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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 6 — Mar. 25, 2013
  • pp: 7599–7607
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High harmonic spectra contributed by HOMO-1 orbital of aligned CO2 molecules

Jiawei Li, Peng Liu, Hua Yang, Liwei Song, Shitong Zhao, Hui Lu, Ruxin Li, and Zhizhan Xu  »View Author Affiliations


Optics Express, Vol. 21, Issue 6, pp. 7599-7607 (2013)
http://dx.doi.org/10.1364/OE.21.007599


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Abstract

We observe the high harmonic generation (HHG) from anti-aligned CO2 molecules when the on-axis peak of HHG from HOMO-2 orbital disappears. The harmonic emission at anti-alignment can be attributed to the contribution of HOMO-1 orbital. Simulations reproduce these observations and reveal the angular distributions of tunneling ionization from HOMO and HOMO-1 respectively at different intensity. The determination of HOMO-1 orbital contributions in harmonic spectra is important for the tomography imaging of aligned molecules and analysis of the time evolved harmonic emission.

© 2013 OSA

1. Introduction

High-order harmonic generation (HHG) has been applied in producing ultrafast coherent extreme ultraviolet (XUV) radiation and attosecond pulses, and it has become a tool of investigating molecular structure in an ultrafast time scale. HHG is well explained by the three-step model: electrons tunnel into the continuum from the ground state in the intense laser fields; the electrons are then accelerated by a strong oscillating laser field; ultimately the electrons have a probability of being driven back to recombine with the parent ion and emit high-energy harmonic photons [1

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

]. The information of molecular orbital and/or structure can be retrieved from the recombination probability obtained from the harmonic spectra of pre-aligned molecules [2

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

5

5. C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. 7(10), 822–826 (2011). [CrossRef]

]. In ultrafast intense laser fields, molecules are “kicked” by the laser field which induces Stark force and creates a rotational wave packet. The wave packet dephases quickly after the laser pulse is over and re-phases periodically at the intervals of the rotational period of the molecules (revivals). At the revivals, alignment degree <cos2θ> experiences characteristic modulations indicating the molecules are aligned parallel (alignment) or perpendicular (anti-alignment) to the laser polarization direction. Therefore the corresponding temporal modulation of harmonic generation reveals structural dynamics and rotational dynamics of the molecules [6

6. S. Ramakrishna and T. Seideman, “Information content of high harmonics generated from aligned molecules,” Phys. Rev. Lett. 99(11), 113901 (2007). [CrossRef] [PubMed]

8

8. R. M. Lock, S. Ramakrishna, X. Zhou, H. C. Kapteyn, M. M. Murnane, and T. Seideman, “Extracting continuum electron dynamics from high harmonic emission from molecules,” Phys. Rev. Lett. 108(13), 133901 (2012). [CrossRef] [PubMed]

].

For the linear polyatomic CO2 molecules, both Kanai et al. [9

9. T. Kanai, S. Minemoto, and H. Sakai, “Quantum interference during high-order harmonic generation from aligned molecules,” Nature 435(7041), 470–474 (2005). [CrossRef] [PubMed]

] and Vozzi et al. [10

10. C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, M. Nisoli, R. Torres, E. Heesel, N. Kajumba, J. P. Marangos, C. Altucci, and R. Velotta, “Controlling two-center interference in molecular high harmonic generation,” Phys. Rev. Lett. 95(15), 153902 (2005). [CrossRef] [PubMed]

] observed that the time evolved harmonic emission exhibit inverted modulation versus the alignment parameter<cos2θ>. The modulation inversion can be attributed to the interference of recombining electrons originated from the two oxygen atoms in the CO2 molecule. Further studies indicate the time evolved harmonic spectra can reflect the angular dependence and the phase variation of HHG at different orders [11

