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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 15 — Jul. 16, 2012
  • pp: 16544–16551
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Control of bandwidth and central wavelength of an enhanced extreme ultraviolet spectrum generated in shaped laser field

Chaojin Zhang, Jinping Yao, Jielei Ni, Guihua Li, Ya Cheng, and Zhizhan Xu  »View Author Affiliations


Optics Express, Vol. 20, Issue 15, pp. 16544-16551 (2012)
http://dx.doi.org/10.1364/OE.20.016544


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Abstract

We theoretically investigate the enhancement of a selected spectral range in the high-order harmonic generation driven by the multi-color laser fields. The results show that the central wavelength of the enhanced narrow-bandwidth spectrum can be effectively controlled by adjusting the laser intensity and the time delay between laser pulses of different colors, due to the modified electron trajectory in the shaped laser field. Our approach can offer intense, bandwidth controllable single attosecond pulses for attosecond pump-probe experiments.

© 2012 OSA

In the present work, the synthesized field including three-color laser pulses will interact with argon (Ar) gas, which is numerically calculated by using the Lewenstein model based on the single-active-electron approximation [25

25. J. Yao, Y. Cheng, J. Chen, H. Zhang, H. Xu, H. Xiong, B. Zeng, W. Chu, J. Ni, X. Liu, and Z. Xu, “Generation of narrow-bandwidth, tunable, coherent xuv radiation using high-order harmonic generation,” Phys. Rev. A 83(3), 033835 (2011). [CrossRef]

, 27

27. Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007). [CrossRef] [PubMed]

29

29. M. Lewenstein, Ph. Balcou, M. Y. 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]

]. As expressed in the Ref [9

9. P. C. Li, I. L. Liu, and S. I. Chu, “Optimization of three-color laser field for the generation of single ultrashort attosecond pulse,” Opt. Express 19(24), 23857–23866 (2011). [CrossRef] [PubMed]

], the synthesized laser field consisting of a 5-fs, 800-nm pulse, a 15-fs, 2000-nm pulse and a 25-fs, 2200-nm pulse has the following form:
Es=E1exp[2ln(2)t2/τ12]cos(ω1t)+E2exp[2ln(2)t2/τ22]cos(ω2t)+E3exp[2ln(2)(t+t0)2/τ32]cos[ω3(t+t0)π2].
(1)
Here, ωi and τi (i = 1, 2, 3) denote the angular frequency and the pulse duration of three-color (i.e., 800 nm, 2000nm and 2200nm) laser fields, respectively. We chose the laser intensity I1=1.0×1014W/cm2, I2=1.0×1014W/cm2 andI3=1.5×1014W/cm2 [9

9. P. C. Li, I. L. Liu, and S. I. Chu, “Optimization of three-color laser field for the generation of single ultrashort attosecond pulse,” Opt. Express 19(24), 23857–23866 (2011). [CrossRef] [PubMed]

]. The parameter t0 is the time delay between the 800-nm laser field and 2200-nm laser field. As described in Refs [25

25. J. Yao, Y. Cheng, J. Chen, H. Zhang, H. Xu, H. Xiong, B. Zeng, W. Chu, J. Ni, X. Liu, and Z. Xu, “Generation of narrow-bandwidth, tunable, coherent xuv radiation using high-order harmonic generation,” Phys. Rev. A 83(3), 033835 (2011). [CrossRef]

, 30

30. M. Y. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A 54(1), 742–745 (1996). [CrossRef] [PubMed]

], due to the high-order harmonic signals depending strongly on the quantum-mechanical expectation value of dipole acceleration, the intensity of the nth harmonic can be obtained by calculating the ωn4|dn|2, where ωn is the frequency of the generated XUV photon, and dn is the dipole matrix element for bound-free transitions [11

11. J. Yao, Y. Li, B. Zeng, H. Xiong, H. Xu, Y. Fu, W. Chu, J. Ni, X. Liu, J. Chen, Y. Cheng, and Z. Xu, “Generation of an XUV supercontinuum by optimization of the angle between polarization planes of two linearly polarized pulses in a multicycle two-color laser field,” Phys. Rev. A 82(2), 023826 (2010). [CrossRef]

14

14. Ph. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett. 77(7), 1234–1237 (1996). [CrossRef] [PubMed]

].

