## Influence of large permanent dipoles on molecular orbital tomography |

Optics Express, Vol. 21, Issue 5, pp. 5255-5268 (2013)

http://dx.doi.org/10.1364/OE.21.005255

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### Abstract

The influence of large permanent dipoles on molecular orbital tomography via high-order harmonic generation (HHG) is investigated in this work. It is found that, owing to the modification of the angle-dependent ionization rate resulting from the Stark shift, the one-side-recollision condition for the tomographic imaging can not be satisfied even with the few-cycle driving pulses. To overcome this problem, we employ a tailored driving pulse by adding a weak low-frequency pulse to the few-cycle laser pulse to control the HHG process and the recollision of the continuum electrons are effectively restricted to only one side of the core. Then we carried out the orbital reconstruction in both the length and velocity forms. The results show that, the orbital structure can only be successfully reproduced by using the dipole matrix elements projected perpendicular to the permanent dipole in both forms.

© 2013 OSA

## 1. Introduction

1. M. Lein, “Molecular imaging using recolliding electrons,” J. Phys. B: At. Mol. Opt. Phys. **40**, R135–R173 (2007) [CrossRef] .

5. Y. M. Zhou, C. Huang, Q. Liao, and P. X. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett. **109**, 053004 (2012) [CrossRef] [PubMed] .

*et al*in [6

6. 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**, 867–871 (2004) [CrossRef] [PubMed] .

_{2}. Since then, the MOT has attracted a great deal of attention for its great significance in uncovering the basic properties of molecules and chemical reactions [7

7. S. Haessler, J Caillat, and P Salières, “Self-probing of molecules with high harmonic generation,” J. Phys. B: At. Mol. Opt. Phys. **44**, 203001 (2011) [CrossRef] .

13. Z. Diveki, R. Guichard, J. Caillat, A. Camper, S. Haessler, T. Auguste, T. Ruchon, B. Carré, A. Maquet, R. Taïeb, and P. Salières, “Molecular orbital tomography from multi-channel harmonic emission in N_{2},” Chem. Phys.http://dx.doi.org/10.1016/j.chemphys.2012.03.021 (2012).

*et al*[14

14. Elmar V. van der Zwan, C. C. Chirilǎ, and M. Lein, “Molecular orbital tomography using short laser pulses,” Phys. Rev. A **78**, 033410 (2008) [CrossRef] .

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

16. 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**, 2117–2132 (1994) [CrossRef] [PubMed] .

^{2+}was successfully reconstructed in their simulation. Besides, one can also consider using an

*ω*+ 2

*ω*two-color laser pulse for the MOT of nonsymmetric orbitals [7

7. S. Haessler, J Caillat, and P Salières, “Self-probing of molecules with high harmonic generation,” J. Phys. B: At. Mol. Opt. Phys. **44**, 203001 (2011) [CrossRef] .

17. M. Y. Qin, X. S. Zhu, Q. B. Zhang, and P. X. Lu, “Tomographic imaging of asymmetric molecular orbitals with two-color multicycle laser field,” Opt. Lett. **37**, 5208–5210 (2012) [CrossRef] [PubMed] .

*ab initio*orbital and the influence of the nonsymmetric electron distribution on the reconstructed result in MOT is discussed at the end.

## 2. Theoretical model

### 2.1. Simulating the HHG

16. 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**, 2117–2132 (1994) [CrossRef] [PubMed] .

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

23. C. C. Chirilă, “Analysis of the strong field approximation for harmonic generation and multiphoton ionization in intense ultrashort laser pulses,” PhD Thesis http://massey.dur.ac.uk/resources/cpchirila/chirilathesis.pdf.

*a*,

_{ion}*a*and

_{prop}*a*are the amplitudes of tunneling ionization, propagation after tunneling and recombination.

_{rec}*t*is the approximate saddle time determined by solving

_{d}**A**

*(*

_{f}*t*) is the vector potential corresponding to the electric field

**F**(

*t*), and

**p**

*is the stationary momentum calculated by For atoms the amplitudes in Eq. (1) are given by*

_{st}*I*is the ionization energy and Ψ

_{p}*is the ground state in the form of hydrogenlike atom [16*

_{g}16. 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**, 2117–2132 (1994) [CrossRef] [PubMed] .

**k**=

**p**

*+*

_{st}**A**

*(*

_{f}*t*) is the momentum of the return electron at the instant of recombination.

