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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 20610–20615
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Two-color field for the generation of an isolated attosecond pulse in water-window region

Wenxiang Chen, Guanglong Chen, and Dong Eon Kim  »View Author Affiliations


Optics Express, Vol. 19, Issue 21, pp. 20610-20615 (2011)
http://dx.doi.org/10.1364/OE.19.020610


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Abstract

For the investigation of various ultrafast electron dynamics, an isolated attosecond pulse in a broad spectral range is necessary. The generation of isolated attosecond pulses demands the manipulation of the electric field of a laser. We propose a two-color field scheme for generating an isolated attosecond pulse in the water-window region. Two-color fields are generated by mixing two equally-strong pulsed color fields. The investigation shows that an isolated attosecond pulse with a photon energy of near 500 eV and a pulse duration of 125 – 188 attoseconds can be generated using 10 - 15 fs FWHM laser fields.

© 2011 OSA

1. Introduction

These isolated attosecond pulses have been used in studying electron dynamics in atoms [8

8. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419(6909), 803–807 (2002). [CrossRef] [PubMed]

10

10. E. Goulielmakis, Z. H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466(7307), 739–743 (2010). [CrossRef] [PubMed]

], in molecules and in condensed matter system [11

11. A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449(7165), 1029–1032 (2007). [CrossRef] [PubMed]

]. These are remarkable achievements; yet, for wider spread of attosecond pulses in various electron dynamics, attosecond pulses of different photon energies still need to be produced.

The effect of the mixing of pulsed two color fields on the generation of an isolated attosecond pulse has been investigated. Recently, a continuum around ~80 eV was obtained by a superposition of fields at 1290nm and 780nm [12

12. T. Siegel, R. Torres, D. J. Hoffmann, L. Brugnera, I. Procino, A. Zaïr, J. G. Underwood, E. Springate, I. C. E. Turcu, L. E. Chipperfield, and J. P. Marangos, “High harmonic emission from a superposition of multiple unrelated frequency fields,” Opt. Express 18(7), 6853–6862 (2010). [CrossRef] [PubMed]

]. Moreover, a continuum around ~200 eV was generated by an intense ultrashort two-color driver [13

13. F. Calegari, C. Vozzi, M. Negro, G. Sansone, F. Frassetto, L. Poletto, P. Villoresi, M. Nisoli, S. De Silvestri, and S. Stagira, “Efficient continuum generation exceeding 200 eV by intense ultrashort two-color driver,” Opt. Lett. 34(20), 3125–3127 (2009). [CrossRef] [PubMed]

]. It was also reported that the difference between the square of the strongest two-color field amplitude and the 2nd strongest two-color field amplitude is approximately proportional to the continuum length, thus inversely proportional to the attosecond pulse duration [7

7. B. Kim, J. An, Y. Yu, Y. Cheng, Z. Xu, and D. E. Kim, “Optimization of multi-cycle two-color laser fields for the generation of an isolated attosecond pulse,” Opt. Express 16(14), 10331–10340 (2008). [CrossRef] [PubMed]

]. In other words, the bigger the difference is, the narrower the isolated attosecond pulse will be.

This paper reports that the proper mixing of two equally strong laser fields can lead to isolated attosecond pulses as short as 125 as inside the water window region. This extension of the photon energy allows us to investigate the quantum effects in atoms and molecules on a broader photon energy range [16

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

].

2. Continuum analysis

To find an optimum wavelength of the 2nd color, we have done a series of simulations for various wavelengths of the 2nd color from 300 nm to 2800 nm for a fixed pulse duration to find out the highest value for R. The results are shown in Fig. 1
Fig. 1 The change of the ratio, R, with respect to the wavelength of the second color for a given pulse duration. The wavelength of the first color is fixed at 800 nm. Different color corresponds to different pulse durations. A (Red): 5 fs FWHM for 800 nm, 5 fs FWHM for 2nd color; B (blue): 5 fs FWHM for 800 nm, 10 fs FWHM for 2nd color; C (black): 10 fs FWHM for 800 nm, 10 fs FWHM for 2nd color; D (green): 10 fs FWHM for 800 nm, 15 fs FWHM for 2nd color. The intensities of both colors are fixed at 3×1014 W/cm2. The carrier envelop phase (CEP) of each of two color fields has been set to be zero.
.

