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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 3 — Feb. 11, 2013
  • pp: 3259–3264
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Enhanced narrow-bandwidth emission during high-order harmonic generation from aligned molecules

Chaojin Zhang, Jinping Yao, Fadhil A. Umran, Jielei Ni, Bin Zeng, Guihua Li, and Di Lin  »View Author Affiliations


Optics Express, Vol. 21, Issue 3, pp. 3259-3264 (2013)
http://dx.doi.org/10.1364/OE.21.003259


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Abstract

We theoretically investigate the selective enhancement of high-harmonic generation (HHG) in a small spectral range when an orthogonal-polarized two-color laser field interacts with aligned O2 molecules. It is shown clearly that the enhanced narrow-bandwidth emission near the cutoff of the HHG spectrum can be effectively controlled by the molecular alignment angle, laser intensity and the relative phase of two-color laser fields. Furthermore, the strong dependence of narrow-bandwidth HHG on molecular alignment angle indicates that it encodes information about O2 molecular orbitals, so it may be an alternative method for reconstruction of O2 molecular orbitals.

© 2013 OSA

In recent decades, the advanced ultrafast laser technology opens the way for investigating high-order harmonic generation (HHG) in a strong field regime, which has great potential for applications in high-contrast X-ray microscopy, molecular tomography and etc [1

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

7

7. 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]

]. In a broad range of fields such as biological imaging, nanolithography, and XUV interferometry, it is of great importance and necessary to precise control of central wavelength and bandwidth of HHG. Although the rapid development of optical coating in the XUV region makes it possible to filter out a specific spectral range in the plateau of the HHG spectra [8

8. L. B. D. 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).

, 9

9. K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Pattern formation and flow control of fine particles by laser-scanning micromanipulation,” Opt. Lett. 16(19), 1463–1465 (1991). [CrossRef] [PubMed]

], it is not the best method due to extra optical losses added on XUV emission, high cost and poor capacity of wavelength tunability. To solve these problems, a few all-optical methods [10

10. 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]

13

13. 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]

] have been proposed. Recently, some groups theoretically [10

10. 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]

12

12. 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]

] and experimentally [13

13. 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]

] reported the generation of the narrow-bandwidth, wavelength-tunable coherent light sources via HHG by using waveform tailoring and control techniques. The driving laser field with a specific waveform, which is constructed by either parallel- or orthogonal-polarized two-color or multi-color laser fields, can effectively manipulate electron trajectories, leading to narrow-bandwidth HHG.

In order to obtain a clear insight for the generation of narrow-bandwidth XUV radiation, time frequency analyses for y-component dipole moments are performed in both cases of ϕ = 65° and ϕ = 85°. As shown in Fig. 2(a)
Fig. 2 Time-frequency analyses for y-component dipole moments corresponding to HHG spectra of Fig. 1 at (a) ϕ = 65° and (b) ϕ = 85°.
, at the relative phase ϕ = 65°, there are some electron trajectories that contribute to HHG in the plateau, but the trajectory around ~0.5 optical cycle is much stronger than the other ones, resulting in a broad supercontinuum spectrum with a weak modulation (See Fig. 1(a)). In contrast, when the relative phase of laser fields increases to ϕ = 85°, as indicated in Fig. 2(b), the strongest electron trajectory appeared at ϕ = 65° is well suppressed. Instead, a new trajectory with a comparable intensity appears near cutoff of HHG spectrum and covers a small spectral range from ~60 eV to ~70 eV, resulting in narrow-bandwidth XUV emission. To gain further understanding, we performed analyses of classical electron trajectories based on three-step model of HHG [22

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

]. In Figs. 3(a)
Fig. 3 The minimum distance of electron from its parent ion (black solid curve), photon energy (red dashed curve) and ionization rate (gray filled area) as a function of birth time at (a) ϕ = 65° and (b) ϕ = 85°. 2D classical trajectories for the electrons ionized at t0 for (c) ϕ = 65° and (d) ϕ = 85°. Initial position of the electron is indicated by red dots in all figures.
and 3(b), we compared ionization rate (gray filled area), photon energy (red dashed line) and minimum distance of the electron from its parent ion when it is driven back (black solid line) at ϕ = 65° and ϕ = 85°. According to time frequency analyses, we can know that the electron born around t0 which is indicated by red dot in Fig. 3(b) mainly contributes to the narrow-bandwidth HHG. Clearly, around t0, he minimum distance of the electron from the molecular ion at ϕ = 85° is much smaller than that at ϕ = 65°, so that the electron still has a probability to recombine with its parent ion due to the spreading of the electron wave packet [31

