## Isolated attosecond pulse generation with the stability against the carrier-envelope phase shift and with the high-beam quality from CO gas medium |

Optics Express, Vol. 19, Issue 27, pp. 26174-26185 (2011)

http://dx.doi.org/10.1364/OE.19.026174

Acrobat PDF (1163 KB)

### Abstract

We theoretically investigate the isolated attosecond pulse generation with a 1300-nm infrared few-cycle laser pulse from the CO medium. It is found that the supercontinuum in the plateau from CO in the microscopic level can be generated for nearly all the carrier-envelop phase(CEP) of the driving pulse. The macroscopic investigation shows that when the molecular axis is parallel to the electric field, the supercontinuum can be phase-matched in broader spectral range than the antiparallel case and achieve a good beam quality with the divergence angle of 0.2 mrad, which benefits for some potential applications of ultrafast detections with high spatial and temporal resolutions.

© 2011 OSA

## 1. Introduction

4. P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics” Phys. Rev. Lett. **77**, 1234–1237 (1996). [PubMed]

5. P. Corkum, “Plasma perspective on strong-filed multiphoton ionization,” Phys. Rev. Lett. **71**, 1994–1997 (1993). [PubMed]

10. Y. Zheng, Z. Zeng, X. Li, X. Chen, P. Liu, H. Xiong, H. Lu, S. Zhao, P. Wei, L. Zhang, X. Wang, J. Liu, Y. Cheng, R. Li, and Z. Xu, “Enhancement and broadening of extreme-ultraviolet supercontinuum in a relative phase controlled two-color laser field,” Opt. Lett. **33**, 234–236 (2008). [PubMed]

14. P. Lan, P. Lu, W. Cao, X. Wang, and W. Hong, “Single attosecond pulse generation from asymmetric molecules with a multicycle laser pulse,” Opt. Lett. **32**, 1186–1188 (2007). [PubMed]

15. G. Kamta and A. Bandrauk, “Phase dependence of enhanced ionization in Asymmetric molecules,” Phys. Rev. Lett. **94**, 203003 (2005). [PubMed]

16. Q. Liao, P. Lu, Q. Zhang, Z. Yang, and X. Wang, “Doulbe ionization of HeH^{+} molecules in intense laser fields,” Opt. Express **16**, 17070–17075 (2008). [PubMed]

14. P. Lan, P. Lu, W. Cao, X. Wang, and W. Hong, “Single attosecond pulse generation from asymmetric molecules with a multicycle laser pulse,” Opt. Lett. **32**, 1186–1188 (2007). [PubMed]

17. K. Liu, W. Hong, and P. Lu, “Phase dependence of electron localization in HeH2+ dissociation with an intense few-cycle laser pulse,” Opt. Express **19**, 20279–20287 (2011). [PubMed]

14. P. Lan, P. Lu, W. Cao, X. Wang, and W. Hong, “Single attosecond pulse generation from asymmetric molecules with a multicycle laser pulse,” Opt. Lett. **32**, 1186–1188 (2007). [PubMed]

^{+}, of which the asymmetric structure can afford very intense driving pulse and emit the harmonics with very high photon-energies for broadband supercontinuum generation. However, the orientation of such molecule still remains challenging. The real asymmetric molecules, such as CO, can be oriented by the current laser techniques [20

20. S. De, I. Znakovskaya, D. Ray, F. Anis, N. G. Johnson, I. Bocharaova, M. Magrakvelidze, B. D. Esry, C. L. Cocke, I. V. Litvinyuk, and M. F. Kling, “Field-free orientation of CO molecules by femtosecond two-color laser fields,” Phys. Rev. Lett. **103**, 153002 (2009). [PubMed]

## 2. Theoretical model

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

*E*(

*t*) is the electric field of the laser pulse,

*A*(

*t*) is the corresponding 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.

_{p}*g*(

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

*w*(

*t*′) is the ionization rate, which is calculated by the molecular Ammosov-Delone-Krainov (MO-ADK) tunnelling model [22]: where with

*Z*being the effective Coulomb charge,

_{c}**R**being the Euler angles between the molecular axis and the field direction, and

*C*for CO are calculated by the multiple-scattering method [22, 23].