**a**

*is calculated with the MO-ADK theory [24*

_{ion}24. X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A, **66**, 033402 (2002) [CrossRef] .

*is the HOMO of the molecule obtained from Gaussian 03*

_{g}*ab initio*code [25

25. 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).

*μ*, the ionization energy becomes time-dependent in response to the external electric field [20

_{h}20. M. Abu-samha and L. B. Madsen, “Photoelectron angular distributions from polar molecules probed by intense femtosecond lasers,” Phys. Rev. A, **82**, 043413 (2010) [CrossRef] .

21. X. S. Zhu, Q. B. Zhang, W. Y. Hong, P. X. Lu, and Z. Z. Xu, “Laser-polarization-dependent photoelectron angular distributions from polar molecules,” Opt. Express **19**, 24198–24209 (2011) [CrossRef] [PubMed] .

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. **43**, 155602 (2010) [CrossRef] .

*I*

_{p}_{0}is the field free ionization energy. The permanent dipole

*μ*is calculated by

_{h}*ρ*(

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

*ρ*(

^{H}**r**) = |Ψ

*(*

_{g}**r**)|

^{2}.

**k**is replaced by the effective momentum [27

27. T. Kanai, S. Minemoto, and H. Sakai, “Ellipticity dependence of high-order harmonic generation from aligned molecules,” Phys. Rev. Lett. **98**, 053002 (2007) [CrossRef] [PubMed] .

28. Y. J. Chen, J. Liu, and B. Hu, “Reading molecular messages from high-order harmonic spectra at different orientation angles,” J. Chem. Phys. **130**, 044311 (2009) [CrossRef] [PubMed] .

29. M. Lein, N. Hay, R. Velotta, J. P. Marangos, and P. L. Knight, “Interference effects in high-order harmonic generation with molecules,” Phys. Rev. A **66**, 023805 (2002) [CrossRef] .

30. G. L. Kamta and A. D. Bandrauk, “Three-dimensional time-profile analysis of high-order harmonic generation in molecules: nuclear interferences in **71**, 053407 (2005) [CrossRef] .

*γ*(

*k*) is given by This k-dependent factor avoids the unreasonable fact that all the return electrons have momenta larger than

*γ*(

*k*) also suppresses the strong background noises resulting from the jump of

**k**

*over the gap from*

_{eff}*γ*= 1 for

*k*

^{2}≥

*I*, this term only affects the HHG of very low orders.

_{p}### 2.2. Reconstruction method

*θ*. In addition, one should also calculated or measure the high-order harmonic spectrum from the reference atom with the ionization energy similar to that of the target molecule. Then the recombination dipole moment

**d**

*and the dipole velocity*

^{L}**d**

*for the molecular orbital in both x’ and y’ components are obtained by [7*

^{V}7. S. Haessler, J Caillat, and P Salières, “Self-probing of molecules with high harmonic generation,” J. Phys. B: At. Mol. Opt. Phys. **44**, 203001 (2011) [CrossRef] .

*φ*denote the complex electric field, amplitude and phase of the high-order harmonic radiation respectively.

*η*is the scaling factor in molecules depending on the ionization angle

*θ*calculated by the MO-ADK theory.

_{i}*ω*=

*qω*is the harmonic frequency of the q-th order. The relation between

_{L}*ω*and

*k*is determined by the energy conversation

*ω*=

*k*

^{2}/2. To subtract the additional acquired Stark phase from

*E*, the first-order Stark phase

^{mol}18. A. Etches, M. Gaarde, and L. Madsen, “Laser-induced bound-state phases in high-order-harmonic generation,” Phys. Rev. A **86**, 023818 (2012) [CrossRef] .

18. A. Etches, M. Gaarde, and L. Madsen, “Laser-induced bound-state phases in high-order-harmonic generation,” Phys. Rev. A **86**, 023818 (2012) [CrossRef] .

*(*

_{ref}**k**) is the Fourier transform of the ground state of the reference atom Ψ

*(*

_{ref}**r**).

