## Broadband large-ellipticity harmonic generation with polar molecules |

Optics Express, Vol. 19, Issue 25, pp. 25084-25092 (2011)

http://dx.doi.org/10.1364/OE.19.025084

Acrobat PDF (836 KB)

### Abstract

We investigate the polarization properties of high harmonic generation from polar molecules with a linearly polarized field. It is found that elliptically polarized harmonics are observed in a wide spectral range from the plateau to the cutoff. Further analyses show that the nonsymmetric structure of the highest occupied molecular orbital is the origin of ellipticity of the harmonics. The results provide a method for generation of large-ellipticity XUV pulses, which will benefit the application of HHG as a tool of detection in materials and biology science.

© 2011 OSA

## 1. Introduction

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

5. 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]

6. J. Itatani, J. Levesque, D. Zeidler, Hiromichi 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]

8. M. Lein, N. Hay, R. Velotta, J. P. Marangos, and P. L. Knight, “Role of the intramolecular phase in high-harmonic generation,” Phys. Rev. Lett **88**, 183903 (2002). [CrossRef] [PubMed]

9. 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]

11. W. Hong, P. Lu, P. Lan, Q. Zhang, and X. 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]

12. E. Hijano, C. Serrat, G. N. Gibson, and J. Biegert, “Orbital geometry determined by orthogonal high-order harmonic polarization components,” Phys. Rev. A **81**, 041401(R) (2010). [CrossRef]

14. S. Ramakrishna, Paul A. J. Sherratt, A. D. Dutoi, and T. Seideman, “Origin and implication of ellipticityin high-order harmonic generation from aligned molecules,” Phys. Rev. A **81**, 021802(R) (2010). [CrossRef]

*et al.*[15

15. Y. Mairesse, J. Higuet, N. Dudovich, D. Shafir, B. Fabre, E. Mével, E. Constant, S. Patchkovskii, Z. Walters, M. Yu. Ivanov, and O. Smirnova, “Hihg harmonic spectroscopy of multichannel dynamics in strong-field ionization,” Phys. Rev. Lett **104**, 213601 (2010). [CrossRef] [PubMed]

_{2}to track multichannel dynamics during strong-field ionization. In addition, the search for ellipticity in HHG is also motivated by the generation of elliptically (even circularly) polarized attosecond pulses in the xuv regime [16

16. O. Smirnova, S. Patchkovskii, Y. Mairesse, N. Dudovich, D. Villeneuve, P. Corkum, and Misha Yu. Ivanov, “Attosecond circular dichroism spectroscopy of polyatomic molecules,” Phys. Rev. Lett **102**, 063601 (2009). [CrossRef] [PubMed]

17. V. V. Strelkov, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “Origin for ellipticity of high-order harmonics generated in atomic gases and the sublaser-cycle evolution of harmonic polarization,” Phys. Rev. Lett **107**, 043902 (2011). [CrossRef] [PubMed]

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

19. X. Zhou, R. Lock, N. Wagner, W. Li, H. C. Kapteyn, and M. M. Murnane, “Elliptically polarized high-order harmonic emission from molecules in linearly polarized laser fields,” Phys. Rev. Lett **102**, 073902 (2009). [CrossRef] [PubMed]

23. P. A. Sherratt, S. Ramakrishna, and T. Seideman, “Signatures of the molecular potential in the ellipticity of high-order harmonics from aligned molecules,” Phys. Rev. A **83**, 053425(R) (2011). [CrossRef]

20. A. Etches, C. B. Madsen, and L. B. Madsen, “Inducing elliptically polarized high-order harmonics from aligned molecules with linearly polarized femtosecond pulses,” Phys. Rev. A **81**, 013409 (2010). [CrossRef]

21. S.-K. Son, D. A. Telnov, and S.-I Chu, “Probing the origin of elliptical high-order harmonic generation from aligned molecules in linearly polarized laser fields,” Phys. Rev. A. **82**, 043829 (2010). [CrossRef]

