## Spatial coherence control of xuv supercontinuum generation by two-color laser field |

Optics Express, Vol. 19, Issue 10, pp. 9986-9994 (2011)

http://dx.doi.org/10.1364/OE.19.009986

Acrobat PDF (818 KB)

### Abstract

We investigate the spatial characteristics of xuv supercontinuum generation in the two-color laser field consisting of a fundamental and a weak second harmonic field. By optimizing the synthesized two-color field, the spatial profile of the xuv supercontinuum varies from annular-like to Gaussian-like and then the spatial quality is improved effectively, which is beneficial for its potential applications. Moreover, our calculation shows that the spatial quality of the supercontinuum is stable when the intensity of the controlling field varies in the acceptable fluctuation.

© 2011 OSA

## 1. Introduction

1. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427 , 817–821 (2004). [CrossRef]

2. A. E. Kaplan, “Subfemtosecond Pulses in Mode-Locked 2π Solitons of the Cascade Stimulated Raman Scattering,” Phys. Rev. Lett. **73**, 1243 (1994). [CrossRef] [PubMed]

3. K. Lee, Y. H. Cha, M. S. Shin, B. H. Kim, and D. Kim, “Relativistic nonlinear Thomson scattering as attosecond x-ray source,” Phys. Rev. E **67**, 026502 (2003). [CrossRef]

4. P. Lan, P. Lu, W. Cao, and X. Wang, “Attosecond and zeptosecond x-ray pulses via nonlinear Thomson backscattering,” Phys. Rev. E **72**, 066501 (2005). [CrossRef]

5. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature **414**, 509–513 (2001). [CrossRef] [PubMed]

6. T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. **97**, 163901 (2006). [CrossRef] [PubMed]

7. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of Attosecond Pulse in the ’Single-Cycle’ Regime,” Phys. Rev. Lett. **78**, 1251 (1997). [CrossRef]

9. W. Cao, P. Lu, P. Lan, X. Wang, and G. Yang, “Efficient isolated attosecond pulse gene ration with a multi-cycle two-color laser field,” Opt. Express **15**, 530 (2007). [CrossRef] [PubMed]

*as*[1

1. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427 , 817–821 (2004). [CrossRef]

*as*), and then its applications are significantly limited. Many efforts have been paid to broaden the bandwidth of the supercontinuum and shorten the pulse duration. In a recent work, Goulielmakis

*et.al.*has employed an extremely short laser pulse of 3.3fs to produce a 40-eV supercontinuum [10

10. 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**, 1614–1617 (2008). [CrossRef] [PubMed]

11. P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. **71**,1994 (1993). [CrossRef] [PubMed]

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

13. Q. Zhang, P. Lu, P. Lan, W. Hong, and Z. Yang, “Multi-cycle laserdriven broadband supercontinuum with a modulated polarization gating,” Opt. Express **16**, 9795–9803 (2008). [CrossRef] [PubMed]

14. W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett. **34**, 2102–2104 (2009). [CrossRef] [PubMed]

15. P. Lan, P. Lu, Q. 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**, 043413 (2009). [CrossRef]

15. P. Lan, P. Lu, Q. 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**, 043413 (2009). [CrossRef]

10. 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**, 1614–1617 (2008). [CrossRef] [PubMed]

16. W. Cao, P. Lu, P. Lan, X. Wang, and Y. Li, “Control of the launch of attosecond pulses,” Phys. Rev. A **75**, 063423 (2007). [CrossRef]

17. J. E. Muffett, C. G. Wahlström, and M. H. R. Hutchinson, “Numerical modelling of the spatial profiles of high-order harmonics,” J. Phys. B **27**, 5693–5706 (1994). [CrossRef]

22. Y. Tamaki, J. Itatani, M. Obara, and K. Midorikawa, “Optimization of conversion efficiency and spatial quality of high-order harmonic generation,” Phys. Rev. A **62**, 063802 (2000). [CrossRef]

*è*res [19

19. P. Salières, T. Ditmire, K. S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B **27**, L217–L222 (1994). [CrossRef]

*et al.*found that the spatial profile of the harmonic in the cutoff region is almost Gaussian in experiment using one-color laser pulse. Moreover, the same group demonstrated that the spatial properties can be controlled and optimized by moving the laser focus position relative to the nonlinear medium [20

20. P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence Control of High-order Harmonics,” Phys. Rev. Lett. **74**, 3776 (1995). [CrossRef] [PubMed]