We first study the narrow-bandwidth XUV radiation appeared in the plateau region of the high-order harmonic spectrum by controlling the waveform of the driving field. As shown in Fig. 1(a)
Fig. 1 (a) High-order harmonic spectra driven by two-color field and three-color field. (b) The enhanced harmonic spectrum in a linear scale.
, with a driving field synthesized by 800-nm and 2000-nm pulses, high-order harmonic spectrum has a typical plateau where harmonics at different orders have almost the same intensity. Surprisingly, when a 2200-nm laser field at an optimized delay (t0 = −0.2fs) is superposed on the two-color field, HHG around 141 eV is enhanced by even one order of magnitude within an extremely narrow spectral range. As indicated in Fig. 1(b), the selected XUV radiation shows a smooth spectral profile and its bandwidth is estimated to be ~3 eV [full width at half maximum (FWHM)], which allows us to generate isolated attosecond pulses with a narrow spectral bandwidth. Due to the limit enhanced spectral bandwidth, this method is not so efficient for the isolated attosecond pulse generation. When the low-order harmonics are filtered, an isolated attosecond can be obtained by performing inverse Fourier transformation in the energy range from 100 eV to 300 eV. Just as shown in Fig. 2(a)
Fig. 2 The temporal profiles of attosecond pulses generated by Fourier transformation of the high-order harmonics in the spectral range from 100 eV to 300 eV (a) without and (b) with the dispersion compensation. All parameters are the same as the red solid line of Fig. 1(a).
, a main attosecond pulse with the 155-as pulse duration accompanied by a satellite attosecond pulse is directly obtained. After phase compensation, an isolated, ~34-as pulse is created, which is close to one atomic unit (i. e., ~24 as), as indicated in Fig. 2(b).

More interestingly, the photon energy (i.e., wavelength) of the selected enhanced XUV radiation critically depends on the time delay t0 between the third field at 2200 nm and the other two fields. In Fig. 3
Fig. 3 High-order harmonic spectra generated by the synthesized field for different time delays of the field at 2200 nm.
, one can clearly see that when the time delay t0 is adjusted to 0.2 fs from −0.3 fs, the central photon energy of the narrow-bandwidth XUV radiation will gradually shift from ~120 eV to ~250 eV. Therefore, it will be easy to tune the central wavelength of the narrow-bandwidth XUV radiation in an extremely broad spectral range, which shows a significant advantage as compared to the report [26

26. Z. Zeng, Y. Cheng, Y. Fu, X. Song, R. Li, and Z. Xu, “Tunable high-order harmonic generation and the role of the folded quantum path,” Phys. Rev. A 77(2), 023416 (2008). [CrossRef]

]. With the increase of the time delay, the selected XUV radiation will become weak as well as broad, and finally disappear. In addition, it is also worthy pointing out that this effect of spectral selection can be observed over a large delay scale. That is to say, the requirement of this method on the vibration of time delay or carrier-envelope phase jitter is as strict as Ref [25

25. J. Yao, Y. Cheng, J. Chen, H. Zhang, H. Xu, H. Xiong, B. Zeng, W. Chu, J. Ni, X. Liu, and Z. Xu, “Generation of narrow-bandwidth, tunable, coherent xuv radiation using high-order harmonic generation,” Phys. Rev. A 83(3), 033835 (2011). [CrossRef]

], which is in favor of experimental performance in the future.