16. O. Smirnova, S. Patchkovskii, Y. Mairesse, N. Dudovich, D. Villeneuve, P. Corkum, and Misha Yu. Ivanov, “Attosecond circular dichroism spectroscopy of polyatomic molecules,” Phys. Rev. Lett **102**, 063601 (2009). [CrossRef] [PubMed]

*π*of the parallel component is accompanied by the interference minimum position, leading to the phase difference between the two components passing through

*π*/2. Therefore the harmonics in the vicinity of the interference minima are elliptically polarized. Recently, Ramakrishna

*et al.*[14

14. S. Ramakrishna, Paul A. J. Sherratt, A. D. Dutoi, and T. Seideman, “Origin and implication of ellipticityin high-order harmonic generation from aligned molecules,” Phys. Rev. A **81**, 021802(R) (2010). [CrossRef]

_{2}, CO

_{2}, O

_{2}, and N

_{2}. However, the polarization characteristics of the harmonics generated from polar molecules are seldom studied to the best of our knowledge. The orbital symmetry is one of the basic properties of molecules and can embody the difference between the polar and non-polar molecules. Nonetheless, its influence on the elliptical polarization is also seldom investigated.

## 2. Theoretical model

**z**axis, with the molecular axis

**z1**lying in the y–z plane. The orientation angle between the molecular axis (

**z1**) and the driving laser polarization axis (

**z**) is denoted as

*θ*. Note that we only need to consider the

**y**,

**z**components of the harmonic emission, since the

**x**component along the propagation direction of the driving laser cannot be phase matched [19

19. X. Zhou, R. Lock, N. Wagner, W. Li, H. C. Kapteyn, and M. M. Murnane, “Elliptically polarized high-order harmonic emission from molecules in linearly polarized laser fields,” Phys. Rev. Lett **102**, 073902 (2009). [CrossRef] [PubMed]

22. A.-T. Le, R. R. Lucchese, and C. D. Lin, “Polarization and ellipticity of high-order harmonics from aligned molecules generated by linearly polarized intense laser pulses,” Phys. Rev. A **82**, 023814 (2010). [CrossRef]

**a**,

**b**respectively.

*ϕ*represents the rotation angle of the major axis (

**a**) of the HHG ellipse with respect to the polarization axis (

**z**) of the driving laser field. Ellipticity of HHG

*ɛ*is defined as the ratio of the length between the minor and major axes, i.e.

*ɛ*=

*b/a*.

24. 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). [CrossRef] [PubMed]

20. A. Etches, C. B. Madsen, and L. B. Madsen, “Inducing elliptically polarized high-order harmonics from aligned molecules with linearly polarized femtosecond pulses,” Phys. Rev. A **81**, 013409 (2010). [CrossRef]

21. S.-K. Son, D. A. Telnov, and S.-I Chu, “Probing the origin of elliptical high-order harmonic generation from aligned molecules in linearly polarized laser fields,” Phys. Rev. A. **82**, 043829 (2010). [CrossRef]

14. S. Ramakrishna, Paul A. J. Sherratt, A. D. Dutoi, and T. Seideman, “Origin and implication of ellipticityin high-order harmonic generation from aligned molecules,” Phys. Rev. A **81**, 021802(R) (2010). [CrossRef]

23. P. A. Sherratt, S. Ramakrishna, and T. Seideman, “Signatures of the molecular potential in the ellipticity of high-order harmonics from aligned molecules,” Phys. Rev. A **83**, 053425(R) (2011). [CrossRef]

25. S. Ramakrishna and T. Seideman, “Information content of high harmonics generated from aligned molecules,” Phys. Rev. Lett **99**, 113901 (2007). [CrossRef] [PubMed]

**y**,

**z**components of the laser-induced dipole moments responsible for harmonic emission are expressed as (in atomic units)

*E*(

*t*) refers to the electric field of the driving laser pulse,

*A*(

*t*) is its associated vector potential,

*ζ*is a positive constant,

*t*′ and

*t*correspond to the moments of electronic ionization and recombination respectively,

*p*and

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

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

_{p}*g*(

*t*;

