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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 22 — Oct. 22, 2012
  • pp: 24642–24649
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Generation of isolated attosecond pulses of sub-atomic-time durations with multi-cycle chirped polarization gating pulses

Chaojin Zhang, Jinping Yao, and Jielei Ni  »View Author Affiliations


Optics Express, Vol. 20, Issue 22, pp. 24642-24649 (2012)
http://dx.doi.org/10.1364/OE.20.024642


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Abstract

We theoretically investigate the X-ray supercontinuum generated by interaction of multi-cycle, chirped polarization gating pulses with the helium gas. It is shown that with this scheme, an isolated sub-50-attosecond pulse can be obtained straightforwardly without any phase compensation. Interestingly, if one selects an extremely broad spectral range near the high-order harmonic cutoff, an isolated and intense sub-24-attosecond pulse can be generated after phase compensation, which could be used to detect and control the electronic dynamics inside the atoms. Furthermore, it is found that the generation of such a broad and smooth X-ray supercontinuum is not so stringent on the selection of the simulated parameters, allowing for the experimental demonstration of this technique in the future.

© 2012 OSA

In order to obtain a clear insight for generation of the dramatically broadened X-ray supercontinuum, we perform time-frequency analyses for dipole momentums in two cases. From Fig. 2(a)
Fig. 2 The time-frequency analyses of single-atom dipole moments driven by the polarization gating pulse without (a) and with (b) the chirped effects.
, we can clearly see that in this absence of the chirped effect, the harmonic emission occurs every half of an optical cycle of the laser pulse and each emission show up and down arms with nearly equivalent intensities, which is defined as the long trajectory and the short trajectory [12

12. 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]

, 16

16. 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]

, 19

19. M. M. Masoud Mohebbi and S. B. Saeed Batebi, “Generation of 40-as few-cycle pulse through chirp manipulation,” Chin. Opt. Lett. 10(8), 081901–081903 (2012). [CrossRef]

], respectively. Because of the interferences between different quantum trajectories, HHG spectrum is modulated significantly, as indicated in Fig. 1(b). But when the chirped effects are taken into account in the polarization gating technique, there is only a major burst near the emission time of ~1.3T (T is optical period of the laser pulse), as illustrated in Fig. 2(b). In this case, not only the emission from the other half cycles is effectively suppressed, but also a short trajectory is well selected, resulting in an extremely broad and smooth supercontinuum, as shown in Fig. 1(d).

To further understand the underlying physical mechanism behind the dramatically broadened X-ray supercontinuum in the presence of the chirped effects, we depicted the ellipticity of the driving field as a function of time in both cases without and with chirped effects. Figure 3(b)
Fig. 3 The temporal dependence of ellipticity of two counter-rotating polarization gating pulses without (a) and with (b) chirped effect.
clearly shows that when the chirp effect is introduced, the ellipticity of the driving laser field exhibits a rapid variation. It is well known that HHG strongly depends on the ellipticity of the driving laser field [35

35. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70(4), 043802 (2004). [CrossRef]

, 36

36. F. He, C. Ruiz, and A. Becker, “Single attosecond pulse generation with intense mid-infrared elliptically polarized laser pulses,” Opt. Lett. 32(21), 3224–3226 (2007). [CrossRef] [PubMed]

]. Generally, when the ellipticity is up to 0.2, the ionized electron cannot revisit its parent ion and thus HHG will be terminated. Therefore, HHG in the case with chirped effects will be confined within a much narrower temporal window as compared to the case without chirped effect (see Fig. 3(a)). As a result, HHG from the other cycles is effectively suppressed. In this way, a single quantum trajectory is selected (see the Fig. 2(b)), leading to a dramatically broadened X-ray supercontinuum.