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

14

14. R. M. Lock, X. Zhou, W. Li, M. M. Murnane, and H. C. Kapteyn, “Measuring the intensity and phase of high-order harmonic emission from aligned molecules,” Chem. Phys. 366(1-3), 22–32 (2009). [CrossRef]

]. Most recently, the high-order revivals of aligned CO2 molecules have been revealed to extract the informations of continuum electron dynamics from high harmonic emission [8

8. R. M. Lock, S. Ramakrishna, X. Zhou, H. C. Kapteyn, M. M. Murnane, and T. Seideman, “Extracting continuum electron dynamics from high harmonic emission from molecules,” Phys. Rev. Lett. 108(13), 133901 (2012). [CrossRef] [PubMed]

]. Among these studies, only the HOMO orbital has been taken into consideration by assuming that the inner orbital of CO2 molecule does not play dominant role in harmonic emission.

The contribution of inner orbital to harmonic generation has been pointed out even though they have higher ionization potential. From temporal modulation of HHG from aligned N2 molecules, the HOMO-1 orbital of N2 has been shown to contribute to the harmonic spectrum when the molecules are aligned perpendicular to the laser polarization [15

15. B. K. McFarland, J. P. Farrell, P. H. Bucksbaum, and M. Gühr, “High harmonic generation from multiple orbitals in N2.,” Science 322(5905), 1232–1235 (2008). [CrossRef] [PubMed]

19

19. A. T. Le, R. R. Lucchese, and C. D. Lin, “Uncovering multiple orbitals influence in high harmonic generation from aligned N2,” J. Phys. B 42(21), 211001 (2009). [CrossRef]

]. Using the high harmonic interferometry, the HOMO-2 orbital of CO2 was found to be pronounced when the molecules aligned parallel to the laser polarization [3

3. O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460(7258), 972–977 (2009). [CrossRef] [PubMed]

,20

20. C. Jin, A. T. Le, and C. D. Lin, “Analysis of effects of macroscopic propagation and multiple molecular orbitals on the minimum in high-order harmonic generation of aligned CO2,” Phys. Rev. A 83(5), 053409 (2011). [CrossRef]

22

22. H. J. Wörner, J. B. Bertrand, P. Hockett, P. B. Corkum, and D. M. Villeneuve, “Controlling the interference of multiple molecular orbitals in high-harmonic generation,” Phys. Rev. Lett. 104(23), 233904 (2010). [CrossRef] [PubMed]

]. However, it is interesting to note that the experimental observation of HOMO-1 orbital in the temporal evolved harmonic emission from aligned CO2 molecules has not been reported so far. Recently Wu et al. reported the fluorescence emission of CO2+(A2ΠuX2Πg) and CO2+(B2ΣuX2Πg) in neutral CO2 molecules irradiated by intense femtosecond laser pulses, which provides direct evidence that the HOMO-1 orbital is simultaneously involved in the process of tunneling ionization [23

23. C. Wu, H. Zhang, H. Yang, Q. Gong, D. Song, and H. Su, “Tunneling ionization of carbon dioxide from lower-lying orbitals,” Phys. Rev. A 83(3), 033410 (2011). [CrossRef]

]. It is therefore desirable to identify the effect of inner orbital HOMO-1 of CO2 in the harmonic spectra of aligned molecules, because the determination of multi-orbital effect in HHG is a crucial step for the accurate tomography imaging of molecular orbital.

In this work we distinguish the contribution of HOMO-1 orbital in the time evolved harmonic spectra of field-free aligned CO2 molecules through experiments and numerical calculations. The temporal yield of the 25th harmonics (noted as H25) at the 1/2 revival show a peak when the molecules are best aligned along the laser polarization. The peak has been attributed to contribution of HOMO-2 orbital [3

3. O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460(7258), 972–977 (2009). [CrossRef] [PubMed]

] and it appears till H31 in our experiments. However, we found that the harmonic emission at anti-alignment exists for H33 in the cut-off region. This feature suggests the contribution of HOMO-1 orbital of CO2, instead of HOMO-2 or the two-center interference effect of HOMO. The angular distributions of tunneling ionization from the three orbitals of CO2 have been revealed respectively.