*θ*) represents the ground state amplitude at the time

*t*, and can be expressed as [26

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

27. W. Hong, P. Wei, Q. Zhang, S. Wang, and P. Lu, “Mid-infrared modulated polarization gating for ultra-broadband supercontinuum generation,” Opt. Express **18**, 11308–11315 (2010). [CrossRef] [PubMed]

*w*(

*t*′;

*θ*) is the ionization rate, which is calculated by Molecular Ammosov-Delone-Krainov (MO-ADK) model for aligned molecules [28

28. X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A **66**, 033402(2002).Opt. Express **16**, 9795–9803 (2008). [CrossRef]

*d⃗*(

*p*) is the field-free dipole matrix element for transition from the ground state to the continuum state, where p stands for the momentum of the electron.

*d*,

_{y}*d*correspond to its

_{z}**y**,

**z**components, respectively. Within the single active electron approximation (SAE), this transition dipole moment is given by [13

13. J. Levesque, Y. Mairesse, N. Dudovich, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Polarization state of high-order harmonic emission from aligned molecules,” Phys. Rev. Lett **99**, 243001 (2007). [CrossRef]

*ψ*

_{0}(

*x, y,z*;

*θ*) represents the ground state of the target molecule, i.e. the highest occupied molecular orbital (HOMO). The HOMO is obtained using the Gaussian 03 ab initio code [29

29. 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).

*ψ*= exp (

_{p}*ipz*) refers to the electronic continuum state with a momentum p. The harmonic spectrum is then obtained by Fourier transforming the time-dependent dipole acceleration

*a⃗*(

*t*;

*θ*). The equations for the two components are: where

*T*and

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

*q*corresponds to the harmonic order. The spectral intensity (

*I*) and phase (

*φ*) of harmonic components are given by

*I*(

_{j}*q*) = |

*a*(

_{j}*q*)|

^{2},

*φ*(

_{j}*q*) = arg[

*a*(

_{j}*q*)],

*j*=

*y, z*. The ellipticity

*ɛ*is determined by the amplitude ratio and the phase difference of the two components [21

21. S.-K. Son, D. A. Telnov, and S.-I Chu, “Probing the origin of elliptical high-order harmonic generation from aligned molecules in linearly polarized laser fields,” Phys. Rev. A. **82**, 043829 (2010). [CrossRef]

*δ*=

*φ*–

_{y}*φ*. The range of the ellipticity is 0 ≤

_{z}*ɛ*≤ 1. The linear, elliptical, and circular polarization correspond to

*ɛ*= 0, 0 <

*ɛ*< 1, and

*ɛ*= 1 respectively. If

*δ*is 0 or

*π*, the HHG will be linearly polarized. For other values of

*δ*between 0 and

*π*, the HHG will be elliptically polarized. In order to attain high ellipticity, the phase difference must be around

*π*/2.

## 3. Result and discussion

^{14}

*W/cm*

^{2}is used in our simulation. The electric field of the laser pulse is expressed as where

*E*

_{0}is the amplitude of the driving field. Figure 2(a) presents the ellipticity of the harmonic emission at two orientation angles 30° (red line) and 45° (black line). One can see that for the two orientation angles, strongly elliptically polarized harmonics are observed in a wide spectral range covering the plateau to the cutoff. In Fig. 2(b), the phase difference (blue line) and the ellipticity (black line) of the recombination dipole moment [13

13. J. Levesque, Y. Mairesse, N. Dudovich, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Polarization state of high-order harmonic emission from aligned molecules,” Phys. Rev. Lett **99**, 243001 (2007). [CrossRef]

30. Z. Zhao, J. Yuan, and T. Brabec, “Multielectron signatures in the polarization of high-order harmonic radiation,” Phys. Rev. A. **76**, 031404(R) (2007) [CrossRef]

*π*, 0]. Interestingly, the relative phase between the

*y*,

*z*components of the dipole moment is close to −

*π*/2 for all the electronic momenta. As a result, the ellipticity of the dipole moment is quite large, as shown by the black curve. Furthermore, it is also shown that the ellipticity curve of the dipole moment in panel (b) is similar to that of the harmonics at the same orientation angle (black line) in panel (a). The electronic momentum is transformed into the harmonic order by the dispersion relation