The above analysis can be further demonstrated by calculating the return kinetic energy and the ionization rate according to the classical three-step model [15

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

] and the Ammosov-Delone-Krainov (ADK) theory [31

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

]. Figure 5
Fig. 5 The synthesized laser field (blue dashed line), return kinetic energy (red solid line) and the ionization rate (gray filled curve) as a function of birth time at the time delay t0=0.3fs.
shows that the return kinetic energy (red solid line), the ionization rate (gray filled curve) and the synthesized laser field (blue dashed line) as functions of the birth time of the electron at the time delay of −0.3 fs. In Fig. 5, the return kinetic energy of electron shows a small plateau around 120 eV, leading to the selective enhancement of HHG shown in Fig. 3. Further analysis demonstrates that the electron along all paths between path 1 and path 2 will obtain the same kinetic energy. That is to say, the creation of the folded quantum paths is a dominant mechanism of generating narrow-bandwidth XUV radiation. Moreover, with the driving field with such a specific waveform, the ionization rate of the short quantum path is much higher than that of the long quantum path. As a result, the short quantum path plays an important role on selectively enhanced HHG [32

32. H. Du and B. Hu, “Propagation effects of isolated attosecond pulse generation with a multicycle chirped and chirped-free two-color field,” Phys. Rev. A 84(2), 023817 (2011). [CrossRef]

]. Therefore, another reason for this selective enhancement is because the ionization rate is maximum in the folded region of the kinetic energy (see gray filled curve of Fig. 5).

Finally, we examine the feasibility of experimental demonstration of the generation of tunable, narrow-bandwidth XUV radiation using the above technique. For this purpose, we investigate sensitivity of the high-order harmonic spectra to the fluctuation of laser intensity at three wavelengths as well as to the jitter of the time delay between the three laser fields. Numerical simulation shows that the narrow-bandwidth XUV emission still can be observed when 15% intensity fluctuation and 0.1fs change of the time delay is introduced, allowing for experimental demonstration in the future. Moreover, although our simulation is based on a single atom model of the high-order harmonic generation, we believe that the effect of the spectral confinement still can be observed when the propagation effect is considered. Because the well phase-matched harmonics only can be generated for a fixed harmonic order, the bandwidth of the selected XUV radiation will become narrow during propagation. In principle, our technique also could take advantage of the phase matching if the phase-matching condition is optimized for the wavelength of the narrow-bandwidth XUV emission.

To conclude, we propose a new method for generating an enhanced narrow-bandwidth XUV spectrum in the plateau of the high-order harmonic spectrum. The enhancement of the selected spectral region results from the creation of a folded quantum path which leads to constructive interference for the XUV radiation in the selected waveband. The central wavelength of the enhanced XUV spectrum depends significantly on the time delay between the three-color laser pulses and the laser intensity of 2000-nm pulses. Interestingly the tunable narrowband enhancement of the XUV emission can be exploited for other applications such as XUV spectroscopy with a monochromator or seeding of free electron lasers (FEL). Moreover, it also may provide a potential way to generate an intense isolated attosecond light source. For example, an isolated 34-as laser pulse can be obtained with this scheme, given that the dispersion of the supercontinuum is completely compensated. Thanks to the rapid development of the ultrafast OPA technique, the specialized waveform as mentioned above is obtainable which facilitates experimental demonstration of this technique.

Acknowledgments

C. Zhang and J. Yao attribute equally to this work. The work is supported by National Basic Research Program of China (Grant No. 2011CB808102), National Natural Science Foundation of China (Grants No. 11134010, No. 60825406, No. 60921004, No. 61008061, and No. 11104236) and Education Committee Foundation of Jiangsu Province (Grant No. 10KJB140012). C. Zhang gratefully acknowledges the support of K.C.Wong Education Foundation, China and shanghai Postdoctoral Science Foundation funded project (2012M511145 and 12R21416700), and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

References and links

1.

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

2.

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]

3.