*et al.*[21

21. V. Tosa, H. T. Kim, I. J. Kim, and C. H. Nam, “High-order harmonic generation by chirped and self-guided femtosecond laser pulses.I.Spatial and spectral analysis,” Phys. Rev. A **71**, 063807 (2005). [CrossRef]

21. V. Tosa, H. T. Kim, I. J. Kim, and C. H. Nam, “High-order harmonic generation by chirped and self-guided femtosecond laser pulses.I.Spatial and spectral analysis,” Phys. Rev. A **71**, 063807 (2005). [CrossRef]

*ω*+ 2

*ω*laser field. By optimizing the synthesized two-color field, the spatial profile of the xuv supercontinuum varies from annular-like to Gaussian-like, which implies that the spatial quality can be controlled and improved effectively. Moreover, our calculation shows that the spatial quality of the supercontinuum is stable when the intensity of the controlling field varies in the acceptable fluctuation.

## 2. Theoretical model

23. 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**, 2117 (1994). [CrossRef] [PubMed]

*E*(

*t*) is the electric field,

*A*(

*t*) is the vector potential.

*ɛ*is a positive regularization constant.

*p*and

_{st}*S*are the stationary momentum and quasiclassical action, which are given by where

_{st}*I*is the ionization energy of the helium.

_{p}*d*(

*p*) is the dipole matrix element for transitions from the ground state to the continuum state. For hydrogenlike atoms, it can be written as

*g*(

*t*) in the Eq. (1) represents the ground state amplitude:

*ω*(

*t*) is the ionization rate, which is calculated by Ammosov-Delone-Krainov (ADK) tunnelling model [24]: where Z is the net resulting charge of the atom,

^{′}*I*is the ionization potential of the hydrogen atom, and

_{ph}*e*and

*m*are electron charge and mass respectively.

_{e}25. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. D. Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A **61**, 063801 (2000). [CrossRef]

*E*and

_{l}*E*are the laser field and high harmonics, respectively.

_{h}*ω*is the plasma frequency and is given by

_{p}## 3. Result and discussion

^{14}

*W/cm*

^{2}and 2.4×10

^{13}

*W/cm*

^{2}, respectively. The electric field of the synthesized laser pulse is expressed by

*E*

_{0}and

*E*

_{1}are the amplitudes of the driving and controlling field.

*f*(

*t*) and

*ω*

_{0}are the envelope and the frequency. A Gaussian envelope shape is adopted and

*φ*

_{0}is set as 0.

23. 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**, 2117 (1994). [CrossRef] [PubMed]

26. W. Cao, P. Lu, P. Lan, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A **74**, 063821 (2006). [CrossRef]

25. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. D. Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A **61**, 063801 (2000). [CrossRef]

^{18}/

*cm*

^{3}, which corresponds to a gas pressure of 40 Torr at room temperature. The focuses of the fundamental field and controlling field are put at the same position and the beam waists are both 25

*μm*. The entrance of the gas jet is placed 2 mm after the focuses of the laser field. Other parameters are the same as in Fig. 1. The near-field spatial profiles of 40th–60th harmonics at the exit of the medium in the one-color and the two-color fields are shown in Fig. 2, and the corresponding spatial images of the harmonics are also represented in Figs. 2(c) and (d). In the one-color field in Figs. 2(a) and (c), the near-field spatial profile of 40th–60th harmonics in the fundamental field alone is Gaussian-like. It is believed that the spatial quality of HHG with a Gaussian profile is better than that with an annular-like profile, and then the high-order harmonics in the one-color field has a good spatial quality. As we known, the spatial distribution of the laser field and phase matching of HHG in macroscopic medium play an important role in the spatial profile of HHG. When the laser focus is put before the gas target, short trajectory is preferably selected in the propagation and better phase matching of the short trajectory contribution to harmonics in the plateau is obtained off-axis [27

27. M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B **41**, 132001 (2008). [CrossRef]

*μm*and 0

*mm*(seen in Figs. 3(b) and (f)). However, when the beam waist of the controlling field is further decreased to 20

*μm*and the corresponding focus position is 0

*mm*(seen in Figs. 3(c) and (g)), the spatial profile of the HHG becomes a similar rectangle. When the beam waist of the controlling field is reduced to 15

*μm*and the focus position is 0

*mm*(seen in Figs. 3(d) and (h)), the harmonic profile becomes nearly Gaussian, which implies that the spatial quality of the supercontinuum has been optimized. Figure 3 shows that the spatial quality of the broadband supercontinuum in the two-color field can be effectively controlled and optimized.