**44**, 203001 (2011) [CrossRef] .

## 3. Result and discussion

### 3.1. Simulating and controlling the HHG

^{2}driving pulse

*T*

_{0}is the optical cycle and

*φ*

_{0}= 1.25

*π*. This form of laser pulse (with an opposite sign) has been used to accomplish the MOT of the nonsymmetric molecule HeH

^{2+}[14

14. Elmar V. van der Zwan, C. C. Chirilǎ, and M. Lein, “Molecular orbital tomography using short laser pulses,” Phys. Rev. A **78**, 033410 (2008) [CrossRef] .

^{14}W/cm

^{2}and 1.5

*μ*m respectively. Employing the 1.5

*μ*m mid-IR laser source allows us to extend the harmonic spectrum considerably with a low laser intensity below the barrier suppression intensity [12

12. C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. **7**, 822–826 (2011) [CrossRef] .

31. C. Vozzi, R. Torres, M. Negro, L. Brugnera, T. Siegel, C. Altucci, R. Velotta, F. Frassetto, L. Poletto, P. Villoresi, S. De Silvestri, S. Stagira, and J. P. Marangos, “High harmonic generation spectroscopy of hydrocarbons,” Appl. Phys. Lett. **97**, 241103 (2010) [CrossRef] .

*θ*= 10° without taking into account the Stark shift. The harmonic spectrum from the reference atom is also shown in Fig. 3(a) by the dashed curve. Figures 3(b) and (c) show the corresponding time-frequency analyses [26

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. **43**, 155602 (2010) [CrossRef] .

32. P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A **51**, R1750–R1753 (1995) [CrossRef] [PubMed] .

*E*= −

_{g}*I*in response to the external electric field

_{p}*F*(

*t*) is plotted in Fig 2(b). The electron is more likely to be ionized with a high

*E*and is harder to be ionized when

_{g}*E*is low. Therefore, the ionization rate of CO is decreased when

_{g}*μ*is parallel with the electric filed

_{h}*F*and is increased in the antiparallel geometry. In the case of 10° orientation, as shown by the red solid curve in Fig. 2(b), the ionization by P1 is enhanced by the Stark shift and the ionization by P2 is suppressed, leading to the comparable ionization probabilities from both peaks. And these comparable ionization probabilities finally lead to the comparable HHG contributions by electrons returning from opposite sides.

33. E. V. van der Zwan and M. Lein, “Control of recollision wave packets for molecular orbital tomography using short laser pulses,” J. Phys. B: At. Mol. Opt. Phys. **41**, 074009 (2008) [CrossRef] .

*τ*

^{3}, where

*τ*is the time the electron spends in the continuum from ionization to recombination and reflects the effect of wave-packet spreading. After the collection, the return probability of the electron with negative momentum

*P*

_{−}and the return probability of electron with positive momentum

*P*

_{+}are obtained. The ratio of the probabilities

*P*

_{−}/

*P*

_{+}for orientation angles from 0° to 180° is plotted in Fig. 4, where the blue circles and the green diamonds present the calculated results without and with the Stark effect taken into account respectively. Comparing the green diamonds to the blue circles, the Stark shift leads to more recollision with negative momentum especially for the orientation at small angles. The ratio of

*P*

_{−}/

*P*

_{+}is bigger than 0.1 for

*θ*< 60° and goes up to bigger than 1 for

*θ*= 0 and 10°.

^{14}W/cm

^{2}were preferred,

*e.g.*Ref. [12

12. C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. **7**, 822–826 (2011) [CrossRef] .

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. **43**, 155602 (2010) [CrossRef] .

_{2}laser [34

34. C. Serrat and J. Biegert, “All-regions tunable high harmonic enhancement by a periodic static electric field,” Phys. Rev. Lett. **104**, 073901 (2010) [CrossRef] [PubMed] .

35. J. Luo, W. Hong, Q. Zhang, K. Liu, and P. Lu, “Dramatic cutoff extension and broadband supercontinuum generation in multi-cycle two color pulses,” Opt. Express **20**, 9801–9809 (2012) [CrossRef] [PubMed] .

36. W. Y. Hong, P. X. Lu, P. F. Lan, Q. B. Zhang, and X. B. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express **17**, 5139–5146 (2009) [CrossRef] [PubMed] .

37. K. Kovács, E. Balogh, J. Hebling, V. Toşa, and K. Varjú, “Quasi-phase-matching high-harmonic radiation using chirped THz pulses,” Phys. Rev. Lett. **108**, 193903 (2012) [CrossRef] [PubMed] .