W. Yang, X. Song, Z. Zeng, R. Li, and Z. Xu, “Quantum path interferences of electron trajectories in two-center molecules,” Opt. Express 18(3), 2558–2565 (2010). [CrossRef] [PubMed]

4.

H. Xiong, H. Xu, Y. Fu, J. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Xu, E. J. Takahashi, K. Midorikawa, X. Liu, and J. Chen, “Generation of a coherent x ray in the water window region at 1 kHz repetition rate using a mid-infrared pump source,” Opt. Lett. 34(11), 1747–1749 (2009). [CrossRef] [PubMed]

5.

X. Song, Z. Zeng, Y. Fu, B. Cai, R. Li, Y. Cheng, and Z. Xu, “Quantum path control in few-optical-cycle regime,” Phys. Rev. A 76(4), 043830 (2007). [CrossRef]

6.

P. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007). [CrossRef]

7.

M. Fieß, B. Horvath, T. Wittmann, W. Helml, Y. Cheng, B. Zeng, Z. Xu, A. Scrinzi, J. Gagnon, F. Krausz, and R. Kienberger, “Attosecond control of tunneling ionization and electron trajectories,” New J. Phys. 13(3), 033031 (2011). [CrossRef]

8.

Y. Yu, X. Song, Y. Fu, R. Li, Y. Cheng, and Z. Xu, “Theoretical investigation of single attosecond pulse generation in an orthogonally polarized two-color laser field,” Opt. Express 16(2), 686–694 (2008). [CrossRef] [PubMed]

9.

P. C. Li, I. L. Liu, and S. I. Chu, “Optimization of three-color laser field for the generation of single ultrashort attosecond pulse,” Opt. Express 19(24), 23857–23866 (2011). [CrossRef] [PubMed]

10.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Di Mauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008). [CrossRef]

11.

J. Yao, Y. Li, B. Zeng, H. Xiong, H. Xu, Y. Fu, W. Chu, J. Ni, X. Liu, J. Chen, Y. Cheng, and Z. Xu, “Generation of an XUV supercontinuum by optimization of the angle between polarization planes of two linearly polarized pulses in a multicycle two-color laser field,” Phys. Rev. A 82(2), 023826 (2010). [CrossRef]

12.

Z. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A 71(2), 023813 (2005). [CrossRef]

13.

B. Zeng, Y. Yu, W. Chu, J. Yao, Y. Fu, H. Xiong, H. Xu, Y. Cheng, and Z. Xu, “Generation of an intense single isolated attosecond pulse by use of two-colour waveform control,” J. Phys. B 42(14), 145604 (2009). [CrossRef]

14.

Ph. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett. 77(7), 1234–1237 (1996). [CrossRef] [PubMed]

15.

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

16.

S. Tang and X. Chen, “Generation of isolated sub-100-as pulses with 30-fs lasers,” Phys. Rev. A 82(1), 013827 (2010). [CrossRef]

17.

F. Calegari, M. Lucchini, K. S. Kim, F. Ferrari, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “Quantum path control in harmonic generation by temporal shaping of few-optical-cycle pulses in ionizing media,” Phys. Rev. A 84(4), 041802 (2011). [CrossRef]

18.

L. B. Da Silva, T. W. Barbee Jr, R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, “Electron density measurements of high density plasmas using soft X-ray laser interferometry,” Phys. Rev. Lett. 74(20), 3991–3994 (1995). [CrossRef] [PubMed]

19.

H. Du and B. Hu, “Broadband supercontinuum generation method combining mid-infrared chirped-pulse modulation and generalized polarization gating,” Opt. Express 18(25), 25958–25966 (2010). [CrossRef] [PubMed]

20.

J. B. M. Warntjes, A. Gürtler, A. Osterwalder, F. Rosca-Pruna, M. J. J. Vrakking, and L. D. Noordam, “Atomic spectral detection of tunable extreme ultraviolet pulses,” Opt. Lett. 26(19), 1463–1465 (2001). [CrossRef] [PubMed]

21.

