJ - pJ), the high photon number is especially interesting for numerous investigations, such as imaging schemes [2

2. R. L. Sandberg, D. A. Raymondson, C. La-O-Vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34(11), 1618–1620 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-11-1618. [CrossRef] [PubMed]

4

4. R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi, “Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams,” Phys. Rev. Lett. 99(9), 098103 (2007). [CrossRef] [PubMed]

]. These applications will greatly benefit from compactness and simplicity of such laser systems that enable an increase in photon number, since this will shorten integration and processing times making studies possible in physics, biology or chemistry.

Acknowledgements

This work has been partly supported by the German Federal Ministry of Education and Research (BMBF), Grant 05 ES7GU1, the Helmholtz Institute Jena and the European Research Council (ERC), SIRG 240460-PECS. S.H. acknowledges financial support by the Carl Zeiss Stiftung Germany and A.W. acknowledges financial support by the Graduiertenkolleg 1355 at the University of Hamburg.

References and Links

1.

E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317(5843), 1374–1378 (2007). [CrossRef] [PubMed]

2.

R. L. Sandberg, D. A. Raymondson, C. La-O-Vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34(11), 1618–1620 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-11-1618. [CrossRef] [PubMed]

3.

R. L. Sandberg, C. Song, P. W. Wachulak, D. A. Raymondson, A. Paul, B. Amirbekian, E. Lee, A. E. Sakdinawat, C. La-O-Vorakiat, M. C. Marconi, C. S. Menoni, M. M. Murnane, J. J. Rocca, H. C. Kapteyn, and J. Miao, “High numerical aperture tabletop soft x-ray diffraction microscopy with 70-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 105(1), 24–27 (2008). [CrossRef]

4.

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi, “Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams,” Phys. Rev. Lett. 99(9), 098103 (2007). [CrossRef] [PubMed]

5.

T. Haarlammert and H. Zacharias, “Application of high harmonic radiation in surface science,” Curr. Opin. Solid State Mater. Sci. 13(1-2), 13–27 (2009). [CrossRef]

6.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]

7.

A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B 39(1), R1–R37 (2006). [CrossRef]

8.

J. Eden, “High-order harmonic generation and other intense optical field-matter interactions: review of recent experimental and theoretical advances,” Prog. Quantum Electron. 28(3-4), 197–246 (2004). [CrossRef]

9.

C. Winterfeldt, C. Spielmann, and G. Gerber, “Colloquium: Optimal control of high-harmonic generation,” Rev. Mod. Phys. 80(1), 117–140 (2008). [CrossRef]

10.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, S. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M.-E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4(4), 296–300 (2008). [CrossRef]

11.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97(2), 369–373 (2009). [CrossRef]

12.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008). [CrossRef] [PubMed]

13.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and Th. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100(25), 253901 (2008). [CrossRef] [PubMed]

14.

D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett. 33(10), 1099–1101 (2008), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-10-1099. [CrossRef] [PubMed]

15.

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett. 35(12), 2052–2054 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-12-2052. [CrossRef] [PubMed]

16.

F. Lindner, W. Stremme, M. G. Schätzel, F. Grasbon, G. G. Paulus, H. Walther, R. Hartmann, and L. Strüder, “High-order harmonic generation at a repetition rate of 100 kHz,” Phys. Rev. A 68(1), 013814 (2003). [CrossRef]

17.

M.-C. Chen, M. R. Gerrity, S. Backus, T. Popmintchev, X. Zhou, P. Arpin, X. Zhang, H. C. Kapteyn, and M. M. Murnane, “Spatially coherent, phase matched, high-order harmonic EUV beams at 50 kHz,” Opt. Express 17(20), 17376–17383 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-17376. [CrossRef] [PubMed]

18.

J. Boullet, Y. Zaouter, J. Limpert, S. Petit, Y. Mairesse, B. Fabre, J. Higuet, E. Mével, E. Constant, and E. Cormier, “High-order harmonic generation at a megahertz-level repetition rate directly driven by an ytterbium-doped-fiber chirped-pulse amplification system,” Opt. Lett. 34(9), 1489–1491 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-9-1489. [CrossRef] [PubMed]

19.