*qh̄ω*=

*E*+

_{p}*I*, wherein E

_{p}*is the kinetic energy of the free electron with the momentum p. This phenomenon will be discussed latter.*

_{p}24. 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). [CrossRef] [PubMed]

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

*z*) and perpendicular (

*y*) to the laser polarization. Since the first two steps are identical for the y, z components of the harmonics, the phase difference and amplitude ratio between the two components of the harmonics is mainly contributed by those of the recombination dipole moment

*d⃗*(

^{*}*p*). Hence the ellipticity curves between harmonics and the recombination dipole moment exhibit a similar shape at the same orientation angle, as shown in Fig. 2 and Fig. 3. In other words, the recombination dipole moment

*d⃗*(

^{*}*p*) is responsible for the large ellipticity of the harmonics over a wide spectral range for CO.

_{2}at the same orientation angles with Fig. 2(a). In contrast to CO, the nonzero ellipticity of the harmonics are only obtained in the vicinity of the structure minima in the HHG spectra, where the positions of the minima coincide with those in [30

30. Z. Zhao, J. Yuan, and T. Brabec, “Multielectron signatures in the polarization of high-order harmonic radiation,” Phys. Rev. A. **76**, 031404(R) (2007) [CrossRef]

16. O. Smirnova, S. Patchkovskii, Y. Mairesse, N. Dudovich, D. Villeneuve, P. Corkum, and Misha Yu. Ivanov, “Attosecond circular dichroism spectroscopy of polyatomic molecules,” Phys. Rev. Lett **102**, 063601 (2009). [CrossRef] [PubMed]

20. A. Etches, C. B. Madsen, and L. B. Madsen, “Inducing elliptically polarized high-order harmonics from aligned molecules with linearly polarized femtosecond pulses,” Phys. Rev. A **81**, 013409 (2010). [CrossRef]

**82**, 043829 (2010). [CrossRef]

_{2}also shows that the ellipticity of the harmonics of CO is larger than that of N

_{2}for most of the orientation angles, as demonstrated in Fig. 2 and Fig. 5 for the orientation angles at 30° and 45°. Therefore our results suggest a potential application of HHG from polar CO molecules in generating the broadband large-ellipticity harmonics, which will benefit the application of HHG as a tool of detection in biology and materials science in the future.

## 4. Conclusion

## Acknowledgments

## References and links

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

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

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

4. | P. Lan, P. Lu, F. Li, Y. Li, and Z. Yang, “Carrier-envelope phase measurement from half-cycle high harmonics,” Opt. Express |

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

6. | J. Itatani, J. Levesque, D. Zeidler, Hiromichi Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature |

7. | M. Lein, “Molecular imaging using recolliding electrons,” J. Phys. B: At. Mol. Opt. Phys |

8. | M. Lein, N. Hay, R. Velotta, J. P. Marangos, and P. L. Knight, “Role of the intramolecular phase in high-harmonic generation,” Phys. Rev. Lett |

9. | 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. |

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

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

12. | E. Hijano, C. Serrat, G. N. Gibson, and J. Biegert, “Orbital geometry determined by orthogonal high-order harmonic polarization components,” Phys. Rev. A |

13. | J. Levesque, Y. Mairesse, N. Dudovich, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Polarization state of high-order harmonic emission from aligned molecules,” Phys. Rev. Lett |

14. | S. Ramakrishna, Paul A. J. Sherratt, A. D. Dutoi, and T. Seideman, “Origin and implication of ellipticityin high-order harmonic generation from aligned molecules,” Phys. Rev. A |

15. | Y. Mairesse, J. Higuet, N. Dudovich, D. Shafir, B. Fabre, E. Mével, E. Constant, S. Patchkovskii, Z. Walters, M. Yu. Ivanov, and O. Smirnova, “Hihg harmonic spectroscopy of multichannel dynamics in strong-field ionization,” Phys. Rev. Lett |