G. Sansone, E. Benedetti, C. Vozzi, S. Stagira, and M. Nisoli, “Attosecond metrology in the few-optical-cycle regime,” New J. Phys. 10(2), 025006 (2008). [CrossRef]

22.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]

23.

A. L. Lytle, X. Zhang, P. Arpin, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-phase matching of high-order harmonic generation at high photon energies using counterpropagating pulses,” Opt. Lett. 33(2), 174–176 (2008). [CrossRef] [PubMed]

24.

E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L’Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-colour laser fields,” New J. Phys. 10(8), 083041 (2008). [CrossRef]

25.

J. Yao, Y. Cheng, J. Chen, H. Zhang, H. Xu, H. Xiong, B. Zeng, W. Chu, J. Ni, X. Liu, and Z. Xu, “Generation of narrow-bandwidth, tunable, coherent xuv radiation using high-order harmonic generation,” Phys. Rev. A 83(3), 033835 (2011). [CrossRef]

26.

Z. Zeng, Y. Cheng, Y. Fu, X. Song, R. Li, and Z. Xu, “Tunable high-order harmonic generation and the role of the folded quantum path,” Phys. Rev. A 77(2), 023416 (2008). [CrossRef]

27.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007). [CrossRef] [PubMed]

28.

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005). [CrossRef]

29.

M. Lewenstein, Ph. Balcou, M. Y. 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]

30.

M. Y. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A 54(1), 742–745 (1996). [CrossRef] [PubMed]

31.

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

32.

H. Du and B. Hu, “Propagation effects of isolated attosecond pulse generation with a multicycle chirped and chirped-free two-color field,” Phys. Rev. A 84(2), 023817 (2011). [CrossRef]

OCIS Codes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.0320) Ultrafast optics : Ultrafast optics
(320.7150) Ultrafast optics : Ultrafast spectroscopy

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 11, 2012
Revised Manuscript: June 18, 2012
Manuscript Accepted: June 26, 2012
Published: July 6, 2012

Citation
Chaojin Zhang, Jinping Yao, Jielei Ni, Guihua Li, Ya Cheng, and Zhizhan Xu, "Control of bandwidth and central wavelength of an enhanced extreme ultraviolet spectrum generated in shaped laser field," Opt. Express 20, 16544-16551 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16544