2. Experimental setup and result

The experiments were performed using a Ti:sapphire based chirped pulse amplification laser system (Legend-USP-HE followed by a cryogenic multi-pass amplifier, Coherent Inc.), which produces 40 fs laser pulses of 1k Hz at the center wavelength of 800 nm with the maximum pulse energy of 10 mJ. In experiments, about 6 mJ of the output energy were used to be split into two beams: one beam used as the pump pulse (for aligning molecules) and the other as the probe pulse (for driving HHG from molecules) whose polarization was the same as the pump beam. The two beams were collinearly focused with a lens (f = 300 mm) onto a pulsed supersonic molecular beam located in a high vacuum chamber. The laser focus was about 1 mm downstream of a 0.5 mm diameter nozzle orifice and about 2mm before it, where only the short trajectory was in the phase-matching condition. Stagnation pressure of CO2 gas (99.998%) was about 2 bar, leading to a rotational temperature of 80 Kelvin (K) according to the estimation based on the parameters of the supersonic molecular beam. The spot size of pump laser beam crossing with molecules was measured to be 150 µm (FWHM) and the laser field intensity was estimated to be 6.0 × 1013 Wcm−2. The probe laser energy was adjustable by using a half-wave plate and a high extinction film polarizer. The HHG spectra were detected by a home-made flat-field grating spectrometer equipped with a soft-x-ray CCD camera (Princeton Instruments, PI: SX 400).

Alignment is important for one to see the contribution of the inner orbitals which are only pronounced at certain angles. We optimized the alignment condition by fine adjusting the intensity of pump pulses, which cannot be very high for avoiding ionization. When CO2 molecules are irradiated by the pump pulses whose duration τon = 40 fs are much shorter than the rotational period Trot = 42.7 ps, nonadiabatic field-free alignment is achieved by instantaneous excitation of a rotational wave packet ψ(t)=ΣJ,MAJ,M(t)|J,M [24

24. H. Stapelfeldt and T. Seideman, “Colloquium: aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75(2), 543–557 (2003). [CrossRef]

26

26. T. Seideman and E. Hamilton, “Nonadiabatic alignment by intense pulses. Concepts, theory, and directions,” Adv. At. Mol. Opt. Phys. 52, 289–329 (2005). [CrossRef]

]. The time evolution of the wave packet can be calculated by solving the time dependent Schrödinger equation (TDSE). The temporal evolved alignment parameter cos2θ(t) is defined as,
cos2θ(t)=JρJJMψ(t)|cos2θ|ψ(t)JM(t).
(1)
where ρJ represents the initial Boltzmann distribution of the molecules over all rotational levels |J,M. The harmonic emissions are then obtained by introducing the probe pulses at the varied time delays for comparing with the modulation of alignment degree.

In the experimental result shown in Fig. 1
Fig. 1 Experimental result of harmonic yields from aligned CO2 molecules for probe laser intensities of ~1.9 × 1014 Wcm−2, as a function of the pump-probe delay time.
, we focus on the temporal variations of molecular alignment and harmonic emission at the 1/2 revival. As the probe pulse energy is about 1.8 mJ, the peak intensity is estimated to be ~1.9 × 1014 Wcm−2. We can see from Fig. 1 that, for H25-H31, on-axis peaks appear at the delay time of 21.2 ps when the molecules are most aligned along the pump laser polarization. The on-axis emission peak increases to the strongest at H29 and disappears at H33.