In order to examine the feasibility of the experimental demonstration of this method, we investigate the influences of the laser intensity, the time delay Td between two counter-rotating chirped polarized pulses and chirp parameter on the HHG spectra and attosecond pulses. As shown in Fig. 5(a)
Fig. 5 (a) The HHG spectra obtained at different laser intensities. (b) The corresponding isolated attosecond pulse. Other parameters are the same as in Fig. 1(d).
, with the increase or decrease of the laser intensity, the cutoff energy of the HHG changes in the same way. However, we always can observe a smooth and broad supercontinuum in all cases. Correspondingly, by selecting HHG spectrum from the 460th to 520th harmonics, the isolated attosecond pulses can also obtained without any phase compensation though theirs shapes are different. At the laser intensity of 1.1 × I0, the intensity of the HHG spectrum in this spectral range (460th~520th harmonics) is lower as compared to the case at the laser intensity of I0, so that the synthesized attosecond pulse is relatively weak in this case, as shown by dotted line in Fig. 5(b). When the laser intensity is reduced to 0.9 × I0, the attosecond pulse shows a double-peak structure, as indicated by the solid line in Fig. 5(b), which could be the result of interference of the long and short trajectories. Generally, the fluctuation of laser intensity is far less than the current assumption ( ± 10%). Therefore, we believe that an isolated attosecond pulse will remain unchanged if intensity fluctuation of laser pulses is controlled within a reasonable range. In addition, we also examined the influence of the delay Td between two counter-rotating chirped polarized gating pulses on the supercontinuum spectrum as well as the attosecond pulses. As shown in Fig. 6
Fig. 6 (a) The HHG spectra obtained at different time delays between two counter-rotating polarization gating pulses. (b) The corresponding isolated attosecond pulse. Other parameters are the same as in Fig. 1(d).
, both HHG spectrum and isolated attosecond pulses only exhibit a slight change when the delay Td increases to 12 fs from 8 fs.

In conclusion, we theoretically proposed a novel method to generate sub-100-as isolated attosecond pulses in the multi-cycle regime. It is shown that HHG can be effectively confined within an extremely narrow temporal window due to the rapidly varying ellipticity when a chirp is added to the two counter-rotating polarization gating pulses. In this way, the harmonic emission occurring at every half optical cycle is effectively reduced to one time, leading to a well isolated attosecond pulse with the pulse duration comparable to an atomic unit. Such short attosecond pulses could have potential applications in detecting and controlling the ultrafast electronic dynamics with an unprecedented time scale. Lastly, we also demonstrated the experimental feasibility of this method by examining the dependence of both HHG spectra and attosecond pulses on the laser intensity, the delay between two counter-rotating polarization gating pulses and the chirp.

Acknowledgments

C. Zhang and J. Yao attribute equally to this work. The authors are grateful to Professor Z. Xu, Y. Cheng and Dr. B. Zeng of SIOM for their help. 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, No. 11204332, 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 Postdoctoral Science Foundation funded project (2012M511145), and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

References and links

1.

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]

2.

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

3.

P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, “Generation of intense continuum extreme-ultraviolet radiation by many-cycle laser fields,” Nat. Phys. 3(12), 846–850 (2007). [CrossRef]

4.

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

5.

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]

6.

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

7.

Y. Li, Q. Zhang, W. Hong, S. Wang, Z. Wang, and P. Lu, “Efficient generation of high beam-quality attosecond pulse with polarization-gating Bessel-Gauss beam from highly-ionized media,” Opt. Express 20(14), 15427–15439 (2012). [CrossRef] [PubMed]

8.

C. Zhang, J. Yao, J. Ni, G. Li, Y. Cheng, and Z. Xu, “Control of bandwidth and central wavelength of an enhanced extreme ultraviolet spectrum generated in shaped laser field,” Opt. Express 20(15), 16544–16551 (2012). [CrossRef]

9.

Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, and Z. Xu, “Dynamic chirp control and pulse compression for attosecond high-order harmonic emission,” Phys. Rev. Lett. 103(4), 043904 (2009). [CrossRef] [PubMed]

10.

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]

11.

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]

12.

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]

13.

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]

14.

C. Altucci, J. W. G. Tisch, and R. Velotta, “Single attosecond light pulses from multi-cycle laser sources,” J. Mod. Opt. 58(18), 1585–1610 (2011). [CrossRef]

15.

W. Hong, P. Lu, P. Lan, Z. Yang, Y. Li, and Q. Liao, “Broadband xuv supercontinuum generation via controlling quantum paths by a low-frequency field,” Phys. Rev. A 77(3), 033410 (2008). [CrossRef]

16.

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]

17.

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]

18.