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References

  1. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009). [CrossRef]
  2. 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]
  3. W. Yang, X. Song, Z. Zeng, R. Li, and Z. Xu, “Quantum path interferences of electron trajectories in two-center molecules,” Opt. Express18(3), 2558–2565 (2010). [CrossRef] [PubMed]
  4. H. Xiong, H. Xu, Y. Fu, J. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Xu, E. J. Takahashi, K. Midorikawa, X. Liu, and J. Chen, “Generation of a coherent x ray in the water window region at 1 kHz repetition rate using a mid-infrared pump source,” Opt. Lett.34(11), 1747–1749 (2009). [CrossRef] [PubMed]
  5. X. Song, Z. Zeng, Y. Fu, B. Cai, R. Li, Y. Cheng, and Z. Xu, “Quantum path control in few-optical-cycle regime,” Phys. Rev. A76(4), 043830 (2007). [CrossRef]
  6. P. Corkum and F. Krausz, “Attosecond science,” Nat. Phys.3(6), 381–387 (2007). [CrossRef]
  7. M. Fieß, B. Horvath, T. Wittmann, W. Helml, Y. Cheng, B. Zeng, Z. Xu, A. Scrinzi, J. Gagnon, F. Krausz, and R. Kienberger, “Attosecond control of tunneling ionization and electron trajectories,” New J. Phys.13(3), 033031 (2011). [CrossRef]
  8. Y. Yu, X. Song, Y. Fu, R. Li, Y. Cheng, and Z. Xu, “Theoretical investigation of single attosecond pulse generation in an orthogonally polarized two-color laser field,” Opt. Express16(2), 686–694 (2008). [CrossRef] [PubMed]
  9. P. C. Li, I. L. Liu, and S. I. Chu, “Optimization of three-color laser field for the generation of single ultrashort attosecond pulse,” Opt. Express19(24), 23857–23866 (2011). [CrossRef] [PubMed]
  10. P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Di Mauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys.4(5), 386–389 (2008). [CrossRef]
  11. J. Yao, Y. Li, B. Zeng, H. Xiong, H. Xu, Y. Fu, W. Chu, J. Ni, X. Liu, J. Chen, Y. Cheng, and Z. Xu, “Generation of an XUV supercontinuum by optimization of the angle between polarization planes of two linearly polarized pulses in a multicycle two-color laser field,” Phys. Rev. A82(2), 023826 (2010). [CrossRef]
  12. Z. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A71(2), 023813 (2005). [CrossRef]
  13. B. Zeng, Y. Yu, W. Chu, J. Yao, Y. Fu, H. Xiong, H. Xu, Y. Cheng, and Z. Xu, “Generation of an intense single isolated attosecond pulse by use of two-colour waveform control,” J. Phys. B42(14), 145604 (2009). [CrossRef]
  14. Ph. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett.77(7), 1234–1237 (1996). [CrossRef] [PubMed]
  15. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett.71(13), 1994–1997 (1993). [CrossRef] [PubMed]
  16. S. Tang and X. Chen, “Generation of isolated sub-100-as pulses with 30-fs lasers,” Phys. Rev. A82(1), 013827 (2010). [CrossRef]
  17. F. Calegari, M. Lucchini, K. S. Kim, F. Ferrari, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “Quantum path control in harmonic generation by temporal shaping of few-optical-cycle pulses in ionizing media,” Phys. Rev. A84(4), 041802 (2011). [CrossRef]
  18. L. B. Da Silva, T. W. Barbee, R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, “Electron density measurements of high density plasmas using soft X-ray laser interferometry,” Phys. Rev. Lett.74(20), 3991–3994 (1995). [CrossRef] [PubMed]
  19. H. Du and B. Hu, “Broadband supercontinuum generation method combining mid-infrared chirped-pulse modulation and generalized polarization gating,” Opt. Express18(25), 25958–25966 (2010). [CrossRef] [PubMed]
  20. J. B. M. Warntjes, A. Gürtler, A. Osterwalder, F. Rosca-Pruna, M. J. J. Vrakking, and L. D. Noordam, “Atomic spectral detection of tunable extreme ultraviolet pulses,” Opt. Lett.26(19), 1463–1465 (2001). [CrossRef] [PubMed]
  21. G. Sansone, E. Benedetti, C. Vozzi, S. Stagira, and M. Nisoli, “Attosecond metrology in the few-optical-cycle regime,” New J. Phys.10(2), 025006 (2008). [CrossRef]
  22. X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys.3(4), 270–275 (2007). [CrossRef]
  23. A. L. Lytle, X. Zhang, P. Arpin, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-phase matching of high-order harmonic generation at high photon energies using counterpropagating pulses,” Opt. Lett.33(2), 174–176 (2008). [CrossRef] [PubMed]
  24. E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L’Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-colour laser fields,” New J. Phys.10(8), 083041 (2008). [CrossRef]
  25. J. Yao, Y. Cheng, J. Chen, H. Zhang, H. Xu, H. Xiong, B. Zeng, W. Chu, J. Ni, X. Liu, and Z. Xu, “Generation of narrow-bandwidth, tunable, coherent xuv radiation using high-order harmonic generation,” Phys. Rev. A83(3), 033835 (2011). [CrossRef]
  26. Z. Zeng, Y. Cheng, Y. Fu, X. Song, R. Li, and Z. Xu, “Tunable high-order harmonic generation and the role of the folded quantum path,” Phys. Rev. A77(2), 023416 (2008). [CrossRef]
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