E. Takahashi, Y. Nabekawa, and K. Midorikawa, “Generation of 10- microJ coherent extreme-ultraviolet light by use of high-order harmonics,” Opt. Lett. 27(21), 1920–1922 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-21-1920. [CrossRef]

20.

I. J. Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92(2), 021125 (2008). [CrossRef]

21.

F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32(24), 3495–3497 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-24-3495. [CrossRef] [PubMed]

22.

S. Hädrich, J. Rothhardt, T. Eidam, J. Limpert, and A. Tünnermann, “High energy ultrashort pulses via hollow fiber compression of a fiber chirped pulse amplification system,” Opt. Express 17(5), 3913–3922 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3913. [CrossRef] [PubMed]

23.

J. Rothhardt, S. Hädrich, E. Seise, M. Krebs, F. Tavella, A. Willner, S. Düsterer, H. Schlarb, J. Feldhaus, J. Limpert, J. Rossbach, and A. Tünnermann, “High average and peak power few-cycle laser pulses delivered by fiber pumped OPCPA system,” Opt. Express 18(12), 12719–12726 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-12-12719. [CrossRef] [PubMed]

24.

http://henke.lbl.gov/optical_constants/filter2.html

25.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. 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]

26.

X. He, M. Miranda, J. Schwenke, O. Guilbaud, T. Ruchon, C. Heyl, E. Georgadiou, R. Rakowski, A. Persson, M. B. Gaarde, and A. L’Huillier, “Spatial and spectral properties of the high-order harmonic emission in argon for seeding applications,” Phys. Rev. A 79(6), 063829 (2009). [CrossRef]

27.

M. V. Ammosov, N. B. Delone, and V. P. Kraĭnov, “Tunnel ionization of complex atoms and of atomic ions in an altering electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

28.

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993). [CrossRef] [PubMed]

29.

K. Miyazaki and H. Takada, “High-order harmonic generation in the tunneling regime,” Phys. Rev. A 52(4), 3007–3021 (1995). [CrossRef] [PubMed]

30.

H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of Nonadiabatic Blueshift of High Harmonics in an Intense Femtosecond Laser Field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999). [CrossRef]

31.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009). [CrossRef] [PubMed]

OCIS Codes
(140.3510) Lasers and laser optics : Lasers, fiber
(190.7110) Nonlinear optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 7, 2010
Revised Manuscript: August 5, 2010
Manuscript Accepted: August 10, 2010
Published: September 8, 2010

Citation
S. Hädrich, J. Rothhardt, M. Krebs, F. Tavella, A. Willner, J. Limpert, and A. Tünnermann, "High harmonic generation by novel fiber amplifier based sources," Opt. Express 18, 20242-20250 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20242