The on-axis peak can be due to the emission from the HOMO-2 orbital which favors ionization at parallel alignment [3

3. O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460(7258), 972–977 (2009). [CrossRef] [PubMed]

,20

20. C. Jin, A. T. Le, and C. D. Lin, “Analysis of effects of macroscopic propagation and multiple molecular orbitals on the minimum in high-order harmonic generation of aligned CO2,” Phys. Rev. A 83(5), 053409 (2011). [CrossRef]

22

22. H. J. Wörner, J. B. Bertrand, P. Hockett, P. B. Corkum, and D. M. Villeneuve, “Controlling the interference of multiple molecular orbitals in high-harmonic generation,” Phys. Rev. Lett. 104(23), 233904 (2010). [CrossRef] [PubMed]

]. Because of the higher ionization potential, contribution from inner orbital is pronounced near the cut-off. Using the method of high harmonic interferometry, O. Smirnova et al. had observed the contribution of HOMO-2 orbital to harmonic yield at parallel alignment near cut-off from aligned CO2 molecules [3

3. O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460(7258), 972–977 (2009). [CrossRef] [PubMed]

]. Therefore HOMO-2 orbital can make contribution to the on-axis emission peaks for H25-H31, but it is interesting to see that the on-axis peak disappears at H33 while there is still harmonic emission at the anti-alignment condition.

3. Theory simulation and angular distributions of HHG

In order to clarify the effects of inner orbital, numerical calculations are performed using the extended Lewenstein strong field approximation model [31

31. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]

34

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

]. In this model, the time-dependent dipole moment for a molecule aligned along the z axis is calculated by using:
r(t)=i0dτ(πε+iτ/2)3/2[cosθdz(t)+sinθdy(t)]×[cosθdz(tτ)+sinθdy(tτ)]×E(tτ)exp[iSst(t,τ)]a(θ,t)a(θ,tτ)+c.c..
(3)
where dz and dy are the z and y components of the transition dipole moment from the initial state to the continuum state approximated by plane wave [34

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

]:
dy=1(2π)3/2ei(pxx+pyy+pzz)yϕ(x,y,z)dxdydz,
(4)
and the dz has a similar equation. E(t) is the laser filed linearly polarized on the y - z plane with an angle θ versus the molecular axis. When we consider the contribution to the HHG from more than one orbital, the dipoles are added up coherently. The wavefunction φ(x,y,z) of each molecular orbital is calculated with the GAMESS code using Hartree-Fock method with the 6-311 + + G** basis set [35

35. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, “General atomic and molecular electronic structure system,” J. Comput. Chem. 14(11), 1347–1363 (1993). [CrossRef]

]. Without considering the Coulomb distortion, the SFA is questionable at lower harmonic orders. However, the experimental result we discuss is near the cut-off where the SFA can give an acceptable prediction [12

12. A. T. Le, R. R. Lucchese, S. Tonzani, T. Morishita, and C. D. Lin, “Quantitative rescattering theory for high-order harmonic generation from molecules,” Phys. Rev. A 80(1), 013401 (2009). [CrossRef]

].

In Eq. (3), Sst is the quasiclassical action at stationary point for the electron propagating in the laser field [31

31. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]

]:
Sst(t,τ)=tτt([pst(t,τ)A(t')]2/2+Ip)dt',
(5)
where pst(t,τ)=tτtA(t')dt'/τ is the canonical momentum at the stationary point, with A the vector potential. And the Ip is the ionization potential which is different for each molecular orbital. The depletion of the neutral molecules is included by a(θ,t)=exp[tW(θ,t')/2dt']. The alignment-dependent ionization probability for each orbital is N(θ)=1exp[W(θ,t)dt], W(θ,t) is the ionization rate for an instantaneous field strength at ionization time, which is calculated using the method of Murray et al. [36

36. R. Murray, W.-K. Liu, and M. Y. Ivanov, “Partial Fourier-transform approach to tunnel ionization: atomic systems,” Phys. Rev. A 81(2), 023413 (2010). [CrossRef]

,37

37. R. Murray, M. Spanner, S. Patchkovskii, and M. Y. Ivanov, “Tunnel ionization of molecules and orbital imaging,” Phys. Rev. Lett. 106(17), 173001 (2011). [CrossRef] [PubMed]

].