K. Zhao and T. Chu, “A single isolated sub-50 attosecond pulse generation with a two-color laser field by a frequency-chirping technique,” Chem. Phys. Lett. 511(1-3), 166–171 (2011). [CrossRef]

19.

M. M. Masoud Mohebbi and S. B. Saeed Batebi, “Generation of 40-as few-cycle pulse through chirp manipulation,” Chin. Opt. Lett. 10(8), 081901–081903 (2012). [CrossRef]

20.

P. Zou, Z. Zeng, Y. Zheng, Y. Lu, P. Liu, R. Li, and Z. Xu, “Coherent control of broadband isolated attosecond pulses in a chirped two-color laser field,” Phys. Rev. A 81(3), 033428 (2010). [CrossRef]

21.

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

22.

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]

23.

C. Altucci, R. Esposito, V. Tosa, and R. Velotta, “Single isolated attosecond pulse from multicycle lasers,” Opt. Lett. 33(24), 2943–2945 (2008). [CrossRef] [PubMed]

24.

C. Altucci, R. Velotta, V. Tosa, P. Villoresi, F. Frassetto, L. Poletto, C. Vozzi, F. Calegari, M. Negro, S. De Silvestri, and S. Stagira, “Interplay between group-delay-dispersion-induced polarization gating and ionization to generate isolated attosecond pulses from multicycle lasers,” Opt. Lett. 35(16), 2798–2800 (2010). [CrossRef] [PubMed]

25.

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

26.

S. Tang and X. Chen, “Method to generate isolated attosecond pulses with many-cycle laser fields,” Phys. Rev. A 85(6), 063816 (2012). [CrossRef]

27.

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]

28.

Y. Xiang, J. Miao, Y. Niu, S. Gong, R. Li, and Z. Xu, “Isolated sub-100 attosecond pulse generation driven by a multi-cycle chirped laser pulse and a polarization gating,” J. Phys. B 45(11), 115601 (2012). [CrossRef]

29.

P. Li, X. Zhou, G. Wang, and Z. Zhao, “Isolated sub-30-as pulse generation of an He+ ion by an intense few-cycle chirped laser and its high-order harmonic pulses,” Phys. Rev. A 80(5), 053825 (2009). [CrossRef]

30.

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-x-ray harmonic emission,” Phys. Rev. A 58(1), R30–R33 (1998). [CrossRef]

31.

P. Lan, P. Lu, Q. Li, F. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79(4), 043413 (2009). [CrossRef]

32.

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]

33.

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]

34.

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]

35.

Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70(4), 043802 (2004). [CrossRef]

36.

F. He, C. Ruiz, and A. Becker, “Single attosecond pulse generation with intense mid-infrared elliptically polarized laser pulses,” Opt. Lett. 32(21), 3224–3226 (2007). [CrossRef] [PubMed]

37.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005).

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

ToC Category:
Ultrafast Optics

History
Original Manuscript: July 31, 2012
Revised Manuscript: September 27, 2012
Manuscript Accepted: September 28, 2012
Published: October 12, 2012

Citation
Chaojin Zhang, Jinping Yao, and Jielei Ni, "Generation of isolated attosecond pulses of sub-atomic-time durations with multi-cycle chirped polarization gating pulses," Opt. Express 20, 24642-24649 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-24642