_{l}*is the HOMO of CO obtained with the Gaussian 03*

_{CO}*ab initio*code [24

24. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, “Gaussian 03, Revision C.02,” Gaussian Inc., Wallingford, CT (2010).

*I*

_{p}_{0}is the field free ionization energy,

*μ*is the permanent dipole of HOMO of CO and

_{h}**E**(

*t*) is the external field. The permanent dipole of HOMO is calculated to be 1.72 a.u. (4.37 D) by [25] where

*ρ*(

^{H}**r**) is the electron density of the HOMO calculated by

*ρ*(

^{H}**r**) = ∫

*d*

**r**Ψ

^{*}(

**r**)Ψ(

**r**).

*a⃗*(

*t*): where

*T*and

*ω*are the duration and frequency of the driving pulse, respectively.

*q*corresponds to the harmonic order.

*E*and

_{f}*E*are laser and harmonic fields,

_{h}*P*(

_{nl}*ρ,z,t*) = [

*n*

_{0}–

*n*(

_{e}*ρ*,

*z,t*)]

*d*(

_{nl}*ρ*,

*z,t*) is the nonlinear polarization generated by the medium.

*n*

_{0}is the gas density and

## 3. Result and discussion

^{14}

*W/cm*

^{2}to keep the molecule far from being highly ionized and avoid breaking the inverse asymmetry of the ionization process in the adjacent two half-cycles. The electric field of the driving pulse is expressed as where

*E*

_{0},

*T*

_{0}and

*ϕ*are the amplitude, optical cycle and carrier-envelope phase(CEP) of the driving field, respectively. First the CEP is set to zero. Figures 1(a)–(c) are the ionization rates of the CO molecules when the molecular axis is parallel, perpendicular and antiparallel to the electric field, respectively. For the parallel case, there are two main equivalent ionization peaks during the pulse. The electrons ionized in the peak would be accelerated in the next half-cycle with the strongest electric field and obtain the highest kinetic energy while the kinetic energy of the electrons for the other peak is much lower, leading to the continuous high-harmonic generation with a broad bandwidth. For the perpendicular case, the ionization property is nearly the same as the cases for the atoms or the symmetric molecules, then the supercontinuum can only be generated near the cutoff. For the antiparallel case, there is only one main ionization peak corresponding for the HHG, which forms a “standard” ionization gate and then the harmonics in the plateau would merge to a broadband supercontinuum. However, the electrons in this case are accelerated in the half-cycle with the second highest electric field, then the harmonic cutoff is lower than that of the parallel case.

*P*

_{1},

*P*

_{2}and

*P*

_{3}. When the molecular axis is parallel to the laser electric field, the harmonic yield for

*P*

_{2}is much higher than those for

*P*

_{1}and

*P*

_{3}due to the ionization properties shown in Fig. 1(a). And for the antiparallel case, the harmonic yield for

*P*

_{3}is dominant during the pulse since the electric field and the molecule gate the ionization process of the electrons corresponding for

*P*

_{3}.

*π*, the two-peak structure of the ionization rate can also lead the the supercontinuum generation in the plateau, according to the above analysis. Then we can conclude that the supercontinuum can be produced in the plateau by using a two-cycle driving pulse with arbitrary CEPs. This can be confirmed by the result shown in Fig. 3(b), in which the harmonics in the plateau merge to supercontinua for nearly all the CEPs but different cutoff energies. For the perpendicular case, there are more than two ionization peaks during the pulse for all the CEPs, then the continuous harmonics can only be observed near the cutoff.

*μ*m and 0.5-mm long gas jet with the gas density of 2.6×10

^{18}/cm

^{3}. The gas jet is placed 1 mm after the laser focus. Figure 6(a) and (b) show the spectra of the macroscopic harmonics for the alignment angles of 0°, 30°, 60°, and 120°, 150°, 180°, respectively. For comparison, the macroscopic spectrum for the perpendicular case is also presented in both Fig. 6(a) and (b) by the dashed lines. One can clearly see that the interference fringes through the plateau to the cutoff are mostly removed for all the angles. For the alignment angles of 0°, 30°, 60°, the supercontinua are well phase-matched from about 70th to the cutoff, while the phase-matched harmonics are only covered by about 20 harmonic orders for the angles of 120°, 150°, 180°. Moreover, there are some small irregular modulations in the supercontinuum for such angles.

