Abstract

By solving the time-dependent Schrödinger equation both in simplified one-dimensional coordinate and three-dimensional cylindrical coordinate systems, the high-order harmonic generation from H2+ in spatially symmetric and asymmetric nonhomogeneous laser fields was studied. At large internuclear distances, minima were clearly observed in high energy part of harmonic spectra, which can be attributed to two-center interference in diatomic molecule. Compared with previous studies, the minima in nonhomogeneous laser field are more distinct. Remarkably, the positions of the minima are different in these two types of fields, which demonstrate that interference effects are greatly influenced by laser parameters. Besides, the asymmetric nonhomogeneous field leads to an asymmetric recollision of the ionized electron, and both odd and even order harmonics could be emitted, which is explained in detail based on quantum dynamics calculations.

© 2016 Optical Society of America

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2016 (3)

H. Y. Zhong, J. Guo, W. Feng, P. C. Li, and X. S. Liu, “Comparison of high harmonic generation and attosecond pulse from 3D hydrogen atom in three kinds of inhomogeneous fields,” Phys. Lett. A 380(1–2), 188–193 (2016).
[Crossref]

I. Yavuz, M. F. Ciappina, A. Chacón, Z. Altun, M. F. Kling, and M. Lewenstein, “Controlling electron localization in H2+ by intense plasmon-enhanced laser fields,” Phys. Rev. A 93(3), 033404 (2016).
[Crossref]

M. Yamaguchi and K. Nobusada, “Photodissociation path in H2+ induced by nonuniform optical near fields: Two-step excitation via vibrationally excited states,” Phys. Rev. A 93(2), 023416 (2016).
[Crossref]

2015 (7)

P. Hu, Y. Niu, Y. Xiang, S. Gong, and C. Liu, “Carrier-envelope phase dependence of molecular harmonic spectral minima induced by mid-infrared laser pulses,” Opt. Express 23(18), 23834–23844 (2015).
[Crossref] [PubMed]

N. V. Golubev and A. I. Kuleff, “Control of charge migration in molecules by ultrashort laser pulses,” Phys. Rev. A 91(5), 051401(R) (2015).

I. Yavuz, Y. Tikman, and Z. Altun, “High-order-harmonic generation from H2+ molecular ions near plasmon-enhanced laser fields,” Phys. Rev. A 92(2), 023413 (2015).
[Crossref]

X. L. Ge, H. Du, Q. Wang, J. Guo, and X. S. Liu, “Selection of quantum path in high-order harmonics and isolated sub-100 attosecond generation in few-cycle spatially inhomogeneous laser fields,” Chin. Phys. B 24(2), 023201 (2015).
[Crossref]

L. Q. Feng, “Molecular harmonic extension and enhancement from H2+ ions in the presence of spatially inhomogeneous fields,” Phys. Rev. A 92(5), 053832 (2015).
[Crossref]

C. Yu, H. Wei, X. Wang, A. T. Le, R. Lu, and C. D. Lin, “Reconstruction of two-dimensional molecular structure with laser-induced electron diffraction from laser-aligned polyatomic molecules,” Sci. Rep. 5, 15753 (2015).
[Crossref] [PubMed]

Y. Chou, P. C. Li, T. S. Ho, and S. I. Chu, “Generation of an isolated few-attosecond pulse in optimized inhomogeneous two-color fields,” Phys. Rev. A 92(2), 023423 (2015).
[Crossref]

2014 (5)

X. Cao, S. Jiang, C. Yu, Y. Wang, L. Bai, and R. Lu, “Generation of isolated sub-10-attosecond pulses in spatially inhomogenous two-color fields,” Opt. Express 22(21), 26153–26161 (2014).
[Crossref] [PubMed]

Q. Liao and U. Thumm, “Attosecond time-resolved photoelectron dispersion and photoemission time delays,” Phys. Rev. Lett. 112(2), 023602 (2014).
[Crossref] [PubMed]

C. Yu, Y. H. Wang, X. Cao, S. C. Jiang, and R. F. Lu, “Isolated few-attosecond emission in a multicycle asymmetrically nonhomogeneous twocolor laser field,” J. Phys. At. Mol. Opt. Phys. 47(22), 225602 (2014).
[Crossref]

H. Ahmadi, A. Maghari, H. Sabzyan, A. R. Niknam, and M. Vafaee, “Effect of nuclear motion on high-order-harmonic generation of H2+ in intense ultrashort laser pulses,” Phys. Rev. A 90(4), 043411 (2014).
[Crossref]

M. D. Śpiewanowski, A. Etches, and L. B. Madsen, “High-order-harmonic generation from field-distorted orbitals,” Phys. Rev. A 89(4), 043407 (2014).
[Crossref]

2013 (4)