16. | O. Smirnova, S. Patchkovskii, Y. Mairesse, N. Dudovich, D. Villeneuve, P. Corkum, and Misha Yu. Ivanov, “Attosecond circular dichroism spectroscopy of polyatomic molecules,” Phys. Rev. Lett |

17. | V. V. Strelkov, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “Origin for ellipticity of high-order harmonics generated in atomic gases and the sublaser-cycle evolution of harmonic polarization,” Phys. Rev. Lett |

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

19. | X. Zhou, R. Lock, N. Wagner, W. Li, H. C. Kapteyn, and M. M. Murnane, “Elliptically polarized high-order harmonic emission from molecules in linearly polarized laser fields,” Phys. Rev. Lett |

20. | A. Etches, C. B. Madsen, and L. B. Madsen, “Inducing elliptically polarized high-order harmonics from aligned molecules with linearly polarized femtosecond pulses,” Phys. Rev. A |

21. | S.-K. Son, D. A. Telnov, and S.-I Chu, “Probing the origin of elliptical high-order harmonic generation from aligned molecules in linearly polarized laser fields,” Phys. Rev. A. |

22. | A.-T. Le, R. R. Lucchese, and C. D. Lin, “Polarization and ellipticity of high-order harmonics from aligned molecules generated by linearly polarized intense laser pulses,” Phys. Rev. A |

23. | P. A. Sherratt, S. Ramakrishna, and T. Seideman, “Signatures of the molecular potential in the ellipticity of high-order harmonics from aligned molecules,” Phys. Rev. A |

24. | 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 |

25. | S. Ramakrishna and T. Seideman, “Information content of high harmonics generated from aligned molecules,” Phys. Rev. Lett |

26. | P. Lan, P. Lu, Q. Li, F. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A |

27. | W. Hong, P. Wei, Q. Zhang, S. Wang, and P. Lu, “Mid-infrared modulated polarization gating for ultra-broadband supercontinuum generation,” Opt. Express |

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

29. | 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, |

30. | Z. Zhao, J. Yuan, and T. Brabec, “Multielectron signatures in the polarization of high-order harmonic radiation,” Phys. Rev. A. |

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

**OCIS Codes**

(190.4160) Nonlinear optics : Multiharmonic generation

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

(300.6560) Spectroscopy : Spectroscopy, x-ray

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: October 13, 2011

Revised Manuscript: November 9, 2011

Manuscript Accepted: November 10, 2011

Published: November 23, 2011

**Citation**

Meiyan Qin, Xiaosong Zhu, Qingbin Zhang, Weiyi Hong, and Peixiang Lu, "Broadband large-ellipticity harmonic generation with polar molecules," Opt. Express **19**, 25084-25092 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25084