## 4. Conclusion

^{14}

*W/cm*

^{2}according to our calculation.

## 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 (London) |

2. | M. I. Stockman, M. F. Kling, U. Kleineberg, and F. Krausz, “Attosecond nanoplasmonic-field
microscope,” Nat. Photonics |

3. | F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. |

4. | P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics” Phys. Rev. Lett. |

5. | P. Corkum, “Plasma perspective on strong-filed multiphoton ionization,” Phys. Rev. Lett. |

6. | I. Christov, M. Murnane, and H. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett. |

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

8. | P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A |

9. | 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 |

10. | Y. Zheng, Z. Zeng, X. Li, X. Chen, P. Liu, H. Xiong, H. Lu, S. Zhao, P. Wei, L. Zhang, X. Wang, J. Liu, Y. Cheng, R. Li, and Z. Xu, “Enhancement and broadening of extreme-ultraviolet supercontinuum in a relative phase controlled two-color laser field,” Opt. Lett. |

11. | W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A |

12. | P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A |

13. | W. Hong, Y. Li, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Control of quantum paths in the multicycle regime and efficient broadband attosecond pulse generation,” J. Opt. Soc. Am. B |

14. | P. Lan, P. Lu, W. Cao, X. Wang, and W. Hong, “Single attosecond pulse generation from asymmetric molecules with a multicycle laser pulse,” Opt. Lett. |

15. | G. Kamta and A. Bandrauk, “Phase dependence of enhanced ionization in Asymmetric molecules,” Phys. Rev. Lett. |

16. | Q. Liao, P. Lu, Q. Zhang, Z. Yang, and X. Wang, “Doulbe ionization of HeH |

17. | K. Liu, W. Hong, and P. Lu, “Phase dependence of electron localization in HeH2+ dissociation with an intense few-cycle laser pulse,” Opt. Express |

18. | Q. Li, W. Hong, Q. Zhang, S. Wang, and P. Lu, “Isolated-attosecond-pulse generation from asymmetric molecules with an |

19. | Q. Zhang, P. Lu, W. Hong, Q. Liao, and S. Wang, “Control of high-order harmonic generation from molecules lacking inversion symmetry with a polarization gating method,” Phys. Rev. A |

20. | S. De, I. Znakovskaya, D. Ray, F. Anis, N. G. Johnson, I. Bocharaova, M. Magrakvelidze, B. D. Esry, C. L. Cocke, I. V. Litvinyuk, and M. F. Kling, “Field-free orientation of CO molecules by femtosecond two-color laser fields,” Phys. Rev. Lett. |

21. | M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A |

22. | X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A |

23. | D. Dill and J. L. Dehmer, “Electronmolecule scattering and molecular photoionization using the multiplescattering method,” J. Chem. Phys. |

24. | M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, “Gaussian 03, Revision C.02,” Gaussian Inc., Wallingford, CT (2010). |

25. | M. Abu-samha and L. B. Madsen, “Photoelectron angular distributions from polar molecules probed by intense femtosecond lasers,” Phys. Rev. A |

26. | A. Etches and L. B. Madsen, “Extending the strong-field approximation of high-order harmonic generation to polar molecules: gating mechanisms and extension of the harmonic cutoff,” J. Phys. B: At. Mol. Opt. Phys. |

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

28. | C. Jin, A. Le, and C. D. Lin, “Medium propagation effects in high-order harmonic generation of Ar and N |

**OCIS Codes**

(020.4180) Atomic and molecular physics : Multiphoton processes

(260.3230) Physical optics : Ionization

(270.6620) Quantum optics : Strong-field processes

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: November 2, 2011

Revised Manuscript: November 24, 2011

Manuscript Accepted: November 25, 2011

Published: December 7, 2011

**Citation**

Weiyi Hong, Qingbin Zhang, Xiaosong Zhu, and Peixiang Lu, "Isolated attosecond pulse generation with the stability against the carrier-envelope phase shift and with the high-beam quality from CO gas medium," Opt. Express **19**, 26174-26185 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26174