Figure 1 presents how the ratio of the two-color field changes with respect to the wavelength of the second color for a fixed pulse duration. Note that there are many maxima in the ratio R. Since the ratio is approximately inversely proportional to the duration of isolated attosecond pulses, the two-color fields corresponding to these local maxima are good candidates for high-order harmonic generation with a long continuum. Moreover, we note that the change of ratio with respect to the wavelength is rather dramatic: the ratio falls rapidly from 2.3 to 1.3 when the wavelength increases from 400 nm to 500 nm (Fig. 1A), which suggests that the duration of the attosecond pulse may sensitively depend on the wavelength of the driving laser. Therefore, if a wavelength is properly chosen, ideal isolated attosecond pulses can be obtained.

3. Generation of isolated attosecond pulses

Now that the optimum two-color fields are obtained, the corresponding continuum energy and attosecond pulse duration can be calculated, applying the Lewenstein model [17

17. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]

] to He atoms. In Fig. 1, the highest ratio of the two-color fields is 2.8 at 1940 nm (the acme of the red line) for 5 fs FWHM. However, this is practically not possible because the period of the 1940 nm color is longer than 5 fs. Thus, this case has to be abandoned.

The second best case is at the ratio of 2.3 (the acme of the blue line) at 1740 nm for 10 fs FWHM, which is practically possible. This two-color field and the corresponding time-frequency diagram produced in the interaction with He are presented in Fig. 2(a) and (b)
Fig. 2 (a) two-color field of an 800nm, 5fs FWHM,3×1014W/cm2 color mixed with a 1740nm, 10fs FWHM, 3×1014 W/cm2, T = 2.7 fs (b) time-frequency diagram (c) time-integrated spectrum (d) isolated attosecond pulse produced by a continuum from 440eV to 490eV. The simulation was done for a two-color field interacting with He atom. The carrier envelop phase (CEP) of 800nm and 1740 nm fields has been set to be zero.
.

As this strong electrical field changes rapidly around t = 0, a bound electron experiences a quick ionization and a high acceleration. Thus, the photons at about t = 1 fs emitted by this electron possess high energy. The time-integrated continuum is presented in Fig. 2(c), which clearly shows the energy of the continuum to be around 500 eV. What is more, if one is able to select this part of continuum, namely, 440eV~490eV using a multilayer mirror or a filter, an isolated single 125 attosecond pulse is expected to be produced. With a careful chirp management, this pulse can be further shortened.

There are other two-color fields that are also promising for HHG as Fig. 1 shows.

Figures 3(a)-(c)
Fig. 3 Simulation result for the interaction of the two color field of an 800 nm, 10 fs FWHM, 3×1014 W/cm2 color and a 1820 nm, 15 fs FWHM, 3×1014 W/cm2 with He. The carrier envelop phase (CEP) of 800nm and 1820 nm fields has been set to be zero. T = 2.7 fs. (a) integrated spectrum (b) time-frequency diagram and (c) isolated attosecond pulse expected from a continuum. An isolated pulse of 188 as is produced by a spectral filter for 470eV~550eV. Helium is used as a working gas medium.
are the results from the interaction of the two-color field of an 800 nm, 10 fs FWHM color and a 1820 nm, 15 fs FWHM with He. And the CEP difference is put at 0. The generated continuums are around 500 eV and an isolated attosecond pulses of about 188 as is expected, when a proper spectral filter for 470eV~550eV is used. Extra chirp management may further shorten them. This case is of great practical meaning since the 15 fs FWHM laser field is currently available by OPA technique.

More simulations were done for local maxima manifested in Fig. 1. The results are listed one by one in Table 1

Table 1. Various Combinations of Two-Color Fields at the Maxima of R Shown in Fig. 1 with their Resulting Attosecond Pulse Widths and the Energy Range of the Generated Continuum

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.The laser intensity is 3×1014 W/cm2 and the working gas is He.