The time evolution of HHG yield for each orbital can be written as
fn(t)N(θ)Sn(θ)|ψ(θ,t)|2sin(θ)dθ,
(6)
where Sn(θ) is obtained through the Fourier transform of the dipole moment, for the (2n + 1)th harmonic from CO2 molecules aligned at a fixed angle θ, and t is the delay time. |ψ(θ,t)|2sin(θ)is the weighted angular distribution of the molecules, in which ψ(θ,t)is obtained by solving the TDSE of rotational wave packet.

4. Result at lower probe laser intensity

In order to elucidate this effect, we calculate the angular distributions of the tunneling ionization from the three orbitals using the method proposed by Murray et al. [36

36. R. Murray, W.-K. Liu, and M. Y. Ivanov, “Partial Fourier-transform approach to tunnel ionization: atomic systems,” Phys. Rev. A 81(2), 023413 (2010). [CrossRef]

,37

37. R. Murray, M. Spanner, S. Patchkovskii, and M. Y. Ivanov, “Tunnel ionization of molecules and orbital imaging,” Phys. Rev. Lett. 106(17), 173001 (2011). [CrossRef] [PubMed]

]. As shown in Fig. 4
Fig. 4 Calculated angular distributions of the tunneling ionization of HOMO (blue line), HOMO-1 (red line) and HOMO-2 (green line) at (a) 1.2 × 1014 Wcm−2 and (b) 1.9 × 1014 Wcm−2 respectively.
, the ionization probability of the HOMO-1 becomes higher with increasing the angle and the HOMO-2 shows an opposite trend. When the laser intensity is 1.2 × 1014 Wcm−2, the tunneling ionization of inner orbitals are weaker than HOMO even at the angles where electronic density is maximum. When the laser intensity is 1.9 × 1014 Wcm−2, the tunneling ionization rate of HOMO-1 increases and becomes much larger than that of HOMO near 90° and the tunneling ionization of HOMO-2 also increases. This result confirms that the lower laser intensity decreases the contributions of HOMO-1 especially at the anti-alignment angle. This suggests that HOMO-1 of CO2 can only be distinguished at higher probe laser intensity, which is consistent with the results on N2 [16

16. C. Jin, J. B. Bertrand, R. R. Lucchese, H. J. Wörner, P. B. Corkum, D. M. Villeneuve, A. T. Le, and C. D. Lin, “Intensity dependence of multiple orbital contributions and shape resonance in high-order harmonic generation of aligned N2 molecules,” Phys. Rev. A 85(1), 013405 (2012). [CrossRef]

].

In our calculation, we have also tried to use even higher driving laser field for the expectation of stronger effect of HOMO-1, however, the ground state depletion effect becomes significant, which suppresses both the contributions of HOMO and HOMO-1. As a result, no clear phenomenon is found from the contribution of HOMO-1.

5. Summary

In conclusion, we have investigated the influence of multiple orbital to the HHG from aligned CO2 molecules as a function of pump-probe delay time. At the relatively high intensity of probe laser, harmonic yields present a small peak when the molecules are best aligned. The on-axis peak disappears near the cut-off which cannot be explained by the two-center interference of the HOMO orbital or the emission from the HOMO-2 orbital. Simulation reproduced the experimental observation, and it shows that the disappearance of the on-axis peak and the much stronger emission at anti-alignment of H33 indicate the harmonic yields around anti-alignment are from the HOMO-1 orbital. The HOMO-1 also contributes to the harmonic emission at the perpendicular alignment for H25-H31. The on-axis peaks at H25-H31 are due to the emission from HOMO-2 and HOMO orbitals. At the lower probe laser intensity, the angular distributions of tunneling ionization from HOMO and HOMO-1 show that contribution from HOMO-1 can be ignored. The experimental observation of the contributions from HOMO-1 to the evolving HHG from the aligned CO2 is the first time. From this work we can learn that HOMO-1 orbital affect the time evolved harmonic spectra significantly when the laser intensity increases, especially at the orders near the cut-off. Our work also suggests that relative contributions from different orbital to harmonic emission are varied for different harmonic orders. We may control their ratio by fine-tuning the laser intensity at a particular order which is useful for the tomography imaging of molecular orbital.

Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant Nos. 60978012, 11274326 and 11134010), the 973 Program of China (2011CB808103), and the State Key Laboratory of High Field Laser Physics of China.

References and links

1.

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

2.

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

3.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460(7258), 972–977 (2009). [CrossRef] [PubMed]

4.

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature 466(7306), 604–607 (2010). [CrossRef] [PubMed]

5.

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. 7(10), 822–826 (2011). [CrossRef]

6.

S. Ramakrishna and T. Seideman, “Information content of high harmonics generated from aligned molecules,” Phys. Rev. Lett. 99(11), 113901 (2007). [CrossRef] [PubMed]

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S. Ramakrishna and T. Seideman, “High-order harmonic generation as a probe of rotational dynamics,” Phys. Rev. A 77(5), 053411 (2008). [CrossRef]

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R. M. Lock, S. Ramakrishna, X. Zhou, H. C. Kapteyn, M. M. Murnane, and T. Seideman, “Extracting continuum electron dynamics from high harmonic emission from molecules,” Phys. Rev. Lett. 108(13), 133901 (2012). [CrossRef] [PubMed]

9.

T. Kanai, S. Minemoto, and H. Sakai, “Quantum interference during high-order harmonic generation from aligned molecules,” Nature 435(7041), 470–474 (2005). [CrossRef] [PubMed]

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C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, M. Nisoli, R. Torres, E. Heesel, N. Kajumba, J. P. Marangos, C. Altucci, and R. Velotta, “Controlling two-center interference in molecular high harmonic generation,” Phys. Rev. Lett. 95(15), 153902 (2005). [CrossRef] [PubMed]

11.

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

12.

A. T. Le, R. R. Lucchese, S. Tonzani, T. Morishita, and C. D. Lin, “Quantitative rescattering theory for high-order harmonic generation from molecules,” Phys. Rev. A 80(1), 013401 (2009). [CrossRef]

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15.

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16.

C. Jin, J. B. Bertrand, R. R. Lucchese, H. J. Wörner, P. B. Corkum, D. M. Villeneuve, A. T. Le, and C. D. Lin, “Intensity dependence of multiple orbital contributions and shape resonance in high-order harmonic generation of aligned N2 molecules,” Phys. Rev. A 85(1), 013405 (2012). [CrossRef]

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C. Jin, A. T. Le, and C. D. Lin, “Analysis of effects of macroscopic propagation and multiple molecular orbitals on the minimum in high-order harmonic generation of aligned CO2,” Phys. Rev. A 83(5), 053409 (2011). [CrossRef]

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C. Wu, H. Zhang, H. Yang, Q. Gong, D. Song, and H. Su, “Tunneling ionization of carbon dioxide from lower-lying orbitals,” Phys. Rev. A 83(3), 033410 (2011). [CrossRef]

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T. Seideman and E. Hamilton, “Nonadiabatic alignment by intense pulses. Concepts, theory, and directions,” Adv. At. Mol. Opt. Phys. 52, 289–329 (2005). [CrossRef]

27.

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(18), 183903 (2002). [CrossRef] [PubMed]

28.

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(2), 023805 (2002). [CrossRef]

29.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taïeb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4(7), 545–549 (2008). [CrossRef]

30.

X. Zhu, Q. Zhang, W. Hong, P. Lan, and P. Lu, “Two-center interference in high-order harmonic generation from heteronuclear diatomic molecules,” Opt. Express 19(2), 436–447 (2011). [CrossRef] [PubMed]

31.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]

32.