31. 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]

]. This can be further proved by classical trajectories as displayed in Fig. 3(c) and 3(d). Furthermore, it is noteworthy that the electrons born around t0, as indicated by blue dotted lines, obtain almost the same kinetic energy. The coherent superposition of multiple electron trajectories results in effective enhancement of HHG in the spectral range around cutoff. In contrast, at ϕ = 65°, the minimum distance between the electron and it parent ion increases with the increase of photon energy, leading to reduced HHG in high-energy region of HHG. In addition, electron trajectories do not overlap, so enhanced HHG cannot be observed. The analyses above indicate that the selectively enhanced narrow-bandwidth HHG is a result of coherent manipulation of electron trajectories by orthogonal-polarized two-color laser fields.

Next, we investigate the influences of intensities of two-color laser fields on the enhanced narrow-bandwidth HHG spectra when the molecular alignment angle and the relative phase are fixed at 45° and 85°, respectively. As shown in Fig. 4(a)
Fig. 4 HHG spectra (a) at different intensities of 800 nm pulses and (b) at different intensities of 1750 nm pulses.
, the narrow-bandwidth HHG spectra almost remain unchanged with the increase or decrease of the intensity of 800 nm laser field (I1). That is to say, the intensity fluctuation of 800 nm pulses hardly affects the narrow-bandwidth XUV emission. In contrast, the narrow-bandwidth HHG is sensitive to the intensity of 1750 nm pulses (I2). As indicated in Fig. 4(b), when I2 is increased to 12.5 × 1013 W/cm2 from 4.5 × 1013 W/cm2, the central photon energy of the enhanced narrow-bandwidth radiation will gradually shift from ~50 eV to ~110 eV, while its intensity gradually decreases. Therefore, we can easily tune the central wavelength of narrow-bandwidth XUV emission by adjusting the intensity of the 1750 nm laser field.

As mentioned above, narrow-bandwidth HHG is coherent superposition of multiple electron trajectories. Therefore, it is independent of target gases. When the atom (Xe) is used in our numerical simulation, the enhanced narrow-bandwidth emission can also be obtained. But in O2 molecular medium, we can investigate the alignment dependence of the narrow-bandwidth HHG. As we know, the molecular alignment angle θ plays an important role in HHG. It is also an additional parameter to affect the enhanced narrow-bandwidth emission as compared to atoms. Numerical simulation demonstrates that the enhanced narrow-bandwidth emission can only be effectively generated in the range of alignment angles from 25° to 65°. At different alignment angles, the central wavelength of the narrow-bandwidth HHG slightly shifts, so we average HHG spectra from 64.2 eV to 65.6 eV covering narrow-bandwidth emissions at each alignment angle. The calculated result is shown in Fig. 5
Fig. 5 The peak intensity of narrow-bandwidth HHG spectra as a function of molecular alignment angles.
. Clearly, at θ≈45°, it is the most beneficial for obtaining the narrow-bandwidth HHG with a high intensity and a clean background. When the alignment angle deviates from 45°, the narrow-bandwidth emission is less enhanced. This is due to that ionization of O2 molecules critically depends on molecular alignment angles. As indicated in [16

16. X. Zhou, X. Tong, Z. Zhao, and C. D. Lin, “Role of molecular orbital symmetry on the alignment dependence of high-order harmonic generation with molecules,” Phys. Rev. A 71(6), 061801 (2005). [CrossRef]

, 17

17. B. Shan, X. Tong, Z. Zhao, Z. Chang, and C. D. Lin, “High-order harmonic cutoff extension of the O2 molecule due to ionization suppression,” Phys. Rev. A 66(6), 061401 (2002). [CrossRef]

], the ionization rate of O2 molecules is maximum at θ≈45°, which is in good agreement with the peak value of Fig. 5. Therefore, the alignment dependence of the narrow-bandwidth emission records the information of O2 molecular orbitals.