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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 (London)427, 817–821 (2004).
- M. I. Stockman, M. F. Kling, U. Kleineberg, and F. Krausz, “Attosecond nanoplasmonic-field microscope,” Nat. Photonics1, 539–544 (2007).
- F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81, 163–234 (2009).
- P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics” Phys. Rev. Lett.77, 1234–1237 (1996). [PubMed]
- P. Corkum, “Plasma perspective on strong-filed multiphoton ionization,” Phys. Rev. Lett.71, 1994–1997 (1993). [PubMed]
- I. Christov, M. Murnane, and H. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett.78, 1251–1254 (1997).
- Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A70, 043802 (2004).
- P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A76, 011402(R) (2007).
- 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. A79, 043413 (2009).
- Y. Zheng, Z. Zeng, X. Li, X. Chen, P. Liu, H. Xiong, H. Lu, S. Zhao, P. Wei, L. Zhang, X. Wang, J. Liu, Y. Cheng, R. Li, and Z. Xu, “Enhancement and broadening of extreme-ultraviolet supercontinuum in a relative phase controlled two-color laser field,” Opt. Lett.33, 234–236 (2008). [PubMed]
- W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A80, 053407 (2009).
- P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A76, 051801(R) (2007).
- W. Hong, Y. Li, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Control of quantum paths in the multicycle regime and efficient broadband attosecond pulse generation,” J. Opt. Soc. Am. B25, 1684–1689 (2009).
- P. Lan, P. Lu, W. Cao, X. Wang, and W. Hong, “Single attosecond pulse generation from asymmetric molecules with a multicycle laser pulse,” Opt. Lett.32, 1186–1188 (2007). [PubMed]
- G. Kamta and A. Bandrauk, “Phase dependence of enhanced ionization in Asymmetric molecules,” Phys. Rev. Lett.94, 203003 (2005). [PubMed]
- Q. Liao, P. Lu, Q. Zhang, Z. Yang, and X. Wang, “Doulbe ionization of HeH+ molecules in intense laser fields,” Opt. Express16, 17070–17075 (2008). [PubMed]
- K. Liu, W. Hong, and P. Lu, “Phase dependence of electron localization in HeH2+ dissociation with an intense few-cycle laser pulse,” Opt. Express19, 20279–20287 (2011). [PubMed]
- Q. Li, W. Hong, Q. Zhang, S. Wang, and P. Lu, “Isolated-attosecond-pulse generation from asymmetric molecules with an ω+2ω/3 multicycle two-color field,” Phys. Rev. A81, 053846 (2010).
- Q. Zhang, P. Lu, W. Hong, Q. Liao, and S. Wang, “Control of high-order harmonic generation from molecules lacking inversion symmetry with a polarization gating method,” Phys. Rev. A79, 053406 (2009).
- S. De, I. Znakovskaya, D. Ray, F. Anis, N. G. Johnson, I. Bocharaova, M. Magrakvelidze, B. D. Esry, C. L. Cocke, I. V. Litvinyuk, and M. F. Kling, “Field-free orientation of CO molecules by femtosecond two-color laser fields,” Phys. Rev. Lett.103, 153002 (2009). [PubMed]
- M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49, 2117–2132 (1994). [PubMed]
- X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A66, 033402 (2002).
- D. Dill and J. L. Dehmer, “Electronmolecule scattering and molecular photoionization using the multiplescattering method,” J. Chem. Phys.61, 692–699 (1974).
- M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, “Gaussian 03, Revision C.02,” Gaussian Inc., Wallingford, CT (2010).
- M. Abu-samha and L. B. Madsen, “Photoelectron angular distributions from polar molecules probed by intense femtosecond lasers,” Phys. Rev. A82, 043413 (2010).
- A. Etches and L. B. Madsen, “Extending the strong-field approximation of high-order harmonic generation to polar molecules: gating mechanisms and extension of the harmonic cutoff,” J. Phys. B: At. Mol. Opt. Phys.43, 155602 (2010).
- E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A61, 063801 (2000).
- C. Jin, A. Le, and C. D. Lin, “Medium propagation effects in high-order harmonic generation of Ar and N2,” Phys. Rev. A83, 023411 (2011).

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