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References

  1. E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317(5843), 1374–1378 (2007). [CrossRef] [PubMed]
  2. R. L. Sandberg, D. A. Raymondson, C. La-O-Vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34(11), 1618–1620 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-11-1618 . [CrossRef] [PubMed]
  3. R. L. Sandberg, C. Song, P. W. Wachulak, D. A. Raymondson, A. Paul, B. Amirbekian, E. Lee, A. E. Sakdinawat, C. La-O-Vorakiat, M. C. Marconi, C. S. Menoni, M. M. Murnane, J. J. Rocca, H. C. Kapteyn, and J. Miao, “High numerical aperture tabletop soft x-ray diffraction microscopy with 70-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 105(1), 24–27 (2008). [CrossRef]
  4. R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi, “Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams,” Phys. Rev. Lett. 99(9), 098103 (2007). [CrossRef] [PubMed]
  5. T. Haarlammert and H. Zacharias, “Application of high harmonic radiation in surface science,” Curr. Opin. Solid State Mater. Sci. 13(1-2), 13–27 (2009). [CrossRef]
  6. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]
  7. A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B 39(1), R1–R37 (2006). [CrossRef]
  8. J. Eden, “High-order harmonic generation and other intense optical field-matter interactions: review of recent experimental and theoretical advances,” Prog. Quantum Electron. 28(3-4), 197–246 (2004). [CrossRef]
  9. C. Winterfeldt, C. Spielmann, and G. Gerber, “Colloquium: Optimal control of high-harmonic generation,” Rev. Mod. Phys. 80(1), 117–140 (2008). [CrossRef]
  10. G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, S. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M.-E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4(4), 296–300 (2008). [CrossRef]
  11. O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97(2), 369–373 (2009). [CrossRef]
  12. S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008). [CrossRef] [PubMed]
  13. A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and Th. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100(25), 253901 (2008). [CrossRef] [PubMed]
  14. D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett. 33(10), 1099–1101 (2008), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-10-1099 . [CrossRef] [PubMed]
  15. I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett. 35(12), 2052–2054 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-12-2052 . [CrossRef] [PubMed]
  16. F. Lindner, W. Stremme, M. G. Schätzel, F. Grasbon, G. G. Paulus, H. Walther, R. Hartmann, and L. Strüder, “High-order harmonic generation at a repetition rate of 100 kHz,” Phys. Rev. A 68(1), 013814 (2003). [CrossRef]
  17. M.-C. Chen, M. R. Gerrity, S. Backus, T. Popmintchev, X. Zhou, P. Arpin, X. Zhang, H. C. Kapteyn, and M. M. Murnane, “Spatially coherent, phase matched, high-order harmonic EUV beams at 50 kHz,” Opt. Express 17(20), 17376–17383 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-17376 . [CrossRef] [PubMed]
  18. J. Boullet, Y. Zaouter, J. Limpert, S. Petit, Y. Mairesse, B. Fabre, J. Higuet, E. Mével, E. Constant, and E. Cormier, “High-order harmonic generation at a megahertz-level repetition rate directly driven by an ytterbium-doped-fiber chirped-pulse amplification system,” Opt. Lett. 34(9), 1489–1491 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-9-1489 . [CrossRef] [PubMed]
  19. E. Takahashi, Y. Nabekawa, and K. Midorikawa, “Generation of 10- microJ coherent extreme-ultraviolet light by use of high-order harmonics,” Opt. Lett. 27(21), 1920–1922 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-21-1920 . [CrossRef]
  20. I. J. Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92(2), 021125 (2008). [CrossRef]
  21. F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32(24), 3495–3497 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-24-3495 . [CrossRef] [PubMed]
  22. S. Hädrich, J. Rothhardt, T. Eidam, J. Limpert, and A. Tünnermann, “High energy ultrashort pulses via hollow fiber compression of a fiber chirped pulse amplification system,” Opt. Express 17(5), 3913–3922 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3913 . [CrossRef] [PubMed]
  23. J. Rothhardt, S. Hädrich, E. Seise, M. Krebs, F. Tavella, A. Willner, S. Düsterer, H. Schlarb, J. Feldhaus, J. Limpert, J. Rossbach, and A. Tünnermann, “High average and peak power few-cycle laser pulses delivered by fiber pumped OPCPA system,” Opt. Express 18(12), 12719–12726 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-12-12719 . [CrossRef] [PubMed]
  24. http://henke.lbl.gov/optical_constants/filter2.html
  25. E. Constant, D. Garzella, P. Breger, E. Mével, Ch. 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]
  26. X. He, M. Miranda, J. Schwenke, O. Guilbaud, T. Ruchon, C. Heyl, E. Georgadiou, R. Rakowski, A. Persson, M. B. Gaarde, and A. L’Huillier, “Spatial and spectral properties of the high-order harmonic emission in argon for seeding applications,” Phys. Rev. A 79(6), 063829 (2009). [CrossRef]
  27. M. V. Ammosov, N. B. Delone, and V. P. Kraĭnov, “Tunnel ionization of complex atoms and of atomic ions in an altering electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).
  28. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993). [CrossRef] [PubMed]
  29. K. Miyazaki and H. Takada, “High-order harmonic generation in the tunneling regime,” Phys. Rev. A 52(4), 3007–3021 (1995). [CrossRef] [PubMed]
  30. H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of Nonadiabatic Blueshift of High Harmonics in an Intense Femtosecond Laser Field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999). [CrossRef]
  31. A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009). [CrossRef] [PubMed]

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