To be concluded, we theoretically investigated narrow-bandwidth HHG from aligned O2 molecules by manipulating electron trajectories with an orthogonal-polarized two-color laser field. It is found that the central wavelength can be effectively tuned in a broad spectral range by changing the intensity of the ~1750 nm laser field. In addition, the enhanced narrow-bandwidth emission is highly sensitive to molecular alignment angles. An intense, background-free narrow-bandwidth HHG spectrum is obtained when the alignment angle is at ~45°, which corresponds to the highest ionization rate of highest occupied orbital of O2 molecules. Therefore, this technique not only has important applications in X-ray microscopy and molecular tomography, but also may provide us an alternative method for extracting the information of O2 molecular orbitals.

Acknowledgments

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. 61008061, No. 11204332, No. 11274220, and No. 11104236), and the Priority Academic Program Development of Jiangsu Higher Education Institutions. C. Zhang gratefully acknowledges the support of K.C.Wong Education Foundation, Qing Lan Project of Jiangsu Province, China and Shanghai Postdoctoral Science Foundation Funded Project (2012M511145 and 12R21416700).

References and links

1.

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

2.

J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84(5), 051802 (2011). [CrossRef]

3.

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]

4.

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]

5.

C. Zhang, J. Yao, and J. Ni, “Generation of isolated attosecond pulses of sub-atomic-time durations with multi-cycle chirped polarization gating pulses,” Opt. Express 20(22), 24642–24649 (2012). [CrossRef] [PubMed]

6.

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]

7.

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]

8.

L. B. D. 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).

9.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Pattern formation and flow control of fine particles by laser-scanning micromanipulation,” Opt. Lett. 16(19), 1463–1465 (1991). [CrossRef] [PubMed]

10.

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]

11.

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]

12.

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]

13.

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]

14.

M. Yu. Emelin, M. Yu. Ryabikin, and A. M. Sergeev, “Frequency tunable single attosecond pulse production from aligned diatomic molecules ionized by intense laser field,” Opt. Express 18(3), 2269–2278 (2010). [CrossRef] [PubMed]

15.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004). [CrossRef] [PubMed]

16.

X. Zhou, X. Tong, Z. Zhao, and C. D. Lin, “Role of molecular orbital symmetry on the alignment dependence of high-order harmonic generation with molecules,” Phys. Rev. A 71(6), 061801 (2005). [CrossRef]

17.

B. Shan, X. Tong, Z. Zhao, Z. Chang, and C. D. Lin, “High-order harmonic cutoff extension of the O2 molecule due to ionization suppression,” Phys. Rev. A 66(6), 061401 (2002). [CrossRef]

18.

Y. Yu, J. Xu, Y. Fu, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Chu, J. Chen, Y. Cheng, and Z. Xu, “Single attosecond pulse generation from aligned molecules using two-color polarization gating,” Phys. Rev. A 80(5), 053423 (2009). [CrossRef]

19.

X. Zhou, X. Tong, Z. Zhao, and C. D. Lin, “Alignment dependence of high-order harmonic generation from N2 and O2 molecules in intense laser fields,” Phys. Rev. A 72(3), 033412 (2005). [CrossRef]

20.

J. Itatani, D. Zeidler, J. Levesque, M. Spanner, D. M. Villeneuve, and P. B. Corkum, “Controlling high harmonic generation with molecular wave packets,” Phys. Rev. Lett. 94(12), 123902 (2005). [CrossRef] [PubMed]

21.

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]

22.

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

23.

D. Pavicić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct measurement of the angular dependence of ionization for N2, O2, and CO2 in intense laser fields,” Phys. Rev. Lett. 98(24), 243001 (2007). [CrossRef] [PubMed]

24.

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).

25.

X. Tong, Z. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66(3), 033402 (2002). [CrossRef]

26.

Z. Zhao, X. Tong, and C. D. Lin, “Alignment-dependent ionization probability of molecules in a double-pulse laser field,” Phys. Rev. A 67(4), 043404 (2003). [CrossRef]

27.