I. Yavuz, “Gas population effects in harmonic emission by plasmonic fields,” Phys. Rev. A 87(5), 053815 (2013).
[Crossref]

J. H. Luo, Y. Li, Z. Wang, Q. B. Zhang, and P. X. Lu, “Ultra-short isolated attosecond emission in mid-infrared inhomogeneous fields without CEP stabilization,” J. Phys. At. Mol. Opt. Phys. 46(14), 145602 (2013).
[Crossref]

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110(5), 053001 (2013).
[Crossref] [PubMed]

Y. Y. Yang, A. Scrinzi, A. Husakou, Q. G. Li, S. L. Stebbings, F. Süßmann, H. J. Yu, S. Kim, E. Rühl, J. Herrmann, X. C. Lin, and M. F. Kling, “High-harmonic and single attosecond pulse generation using plasmonic field enhancement in ordered arrays of gold nanoparticles with chirped laser pulses,” Opt. Express 21(2), 2195–2205 (2013).
[Crossref] [PubMed]

2012 (4)

I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A 85(1), 013416 (2012).
[Crossref]

M. F. Ciappina, S. S. Aćimović, T. Shaaran, J. Biegert, R. Quidant, and M. Lewenstein, “Enhancement of high harmonic generation by confining electron motion in plasmonic nanostrutures,” Opt. Express 20(24), 26261–26274 (2012).
[Crossref] [PubMed]

H. X. He, R. F. Lu, P. Y. Zhang, K. L. Han, and G. Z. He, “Direct multi-photon ionizations of H2+ in intense laser fields,” J. Phys. At. Mol. Opt. Phys. 45(12), 085103 (2012).
[Crossref]

M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A 85(3), 033828 (2012).
[Crossref]

2011 (4)

Y. Wu, J. T. Zhang, H. L. Ye, and Z. Z. Xu, “Intensity-dependent interference effect in high-order harmonic generation from aligned H2+ molecules,” Phys. Rev. A 83(2), 023417 (2011).
[Crossref]

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]

H. X. He, R. F. Lu, P. Y. Zhang, Y. H. Guo, K. L. Han, and G. Z. He, “Theoretical investigation of the origin of the multipeak structure of kinetic-energy-release spectra from charge-resonance-enhanced ionization of H2+ in intense laser fields,” Phys. Rev. A 84(3), 033418 (2011).
[Crossref]

S. L. Stebbings, F. Süßmann, Y.-Y. Yang, A. Scrinzi, M. Durach, A. Rusina, M. I. Stockman, and M. F. Kling, “Generation of isolated attosecond extreme ultraviolet pulses employing nanoplasmonic field enhancement: optimization of coupled ellipsoids,” New J. Phys. 13(11), 073010 (2011).
[Crossref]

2010 (1)

Y. C. Han and L. B. Madsen, “Minimum in the high-order harmonic generation spectrum from molecules: role of excited states,” J. Phys. At. Mol. Opt. Phys. 43(10), 225601 (2010).
[Crossref]

2009 (1)

A. T. Le, R. R. Lucchese, M. T. Lee, and C. D. Lin, “Probing molecular frame photoionization via laser generated high-order harmonics from aligned molecules,” Phys. Rev. Lett. 102(20), 203001 (2009).
[Crossref] [PubMed]

2008 (5)

G. Winterfeldt, C. Spielmann, and G. Gerber, “Colloquium: Optimal control of high-harmonic generation,” Rev. Mod. Phys. 80(1), 117–140 (2008).
[Crossref]

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Y. Mairesse, J. Levesque, N. Dudovich, P. B. Corkum, and D. M. Villeneuve, “High harmonic generation from aligned molecules–amplitude and polarization,” J. Mod. Opt. 55(16), 2591–2602 (2008).
[Crossref]

Y. J. Chen and J. Liu, “High-order harmonic generation from diatomic molecules with large internuclear distance: The effect of two-center interference,” Phys. Rev. A 77(1), 013410 (2008).
[Crossref]

R. F. Lu, P. Y. Zhang, and K. L. Han, “Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6), 066701 (2008).
[Crossref] [PubMed]

2007 (1)

M. F. Ciappina, C. C. Chirilă, and M. Lein, “Influence of Coulomb continuum wave functions in the description of high-order harmonic generation with H2+,” Phys. Rev. A 75(4), 043405 (2007).
[Crossref]

2006 (1)

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[Crossref] [PubMed]

2005 (4)

G. L. Kamta and A. D. Bandrauk, “Three-dimensional time-profile analysis of high-order harmonic generation in molecules: Nuclear interferences in H2+,” Phys. Rev. A 71(5), 053407 (2005).
[Crossref]