As seen in Table 1, if an 800 nm color is mixed with another one from 1500 nm to 1850 nm, high continuum energy can be obtained. However, if an 800 nm color is mixed with a color whose wavelength is below 1000 nm, the continuum energy falls in the range of 100 eV~250 eV. Up to now, a < 5 fs FWHM, 800 nm laser has been used for an isolated attosecond pulse; however, the generation and maintenance of a < 5 fs laser pulse demands extra techniques with care. In this point of view, it is quite encouraging to note in Table 1 that an isolated attosecond pulse can be produced, using 10 fs FWHM, 800 nm light.

4. Comparison between the results from the two-color fields: 800nm + 400nm and 800nm + 1800nm

Since one of the goals of our work is the possibility of using a wider range of wavelength for the second color(300nm-2000nm), we compare the results from the two-color fields 800nm + 400nm and 800 + 1800nm in more details. As the driving field is obtained by a heterodyne mixing of few-optical cycle pulses, the carrier envelop phase (CEP) of each of the two fields should be stabilized. In addition to this, the CEP difference (ΔCEP) between the two field is expected to make an effect. Thus, the influence of CEP difference has been explored. Here we consider four situations: ΔCEP = 0, π/2, π, 3π/2. The CEP of 800 nm light is varied while the CEP of other colors is fixed at CEP = 0. The results are presented in Table 2

Table 2. CEP Effect

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. Note that in this simulation, the FWHMs for 400nm, 800nm and 1800nm color are 10fs, 5fs, and 10fs respectively. The intensity for all these three colors are the same as 3×1014 W/cm2.Continuum energy and attosecond pulses obtained from two color fields, 800nm + 400nm and 800nm + 1800nm in different ΔCEP values. The CEP of the 800 nm light varies as ΔCEP while the CEP of other fields is fixed at 0.

We can observe several points in Table 2. Regardless of ΔCEP change, the continuum energy obtained from the driving field 800nm + 1800nm is always higher than that obtained from the driving field 800nm + 400nm.

It should not be ignored that the continuum energy varies according to ΔCEP. The variation is larger in the case of the 800nm + 1800nm field than in the case of the 800nm + 400nm field. For example, when ΔCEP = π, the continuum energy obtained from the 800nm + 1800nm field is in the range of 280eV~360eV; while ΔCEP = 0, it is around 440eV~530eV. The difference is as large as about 160eV. Note also that there may be more than one pulses generated when ΔCEP is not zero. The time-frequency diagrams for 800nm + 1800nm are presented in Fig. 4
Fig. 4 Time-frequency diagrams for 800nm + 1800nm in different CEP values. ΔCEP for (a)~(d) are 0,π/2,π,3π/2 respectively. T = 2.7fs.
which can help us to understand the transition from single to multiple attosecond pulses. From Fig. 4 it can be noted that the stabilization of ΔCEP is important in generating attosecond pulse by two-color mixing. The pulse duration also varies according to ΔCEP. The variation in the pulse duration is also larger for the 800nm + 1800nm field as in the continuum energy. This can be understood in this way. The 10 fs FWHM of 400 light contains ~7.5 cycles; on the other hand, the 10 fs FWHM of 1800 nm light contains 1.8 cycles. The change of the electric field of a laser is more dramatic in 10 fs FWHM, 1800 nm light.

5. Conclusion

The generation of isolated attosecond pulses demands the manipulation of the electric field of a laser. DOG and ionization gating are two examples of various manipulation schemes. Here we studied the manipulation by two color mixing. This study covered the wide range of laser wavelengths. The focus was made on the case of equal intensity of two color field. Our study provides a scheme to produce an ~190 attosecond pulse in the spectral region of ~500 eV using 10 - 15 fs FWHM laser fields and identities the laser parameters. These lasers are currently available by OPA technique. The efficiency of the two color mixing process is one of important issues to be addressed. The proper treatment should include the propagation effect and phase-matching issue. This issue is currently under active research for real experiments.