28. A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A **46**, 2778 (1992). [CrossRef] [PubMed]

*μm*and the focus position is 0

*mm*(seen in Fig. 5(b)), the laser field on the propagation axes is more intense than that off the axes, thus the harmonics on the axes (seen in Fig. 3(d)) is brighter than that off the axes. It is shown that the integral maps of the two-color field at the ionization times of the trajectories corresponding to the 40th–60th harmonics are consistent with the spatial distribution of HHG.

*mm*, the spatial profile of HHG is annular-like, which implies that the intensity of HHG off the axes is more intense than that on the axes. As the focus position is set as 1

*mm*or 0

*mm*, the spatial profile of HHG becomes Gaussian-like. Figure 6(b) shows that the spatial profiles of HHG in the two-color field with different intensities of the controlling field. Other parameters are the same as those in Fig. 3(d). As shown in Fig. 6(b), the spatial profiles of HHG for the different intensities

*I*

_{2}of the controlling field are all the Gaussian-like shape. When the intensity of the controlling is increased from 2.4 × 10

^{13}

*W/cm*

^{2}to 5.4 × 10

^{13}

*W/cm*

^{2}, i.e. the relative intensity varies from 0.04 to 0.09, the divergence angle of HHG becomes smaller. From Fig. 6, it is shown that the spatial profile of the supercontinuum is stability to the intensity variation of the controlling field and sensitivity to the focus position.

## 4. Conclusion

*ω*+ 2

*ω*laser field. It is shown that HHG can be confined within half optical cycle in the two-color field and then high-efficiency supercontinuum is generated in the plateau, while the spatial profile of the supercontinuum is an annular-like distribution, which limits its application. By optimizing the two-color filed, the spatial profile of the xuv supercontinuum varies from annular-like to Gaussian-like, which shows that the spatial quality of the supercontinuum in the two-color field can be controlled and optimized effectively. Moreover, when the relative intensity the controlling field varies from 0.04 to 0.09, the spatial profile of the supercontinuum shows stability.

## Acknowledgments

## References and links

1. | R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427 , 817–821 (2004). [CrossRef] |

2. | A. E. Kaplan, “Subfemtosecond Pulses in Mode-Locked 2π Solitons of the Cascade Stimulated Raman Scattering,” Phys. Rev. Lett. |

3. | K. Lee, Y. H. Cha, M. S. Shin, B. H. Kim, and D. Kim, “Relativistic nonlinear Thomson scattering as attosecond x-ray source,” Phys. Rev. E |

4. | P. Lan, P. Lu, W. Cao, and X. Wang, “Attosecond and zeptosecond x-ray pulses via nonlinear Thomson backscattering,” Phys. Rev. E |

5. | M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature |

6. | T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. |

7. | I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of Attosecond Pulse in the ’Single-Cycle’ Regime,” Phys. Rev. Lett. |

8. | P. Lan, P. Lu, W. Cao, and X. Wang, “Efficient generation of an isolated single-cycle attosecond pulse,” Phys. Rev. A |

9. | W. Cao, P. Lu, P. Lan, X. Wang, and G. Yang, “Efficient isolated attosecond pulse gene ration with a multi-cycle two-color laser field,” Opt. Express |

10. | 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 |

11. | P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. |

12. | Z. H. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A |

13. | Q. Zhang, P. Lu, P. Lan, W. Hong, and Z. Yang, “Multi-cycle laserdriven broadband supercontinuum with a modulated polarization gating,” Opt. Express |

14. | W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett. |

15. | P. Lan, P. Lu, Q. 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 |

16. | W. Cao, P. Lu, P. Lan, X. Wang, and Y. Li, “Control of the launch of attosecond pulses,” Phys. Rev. A |

17. | J. E. Muffett, C. G. Wahlström, and M. H. R. Hutchinson, “Numerical modelling of the spatial profiles of high-order harmonics,” J. Phys. B |

18. | M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A |

19. | P. Salières, T. Ditmire, K. S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B |

20. | P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence Control of High-order Harmonics,” Phys. Rev. Lett. |

21. | V. Tosa, H. T. Kim, I. J. Kim, and C. H. Nam, “High-order harmonic generation by chirped and self-guided femtosecond laser pulses.I.Spatial and spectral analysis,” Phys. Rev. A |