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### References

- F. Krausz, “Attosecond physics,” Rev. Mod. Phys.81, 163–234(2009). [CrossRef]
- 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). [CrossRef]
- W. Cao, P. Lu, P. Lan, X. Wang, and Y. Li, “Control of the launch of attosecond pulses,” Phys. Rev. A75, 063423 (2007). [CrossRef]
- P. Lan, P. Lu, F. Li, Y. Li, and Z. Yang, “Carrier-envelope phase measurement from half-cycle high harmonics,” Opt. Express16, 5868–5873 (2008). [CrossRef] [PubMed]
- W. Cao, P. Lu, P. Lan, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A74, 063821 (2006). [CrossRef]
- J. Itatani, J. Levesque, D. Zeidler, Hiromichi Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature432, 867–871 (2004). [CrossRef] [PubMed]
- M. Lein, “Molecular imaging using recolliding electrons,” J. Phys. B: At. Mol. Opt. Phys40, R135–R173 (2007). [CrossRef]
- M. Lein, N. Hay, R. Velotta, J. P. Marangos, and P. L. Knight, “Role of the intramolecular phase in high-harmonic generation,” Phys. Rev. Lett88, 183903 (2002). [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]
- Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A70, 043802 (2004). [CrossRef]
- W. Hong, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express17, 5139–5146 (2009). [CrossRef] [PubMed]
- E. Hijano, C. Serrat, G. N. Gibson, and J. Biegert, “Orbital geometry determined by orthogonal high-order harmonic polarization components,” Phys. Rev. A81, 041401(R) (2010). [CrossRef]
- J. Levesque, Y. Mairesse, N. Dudovich, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Polarization state of high-order harmonic emission from aligned molecules,” Phys. Rev. Lett99, 243001 (2007). [CrossRef]
- S. Ramakrishna, Paul A. J. Sherratt, A. D. Dutoi, and T. Seideman, “Origin and implication of ellipticityin high-order harmonic generation from aligned molecules,” Phys. Rev. A81, 021802(R) (2010). [CrossRef]
- Y. Mairesse, J. Higuet, N. Dudovich, D. Shafir, B. Fabre, E. Mével, E. Constant, S. Patchkovskii, Z. Walters, M. Yu. Ivanov, and O. Smirnova, “Hihg harmonic spectroscopy of multichannel dynamics in strong-field ionization,” Phys. Rev. Lett104, 213601 (2010). [CrossRef] [PubMed]
- O. Smirnova, S. Patchkovskii, Y. Mairesse, N. Dudovich, D. Villeneuve, P. Corkum, and Misha Yu. Ivanov, “Attosecond circular dichroism spectroscopy of polyatomic molecules,” Phys. Rev. Lett102, 063601 (2009). [CrossRef] [PubMed]
- V. V. Strelkov, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “Origin for ellipticity of high-order harmonics generated in atomic gases and the sublaser-cycle evolution of harmonic polarization,” Phys. Rev. Lett107, 043902 (2011). [CrossRef] [PubMed]
- Q. Zhang, P. Lu, P. Lan, W. Hong, and Z. Yang, “Multi-cycle laser-driven broadband supercontinuum with a modulated polarization gating, ” Opt. Express16, 9795–9803 (2008). [CrossRef] [PubMed]
- X. Zhou, R. Lock, N. Wagner, W. Li, H. C. Kapteyn, and M. M. Murnane, “Elliptically polarized high-order harmonic emission from molecules in linearly polarized laser fields,” Phys. Rev. Lett102, 073902 (2009). [CrossRef] [PubMed]
- A. Etches, C. B. Madsen, and L. B. Madsen, “Inducing elliptically polarized high-order harmonics from aligned molecules with linearly polarized femtosecond pulses,” Phys. Rev. A81, 013409 (2010). [CrossRef]
- S.-K. Son, D. A. Telnov, and S.-I Chu, “Probing the origin of elliptical high-order harmonic generation from aligned molecules in linearly polarized laser fields,” Phys. Rev. A.82, 043829 (2010). [CrossRef]
- A.-T. Le, R. R. Lucchese, and C. D. Lin, “Polarization and ellipticity of high-order harmonics from aligned molecules generated by linearly polarized intense laser pulses,” Phys. Rev. A82, 023814 (2010). [CrossRef]
- P. A. Sherratt, S. Ramakrishna, and T. Seideman, “Signatures of the molecular potential in the ellipticity of high-order harmonics from aligned molecules,” Phys. Rev. A83, 053425(R) (2011). [CrossRef]
- 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). [CrossRef] [PubMed]
- S. Ramakrishna and T. Seideman, “Information content of high harmonics generated from aligned molecules,” Phys. Rev. Lett99, 113901 (2007). [CrossRef] [PubMed]
- P. Lan, P. Lu, Q. Li, F. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A79, 043413 (2009). [CrossRef]
- W. Hong, P. Wei, Q. Zhang, S. Wang, and P. Lu, “Mid-infrared modulated polarization gating for ultra-broadband supercontinuum generation,” Opt. Express18, 11308–11315 (2010). [CrossRef] [PubMed]
- X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A66, 033402(2002).Opt. Express 16, 9795–9803 (2008). [CrossRef]
- 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).
- Z. Zhao, J. Yuan, and T. Brabec, “Multielectron signatures in the polarization of high-order harmonic radiation,” Phys. Rev. A.76, 031404(R) (2007) [CrossRef]
- P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett71, 1994–1997 (1993). [CrossRef] [PubMed]

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