Acknowledgment

This research has been supported in part by Global Research Laboratory Program [Grant No 2009-00439] and by Leading Foreign Research Institute Recruitment Program [Grant No 2010-00471] through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST).

References and links

1.

M. Schultze, E. Goulielmakis, M. Uiberacker, M. Hofstetter, J. Kim, D. Kim, F. Krausz, and U. Kleineberg, “Powerful 170-attosecond XUV pulses generated with few-cycle laser pulses and broadband multilayer optics,” New J. Phys. 9(7), 243 (2007). [CrossRef]

2.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]

3.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006). [CrossRef] [PubMed]

4.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett. 100(10), 103906 (2008). [CrossRef] [PubMed]

5.

M. J. Abel, T. Pfeifer, P. M. Nagel, W. Boutu, M. J. Bell, C. P. Steiner, D. M. Neumark, and S. R. Leone, “Isolated attosecond pulses from ionization gating of high-harmonic emission,” Chem. Phys. 366(1-3), 9–14 (2009). [CrossRef]

6.

X. Feng, S. Gilbertson, H. Mashiko, H. Wang, S. D. Khan, M. Chini, Y. Wu, K. Zhao, and Z. Chang, “Generation of isolated attosecond pulses with 20 to 28 femtosecond lasers,” Phys. Rev. Lett. 103(18), 183901 (2009). [CrossRef] [PubMed]

7.

B. Kim, J. An, Y. Yu, Y. Cheng, Z. Xu, and D. E. Kim, “Optimization of multi-cycle two-color laser fields for the generation of an isolated attosecond pulse,” Opt. Express 16(14), 10331–10340 (2008). [CrossRef] [PubMed]

8.

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419(6909), 803–807 (2002). [CrossRef] [PubMed]

9.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007). [CrossRef] [PubMed]

10.

E. Goulielmakis, Z. H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466(7307), 739–743 (2010). [CrossRef] [PubMed]

11.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449(7165), 1029–1032 (2007). [CrossRef] [PubMed]

12.

T. Siegel, R. Torres, D. J. Hoffmann, L. Brugnera, I. Procino, A. Zaïr, J. G. Underwood, E. Springate, I. C. E. Turcu, L. E. Chipperfield, and J. P. Marangos, “High harmonic emission from a superposition of multiple unrelated frequency fields,” Opt. Express 18(7), 6853–6862 (2010). [CrossRef] [PubMed]

13.

F. Calegari, C. Vozzi, M. Negro, G. Sansone, F. Frassetto, L. Poletto, P. Villoresi, M. Nisoli, S. De Silvestri, and S. Stagira, “Efficient continuum generation exceeding 200 eV by intense ultrashort two-color driver,” Opt. Lett. 34(20), 3125–3127 (2009). [CrossRef] [PubMed]

14.

C. Vozzi, C. Manzoni, F. Calegari, E. Benedetti, G. Sansone, G. Cerullo, M. Nisoli, S. De Silvestri, and S. Stagira, “Characterization of a high-energy self-phase-stabilized near-infrared parametric source,” J. Opt. Soc. Am. B 25(7), B112–B117 (2008). [CrossRef]

15.

C. Vozzi, F. Calegari, F. Frassetto, L. Poletto, G. Sansone, P. Villoresi, M. Nisoli, S. De Silvestri, and S. Stagira, “Coherent continuum generation above 100 eV driven by an ir parametric source in a two-color scheme,” Phys. Rev. A 79(3), 033842 (2009). [CrossRef]

16.

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

17.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]

18.

J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007). [CrossRef] [PubMed]

19.