_{2}laser with the wavelength of 10.6

*μ*m. The intensity of this pulse is 1% of that of the few-cycle driving pulse and the electric field is

*F*′ =

*F*′

_{0}cos(

*ω*′

*+*

_{L}t*φ*′

_{0}) with

*φ*′

_{0}= 1.7

*π*. The low-frequency field and the tailored field are presented by the dash-dotted green and solid red curves in Fig. 2(a) respectively.

*P*

_{−}/

*P*

_{+}under this tailored field is presented by the red pentagrams in Fig. 4. Comparing to the green diamonds, the recollision with negative momentum is suppressed: the ratio is two orders of magnitude decreased and is below 0.1 for all the orientation angles (for 180° <

*θ*< 360° the ratio at

*θ*equals that at 2

*π*−

*θ*). The result shows that the tailored laser pulse can efficiently restrict the recollision of the continuum electrons to only one side of the core.

*θ*= 10° as shown in Fig. 5(a). And the plateaus on the lower energy side are at least 4 orders of magnitude higher than those on the higher energy side for

*θ*= 90 and 170° as shown in Figs. 5(d) and (g). Therefore, the one-side-recollision condition is met and the HHG by this tailored pulse is satisfying for the MOT of the nonsymmetric target orbital.

### 3.2. Tomographic reconstruction

*θ*from 0° to 360° with the angular step Δ

*θ*= 10°. Figures 6(a) and (b) display the reconstructed orbitals

*ab initio*orbital is also shown in Fig. 7(c). Compared with Fig. 7(c), Fig. 6(b) successfully reproduces the main structure of the nonsymmetric target orbital, while Fig. 6(a) fails to reproduce the structure. There is an artificial structure close to x=0 in Fig. 6(a) with a sharp jump from the negative value to the positive value. This is due to the nonsymmetric distribution of the orbital.

*f*and

_{x}*f*, which are defined as [6

_{y}6. 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**, 867–871 (2004) [CrossRef] [PubMed] .

*and*

^{L}*f*is Both

*f*(

_{x}*x*,

*y*) and

*f*(

_{y}*x*,

*y*) are symmetrically distributed along the y direction and are nonsymmetrically distributed along the x axis, corresponding to the nonsymmetric electric density distribution of the target orbital along the permanent dipole. Therefore, one will have no problem in dividing

*f*by

_{y}*y*to obtain

*f*locates right at

_{y}*y*= 0. But the nodal plane is bent and not coincident with

*x*= 0 for

*f*. As a result, numerical problem arises when dividing

_{x}*f*by

_{x}*x*with x→0, which leads to the artificial structure and sharp jump in Fig. 6(a).

*θ*starts from 5° and increases in the step of 10° to avoid cos(

*θ*) = 0 or sin(

*θ*) = 0 in the denominators in Eqs. (22) and (23).

*ab initio*orbital, it is found that there is still detailed structure missed in the reconstructed results near the left core. This is due to the limited spectral range “detected” for the MOT [17

17. M. Y. Qin, X. S. Zhu, Q. B. Zhang, and P. X. Lu, “Tomographic imaging of asymmetric molecular orbitals with two-color multicycle laser field,” Opt. Lett. **37**, 5208–5210 (2012) [CrossRef] [PubMed] .

*ab initio*orbital. The comparison shows that, the result obtained in the length form agrees with the

*ab initio*orbital well for the positions and amplitudes of the left and middle peaks, but the position of the right peak deviates far away from the

*ab initio*orbital. The result obtained in the velocity form matches the

*ab initio*orbital better for the positions of all the three peaks, but the values at x=−3 and 0 a.u. deviate a lot from those of the

*ab initio*orbital. Both forms have limitation in reproducing the exact shape of the target orbital. Furthermore, the reconstruction of the orbital in the y direction is not satisfying. This error is also observed in the previous works especially for the

*σ*orbital. Besides the limited spectrum range, the imaging errors may also result from several other reasons, such as the discrete sampling in the frequency domain with the interval of 2

*ω*, and the SFA and single-active-electron approximation used in the theoretical model [7

_{L}**44**, 203001 (2011) [CrossRef] .

10. S. Haessler, J. Caillat, W. Boutu, C. Giovanetti-Teixeira, T. Ruchon, T. Auguste, Z. Diveki, P. Breger, A. Maquet, B. Carré, R. Taïeb, and P. Salières, “Attosecond imaging of molecular electronic wavepackets,” Nat. Phys. **6**, 200–206 (2010) [CrossRef] .