M. Y. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A 54(1), 742–745 (1996). [CrossRef] [PubMed]

33.

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

34.

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

35.

M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, “General atomic and molecular electronic structure system,” J. Comput. Chem. 14(11), 1347–1363 (1993). [CrossRef]

36.

R. Murray, W.-K. Liu, and M. Y. Ivanov, “Partial Fourier-transform approach to tunnel ionization: atomic systems,” Phys. Rev. A 81(2), 023413 (2010). [CrossRef]

37.

R. Murray, M. Spanner, S. Patchkovskii, and M. Y. Ivanov, “Tunnel ionization of molecules and orbital imaging,” Phys. Rev. Lett. 106(17), 173001 (2011). [CrossRef] [PubMed]

38.

P. Liu, P. Yu, Z. Zeng, H. Xiong, X. Ge, R. Li, and Z. Xu, “Laser intensity dependence of high-order harmonic generation from aligned CO2 molecules,” Phys. Rev. A 78(1), 015802 (2008). [CrossRef]

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(190.2620) Nonlinear optics : Harmonic generation and mixing

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: February 4, 2013
Revised Manuscript: March 5, 2013
Manuscript Accepted: March 5, 2013
Published: March 19, 2013

Citation
Jiawei Li, Peng Liu, Hua Yang, Liwei Song, Shitong Zhao, Hui Lu, Ruxin Li, and Zhizhan Xu, "High harmonic spectra contributed by HOMO-1 orbital of aligned CO2 molecules," Opt. Express 21, 7599-7607 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-7599


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  27. 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(18), 183903 (2002). [CrossRef] [PubMed]
  28. M. Lein, N. Hay, R. Velotta, J. P. Marangos, and P. L. Knight, “Interference effects in high-order harmonic generation with molecules,” Phys. Rev. A66(2), 023805 (2002). [CrossRef]
  29. W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taïeb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys.4(7), 545–549 (2008). [CrossRef]
  30. X. Zhu, Q. Zhang, W. Hong, P. Lan, and P. Lu, “Two-center interference in high-order harmonic generation from heteronuclear diatomic molecules,” Opt. Express19(2), 436–447 (2011). [CrossRef] [PubMed]
  31. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994). [CrossRef] [PubMed]
  32. M. Y. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A54(1), 742–745 (1996). [CrossRef] [PubMed]
  33. X. X. Zhou, X. M. Tong, Z. X. Zhao, and C. D. Lin, “Role of molecular orbital symmetry on the alignment dependence of high-order harmonic generation with molecules,” Phys. Rev. A71(6), 061801 (2005). [CrossRef]
  34. X. X. Zhou, X. M. Tong, Z. X. Zhao, and C. D. Lin, “Alignment dependence of high-order harmonic generation from N2 and O2 molecules in intense laser fields,” Phys. Rev. A72(3), 033412 (2005). [CrossRef]
  35. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, “General atomic and molecular electronic structure system,” J. Comput. Chem.14(11), 1347–1363 (1993). [CrossRef]
  36. R. Murray, W.-K. Liu, and M. Y. Ivanov, “Partial Fourier-transform approach to tunnel ionization: atomic systems,” Phys. Rev. A81(2), 023413 (2010). [CrossRef]
  37. R. Murray, M. Spanner, S. Patchkovskii, and M. Y. Ivanov, “Tunnel ionization of molecules and orbital imaging,” Phys. Rev. Lett.106(17), 173001 (2011). [CrossRef] [PubMed]
  38. P. Liu, P. Yu, Z. Zeng, H. Xiong, X. Ge, R. Li, and Z. Xu, “Laser intensity dependence of high-order harmonic generation from aligned CO2 molecules,” Phys. Rev. A78(1), 015802 (2008). [CrossRef]

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