V. S. Yakovlev, M. Ivanov, and F. Krausz, “Enhanced phase-matching for generation of soft X-ray harmonics and attosecond pulses in atomic gases,” Opt. Express 15(23), 15351–15364 (2007). [CrossRef] [PubMed]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4160) Nonlinear optics : Multiharmonic generation
(320.0320) Ultrafast optics : Ultrafast optics

ToC Category:
Ultrafast Optics

History
Original Manuscript: August 11, 2011
Revised Manuscript: September 9, 2011
Manuscript Accepted: September 19, 2011
Published: October 3, 2011

Citation
Wenxiang Chen, Guanglong Chen, and Dong Eon Kim, "Two-color field for the generation of an isolated attosecond pulse in water-window region," Opt. Express 19, 20610-20615 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20610


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References

  1. M. Schultze, E. Goulielmakis, M. Uiberacker, M. Hofstetter, J. Kim, D. Kim, F. Krausz, and U. Kleineberg, “Powerful 170-attosecond XUV pulses generated with few-cycle laser pulses and broadband multilayer optics,” New J. Phys.9(7), 243 (2007). [CrossRef]
  2. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science320(5883), 1614–1617 (2008). [CrossRef] [PubMed]
  3. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science314(5798), 443–446 (2006). [CrossRef] [PubMed]
  4. H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett.100(10), 103906 (2008). [CrossRef] [PubMed]
  5. M. J. Abel, T. Pfeifer, P. M. Nagel, W. Boutu, M. J. Bell, C. P. Steiner, D. M. Neumark, and S. R. Leone, “Isolated attosecond pulses from ionization gating of high-harmonic emission,” Chem. Phys.366(1-3), 9–14 (2009). [CrossRef]
  6. X. Feng, S. Gilbertson, H. Mashiko, H. Wang, S. D. Khan, M. Chini, Y. Wu, K. Zhao, and Z. Chang, “Generation of isolated attosecond pulses with 20 to 28 femtosecond lasers,” Phys. Rev. Lett.103(18), 183901 (2009). [CrossRef] [PubMed]
  7. B. Kim, J. An, Y. Yu, Y. Cheng, Z. Xu, and D. E. Kim, “Optimization of multi-cycle two-color laser fields for the generation of an isolated attosecond pulse,” Opt. Express16(14), 10331–10340 (2008). [CrossRef] [PubMed]
  8. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature419(6909), 803–807 (2002). [CrossRef] [PubMed]
  9. M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature446(7136), 627–632 (2007). [CrossRef] [PubMed]
  10. E. Goulielmakis, Z. H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature466(7307), 739–743 (2010). [CrossRef] [PubMed]
  11. A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature449(7165), 1029–1032 (2007). [CrossRef] [PubMed]
  12. T. Siegel, R. Torres, D. J. Hoffmann, L. Brugnera, I. Procino, A. Zaïr, J. G. Underwood, E. Springate, I. C. E. Turcu, L. E. Chipperfield, and J. P. Marangos, “High harmonic emission from a superposition of multiple unrelated frequency fields,” Opt. Express18(7), 6853–6862 (2010). [CrossRef] [PubMed]
  13. F. Calegari, C. Vozzi, M. Negro, G. Sansone, F. Frassetto, L. Poletto, P. Villoresi, M. Nisoli, S. De Silvestri, and S. Stagira, “Efficient continuum generation exceeding 200 eV by intense ultrashort two-color driver,” Opt. Lett.34(20), 3125–3127 (2009). [CrossRef] [PubMed]
  14. C. Vozzi, C. Manzoni, F. Calegari, E. Benedetti, G. Sansone, G. Cerullo, M. Nisoli, S. De Silvestri, and S. Stagira, “Characterization of a high-energy self-phase-stabilized near-infrared parametric source,” J. Opt. Soc. Am. B25(7), B112–B117 (2008). [CrossRef]
  15. C. Vozzi, F. Calegari, F. Frassetto, L. Poletto, G. Sansone, P. Villoresi, M. Nisoli, S. De Silvestri, and S. Stagira, “Coherent continuum generation above 100 eV driven by an ir parametric source in a two-color scheme,” Phys. Rev. A79(3), 033842 (2009). [CrossRef]
  16. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009). [CrossRef]
  17. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994). [CrossRef] [PubMed]
  18. J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett.98(1), 013901 (2007). [CrossRef] [PubMed]
  19. V. S. Yakovlev, M. Ivanov, and F. Krausz, “Enhanced phase-matching for generation of soft X-ray harmonics and attosecond pulses in atomic gases,” Opt. Express15(23), 15351–15364 (2007). [CrossRef] [PubMed]

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