12. C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. **7**, 822–826 (2011) [CrossRef] .

18. A. Etches, M. Gaarde, and L. Madsen, “Laser-induced bound-state phases in high-order-harmonic generation,” Phys. Rev. A **86**, 023818 (2012) [CrossRef] .

## 4. Conclusion

## Acknowledgment

## References and links

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14. | Elmar V. van der Zwan, C. C. Chirilǎ, and M. Lein, “Molecular orbital tomography using short laser pulses,” Phys. Rev. A |

15. | P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett |

16. | 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 |

17. | M. Y. Qin, X. S. Zhu, Q. B. Zhang, and P. X. Lu, “Tomographic imaging of asymmetric molecular orbitals with two-color multicycle laser field,” Opt. Lett. |

18. | A. Etches, M. Gaarde, and L. Madsen, “Laser-induced bound-state phases in high-order-harmonic generation,” Phys. Rev. A |

19. | L. Holmegaard, J. L. Hansen, Line Kalhøj, S. L. Kragh, H. Stapelfeldt, F. Filsinger, J. Küpper, G. Meijer, D. Dimitrovski, M. Abu-samha, C. P. J. Martiny, and L. B. Madsen, “Photoelectron angular distributions from strong-field ionization of oriented molecules,” Nat. Phys. |

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21. | X. S. Zhu, Q. B. Zhang, W. Y. Hong, P. X. Lu, and Z. Z. Xu, “Laser-polarization-dependent photoelectron angular distributions from polar molecules,” Opt. Express |

22. | M. Yu. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A |

23. | C. C. Chirilă, “Analysis of the strong field approximation for harmonic generation and multiphoton ionization in intense ultrashort laser pulses,” PhD Thesis http://massey.dur.ac.uk/resources/cpchirila/chirilathesis.pdf. |

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

25. | 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, “ |

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. | T. Kanai, S. Minemoto, and H. Sakai, “Ellipticity dependence of high-order harmonic generation from aligned molecules,” Phys. Rev. Lett. |

28. | Y. J. Chen, J. Liu, and B. Hu, “Reading molecular messages from high-order harmonic spectra at different orientation angles,” J. Chem. Phys. |

29. | M. Lein, N. Hay, R. Velotta, J. P. Marangos, and P. L. Knight, “Interference effects in high-order harmonic generation with molecules,” Phys. Rev. A |

30. | G. L. Kamta and A. D. Bandrauk, “Three-dimensional time-profile analysis of high-order harmonic generation in molecules: nuclear interferences in |

31. | C. Vozzi, R. Torres, M. Negro, L. Brugnera, T. Siegel, C. Altucci, R. Velotta, F. Frassetto, L. Poletto, P. Villoresi, S. De Silvestri, S. Stagira, and J. P. Marangos, “High harmonic generation spectroscopy of hydrocarbons,” Appl. Phys. Lett. |

32. | P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A |

33. | E. V. van der Zwan and M. Lein, “Control of recollision wave packets for molecular orbital tomography using short laser pulses,” J. Phys. B: At. Mol. Opt. Phys. |

34. | C. Serrat and J. Biegert, “All-regions tunable high harmonic enhancement by a periodic static electric field,” Phys. Rev. Lett. |

35. | J. Luo, W. Hong, Q. Zhang, K. Liu, and P. Lu, “Dramatic cutoff extension and broadband supercontinuum generation in multi-cycle two color pulses,” Opt. Express |

36. | W. Y. Hong, P. X. Lu, P. F. Lan, Q. B. Zhang, and X. B. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express |

37. | K. Kovács, E. Balogh, J. Hebling, V. Toşa, and K. Varjú, “Quasi-phase-matching high-harmonic radiation using chirped THz pulses,” Phys. Rev. Lett. |

**OCIS Codes**

(190.4160) Nonlinear optics : Multiharmonic generation

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 19, 2012

Revised Manuscript: February 17, 2013

Manuscript Accepted: February 19, 2013

Published: February 25, 2013

**Citation**

Xiaosong Zhu, Meiyan Qin, Qingbin Zhang, Yang Li, Zhizhan Xu, and Peixiang Lu, "Influence of large permanent dipoles on molecular orbital tomography," Opt. Express **21**, 5255-5268 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5255

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