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References

  1. 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]
  2. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett.71(13), 1994–1997 (1993). [CrossRef] [PubMed]
  3. P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, “Generation of intense continuum extreme-ultraviolet radiation by many-cycle laser fields,” Nat. Phys.3(12), 846–850 (2007). [CrossRef]
  4. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009). [CrossRef]
  5. 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]
  6. P. Corkum and F. Krausz, “Attosecond science,” Nat. Phys.3(6), 381–387 (2007). [CrossRef]
  7. Y. Li, Q. Zhang, W. Hong, S. Wang, Z. Wang, and P. Lu, “Efficient generation of high beam-quality attosecond pulse with polarization-gating Bessel-Gauss beam from highly-ionized media,” Opt. Express20(14), 15427–15439 (2012). [CrossRef] [PubMed]
  8. C. Zhang, J. Yao, J. Ni, G. Li, Y. Cheng, and Z. Xu, “Control of bandwidth and central wavelength of an enhanced extreme ultraviolet spectrum generated in shaped laser field,” Opt. Express20(15), 16544–16551 (2012). [CrossRef]
  9. Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, and Z. Xu, “Dynamic chirp control and pulse compression for attosecond high-order harmonic emission,” Phys. Rev. Lett.103(4), 043904 (2009). [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. C. Altucci, J. W. G. Tisch, and R. Velotta, “Single attosecond light pulses from multi-cycle laser sources,” J. Mod. Opt.58(18), 1585–1610 (2011). [CrossRef]
  15. W. Hong, P. Lu, P. Lan, Z. Yang, Y. Li, and Q. Liao, “Broadband xuv supercontinuum generation via controlling quantum paths by a low-frequency field,” Phys. Rev. A77(3), 033410 (2008). [CrossRef]
  16. 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]
  17. 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]
  18. K. Zhao and T. Chu, “A single isolated sub-50 attosecond pulse generation with a two-color laser field by a frequency-chirping technique,” Chem. Phys. Lett.511(1-3), 166–171 (2011). [CrossRef]
  19. M. M. Masoud Mohebbi and S. B. Saeed Batebi, “Generation of 40-as few-cycle pulse through chirp manipulation,” Chin. Opt. Lett.10(8), 081901–081903 (2012). [CrossRef]
  20. P. Zou, Z. Zeng, Y. Zheng, Y. Lu, P. Liu, R. Li, and Z. Xu, “Coherent control of broadband isolated attosecond pulses in a chirped two-color laser field,” Phys. Rev. A81(3), 033428 (2010). [CrossRef]
  21. E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L’Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-color laser fields,” New J. Phys.10(8), 083041 (2008). [CrossRef]
  22. H. Du and B. Hu, “Propagation effects of isolated attosecond pulse generation with a multicycle chirped and chirped-free two-color field,” Phys. Rev. A84(2), 023817 (2011). [CrossRef]
  23. C. Altucci, R. Esposito, V. Tosa, and R. Velotta, “Single isolated attosecond pulse from multicycle lasers,” Opt. Lett.33(24), 2943–2945 (2008). [CrossRef] [PubMed]
  24. C. Altucci, R. Velotta, V. Tosa, P. Villoresi, F. Frassetto, L. Poletto, C. Vozzi, F. Calegari, M. Negro, S. De Silvestri, and S. Stagira, “Interplay between group-delay-dispersion-induced polarization gating and ionization to generate isolated attosecond pulses from multicycle lasers,” Opt. Lett.35(16), 2798–2800 (2010). [CrossRef] [PubMed]
  25. Z. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A71(2), 023813 (2005). [CrossRef]
  26. S. Tang and X. Chen, “Method to generate isolated attosecond pulses with many-cycle laser fields,” Phys. Rev. A85(6), 063816 (2012). [CrossRef]
  27. 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]
  28. Y. Xiang, J. Miao, Y. Niu, S. Gong, R. Li, and Z. Xu, “Isolated sub-100 attosecond pulse generation driven by a multi-cycle chirped laser pulse and a polarization gating,” J. Phys. B45(11), 115601 (2012). [CrossRef]
  29. P. Li, X. Zhou, G. Wang, and Z. Zhao, “Isolated sub-30-as pulse generation of an He+ ion by an intense few-cycle chirped laser and its high-order harmonic pulses,” Phys. Rev. A80(5), 053825 (2009). [CrossRef]
  30. Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-x-ray harmonic emission,” Phys. Rev. A58(1), R30–R33 (1998). [CrossRef]
  31. P. Lan, P. Lu, Q. Li, F. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A79(4), 043413 (2009). [CrossRef]
  32. 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. A49(3), 2117–2132 (1994). [CrossRef] [PubMed]
  33. M. Y. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A54(1), 742–745 (1996). [CrossRef] [PubMed]
  34. 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]
  35. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A70(4), 043802 (2004). [CrossRef]
  36. F. He, C. Ruiz, and A. Becker, “Single attosecond pulse generation with intense mid-infrared elliptically polarized laser pulses,” Opt. Lett.32(21), 3224–3226 (2007). [CrossRef] [PubMed]
  37. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005).

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