A. Le, X. Tong, and C. D. Lin, “Evidence of two-center interference in high-order harmonic generation from CO2,” Phys. Rev. A 73(4), 041402 (2006). [CrossRef]

28.

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007). [CrossRef] [PubMed]

29.

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]

30.

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]

31.

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]

OCIS Codes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.7150) Ultrafast optics : Ultrafast spectroscopy

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 10, 2012
Revised Manuscript: January 7, 2013
Manuscript Accepted: January 17, 2013
Published: February 1, 2013

Citation
Chaojin Zhang, Jinping Yao, Fadhil A. Umran, Jielei Ni, Bin Zeng, Guihua Li, and Di Lin, "Enhanced narrow-bandwidth emission during high-order harmonic generation from aligned molecules," Opt. Express 21, 3259-3264 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-3259


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References

  1. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009). [CrossRef]
  2. J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A84(5), 051802 (2011). [CrossRef]
  3. 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]
  4. 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]
  5. C. Zhang, J. Yao, and J. Ni, “Generation of isolated attosecond pulses of sub-atomic-time durations with multi-cycle chirped polarization gating pulses,” Opt. Express20(22), 24642–24649 (2012). [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. L. B. D. 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).
  9. K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Pattern formation and flow control of fine particles by laser-scanning micromanipulation,” Opt. Lett.16(19), 1463–1465 (1991). [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. M. Yu. Emelin, M. Yu. Ryabikin, and A. M. Sergeev, “Frequency tunable single attosecond pulse production from aligned diatomic molecules ionized by intense laser field,” Opt. Express18(3), 2269–2278 (2010). [CrossRef] [PubMed]
  15. J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature432(7019), 867–871 (2004). [CrossRef] [PubMed]
  16. X. Zhou, X. Tong, Z. Zhao, and C. D. Lin, “Role of molecular orbital symmetry on the alignment dependence of high-order harmonic generation with molecules,” Phys. Rev. A71(6), 061801 (2005). [CrossRef]
  17. B. Shan, X. Tong, Z. Zhao, Z. Chang, and C. D. Lin, “High-order harmonic cutoff extension of the O2 molecule due to ionization suppression,” Phys. Rev. A66(6), 061401 (2002). [CrossRef]
  18. Y. Yu, J. Xu, Y. Fu, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Chu, J. Chen, Y. Cheng, and Z. Xu, “Single attosecond pulse generation from aligned molecules using two-color polarization gating,” Phys. Rev. A80(5), 053423 (2009). [CrossRef]
  19. X. Zhou, X. Tong, Z. Zhao, and C. D. Lin, “Alignment dependence of high-order harmonic generation from N2 and O2 molecules in intense laser fields,” Phys. Rev. A72(3), 033412 (2005). [CrossRef]
  20. J. Itatani, D. Zeidler, J. Levesque, M. Spanner, D. M. Villeneuve, and P. B. Corkum, “Controlling high harmonic generation with molecular wave packets,” Phys. Rev. Lett.94(12), 123902 (2005). [CrossRef] [PubMed]
  21. 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]
  22. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett.71(13), 1994–1997 (1993). [CrossRef] [PubMed]
  23. D. Pavicić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct measurement of the angular dependence of ionization for N2, O2, and CO2 in intense laser fields,” Phys. Rev. Lett.98(24), 243001 (2007). [CrossRef] [PubMed]
  24. 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. JETP64, 1191–1194 (1986).
  25. X. Tong, Z. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A66(3), 033402 (2002). [CrossRef]
  26. Z. Zhao, X. Tong, and C. D. Lin, “Alignment-dependent ionization probability of molecules in a double-pulse laser field,” Phys. Rev. A67(4), 043404 (2003). [CrossRef]
  27. A. Le, X. Tong, and C. D. Lin, “Evidence of two-center interference in high-order harmonic generation from CO2,” Phys. Rev. A73(4), 041402 (2006). [CrossRef]
  28. W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett.99(13), 133602 (2007). [CrossRef] [PubMed]
  29. 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]
  30. 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]
  31. 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]

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