22. | Y. Tamaki, J. Itatani, M. Obara, and K. Midorikawa, “Optimization of conversion efficiency and spatial quality of high-order harmonic generation,” Phys. Rev. A |

23. | 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 |

24. | M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP |

25. | E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. D. Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A |

26. | W. Cao, P. Lu, P. Lan, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A |

27. | M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B |

28. | A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A |

**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: March 10, 2011

Revised Manuscript: April 4, 2011

Manuscript Accepted: April 5, 2011

Published: May 6, 2011

**Citation**

Shaoyi Wang, Weiyi Hong, Qingbin Zhang, Kunlong Liu, Xiaosong Zhu, and Peixiang Lu, "Spatial coherence control of xuv supercontinuum generation by two-color laser field," Opt. Express **19**, 9986-9994 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9986

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### References

- R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427 , 817–821 (2004). [CrossRef]
- A. E. Kaplan, “Subfemtosecond Pulses in Mode-Locked 2π Solitons of the Cascade Stimulated Raman Scattering,” Phys. Rev. Lett. 73, 1243 (1994). [CrossRef] [PubMed]
- K. Lee, Y. H. Cha, M. S. Shin, B. H. Kim, and D. Kim, “Relativistic nonlinear Thomson scattering as attosecond x-ray source,” Phys. Rev. E 67, 026502 (2003). [CrossRef]
- P. Lan, P. Lu, W. Cao, and X. Wang, “Attosecond and zeptosecond x-ray pulses via nonlinear Thomson backscattering,” Phys. Rev. E 72, 066501 (2005). [CrossRef]
- M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001). [CrossRef] [PubMed]
- T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006). [CrossRef] [PubMed]
- I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of Attosecond Pulse in the ’Single-Cycle’ Regime,” Phys. Rev. Lett. 78, 1251 (1997). [CrossRef]
- P. Lan, P. Lu, W. Cao, and X. Wang, “Efficient generation of an isolated single-cycle attosecond pulse,” Phys. Rev. A 76, 043808 (2007). [CrossRef]
- W. Cao, P. Lu, P. Lan, X. Wang, and G. Yang, “Efficient isolated attosecond pulse gene ration with a multi-cycle two-color laser field,” Opt. Express 15, 530 (2007). [CrossRef] [PubMed]
- 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, 1614–1617 (2008). [CrossRef] [PubMed]
- P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71,1994 (1993). [CrossRef] [PubMed]
- Z. H. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70, 043802 (2004). [CrossRef]
- Q. Zhang, P. Lu, P. Lan, W. Hong, and Z. Yang, “Multi-cycle laserdriven broadband supercontinuum with a modulated polarization gating,” Opt. Express 16, 9795–9803 (2008). [CrossRef] [PubMed]
- W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett. 34, 2102–2104 (2009). [CrossRef] [PubMed]
- P. Lan, P. Lu, Q. 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, 043413 (2009). [CrossRef]
- W. Cao, P. Lu, P. Lan, X. Wang, and Y. Li, “Control of the launch of attosecond pulses,” Phys. Rev. A 75, 063423 (2007). [CrossRef]
- J. E. Muffett, C. G. Wahlström, and M. H. R. Hutchinson, “Numerical modelling of the spatial profiles of high-order harmonics,” J. Phys. B 27, 5693–5706 (1994). [CrossRef]
- M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747 (1995). [CrossRef] [PubMed]
- P. Salières, T. Ditmire, K. S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994). [CrossRef]
- P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence Control of High-order Harmonics,” Phys. Rev. Lett. 74, 3776 (1995). [CrossRef] [PubMed]
- V. Tosa, H. T. Kim, I. J. Kim, and C. H. Nam, “High-order harmonic generation by chirped and self-guided femtosecond laser pulses.I.Spatial and spectral analysis,” Phys. Rev. A 71, 063807 (2005). [CrossRef]
- Y. Tamaki, J. Itatani, M. Obara, and K. Midorikawa, “Optimization of conversion efficiency and spatial quality of high-order harmonic generation,” Phys. Rev. A 62, 063802 (2000). [CrossRef]
- 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, 2117 (1994). [CrossRef] [PubMed]
- M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).
- E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. D. Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000). [CrossRef]
- W. Cao, P. Lu, P. Lan, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A 74, 063821 (2006). [CrossRef]
- M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B 41, 132001 (2008). [CrossRef]
- A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992). [CrossRef] [PubMed]

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