B. Zimmermann, M. Lein, and J. M. Rost, “Analysis of recombination in high-order harmonic generation in molecules,” Phys. Rev. A 71(3), 033401 (2005).
[Crossref]

J. Hu, K. L. Han, and G. Z. He, “Correlation quantum dynamics between an electron and D2+ molecule with attosecond resolution,” Phys. Rev. Lett. 95(12), 123001 (2005).
[Crossref] [PubMed]

M. Lein, “Attosecond probing of vibrational dynamics with high-harmonic generation,” Phys. Rev. Lett. 94(5), 053004 (2005).
[Crossref] [PubMed]

2004 (4)

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]

V. Roudnev, B. D. Esry, and I. Ben-Itzhak, “Controlling HD+ and H2+ dissociation with the carrier-envelope phase difference of an intense ultrashort laser pulse,” Phys. Rev. Lett. 93(16), 163601 (2004).
[Crossref] [PubMed]

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]

L. V. Vela-Arevalo and J. E. Marsden, “Time-frequency analysis of the restricted three-body problem: transport and resonance transitions,” Class. Quantum Gravity 21(3), S351–S375 (2004).
[Crossref]

2003 (1)

H. Niikura, F. Légaré, R. Hasbani, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Probing molecular dynamics with attosecond resolution using correlated wave packet pairs,” Nature 421(6925), 826–829 (2003).
[Crossref] [PubMed]

2002 (3)

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]

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]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[Crossref] [PubMed]

2001 (4)

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref] [PubMed]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

X. Chu and S. I. Chu, “Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission,” Phys. Rev. A 64(2), 021403(R) (2001).

2000 (1)

X. M. Tong and S. I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802(R) (2000).

1999 (2)

N. A. Papadogiannis, B. Witzel, C. Kalpouzos, and D. Charalambidis, “Observation of attosecond light localization in higher order harmonic generation,” Phys. Rev. Lett. 83(21), 4289–4292 (1999).
[Crossref]

A. D. Bandrauk and H. Yu, “High-order harmonic generation by one- and two-electron molecular ions with intense laser pulses,” Phys. Rev. A 59(1), 539–548 (1999).
[Crossref]

1998 (1)

R. Kopold, W. Becker, and M. Kleber, “Model calculations of high-harmonic generation in molecular ions,” Phys. Rev. A 58(5), 4022–4038 (1998).
[Crossref]

1995 (2)

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(3), R1750–R1753 (1995).
[Crossref] [PubMed]

M. Ivanov, P. B. Corkum, T. Zuo, and A. Bandrauk, “Routes to control of intense-field atomic polarizability,” Phys. Rev. Lett. 74(15), 2933–2936 (1995).
[Crossref] [PubMed]

1993 (2)

M. Y. Ivanov and P. B. Corkum, “Generation of high-order harmonics from inertially confined molecular ions,” Phys. Rev. A 48(1), 580–590 (1993).
[Crossref] [PubMed]

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

1992 (1)

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45(5), 3347–3349 (1992).
[Crossref] [PubMed]

1961 (1)

J. R. Hiskes, “Dissociation of molecular ions by electric and magnetic fields,” Phys. Rev. 122(4), 1207–1217 (1961).
[Crossref]

Acimovic, S. S.

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref] [PubMed]

Ahmadi, H.

H. Ahmadi, A. Maghari, H. Sabzyan, A. R. Niknam, and M. Vafaee, “Effect of nuclear motion on high-order-harmonic generation of H2+ in intense ultrashort laser pulses,” Phys. Rev. A 90(4), 043411 (2014).
[Crossref]

Altun, Z.

I. Yavuz, M. F. Ciappina, A. Chacón, Z. Altun, M. F. Kling, and M. Lewenstein, “Controlling electron localization in H2+ by intense plasmon-enhanced laser fields,” Phys. Rev. A 93(3), 033404 (2016).
[Crossref]

I. Yavuz, Y. Tikman, and Z. Altun, “High-order-harmonic generation from H2+ molecular ions near plasmon-enhanced laser fields,” Phys. Rev. A 92(2), 023413 (2015).
[Crossref]

I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A 85(1), 013416 (2012).
[Crossref]

Antoine, P.

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(3), R1750–R1753 (1995).
[Crossref] [PubMed]

Auge, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref] [PubMed]

Bai, L.

Baker, S.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[Crossref] [PubMed]

Balcou, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref] [PubMed]

Bandrauk, A.

M. Ivanov, P. B. Corkum, T. Zuo, and A. Bandrauk, “Routes to control of intense-field atomic polarizability,” Phys. Rev. Lett. 74(15), 2933–2936 (1995).
[Crossref] [PubMed]

Bandrauk, A. D.

G. L. Kamta and A. D. Bandrauk, “Three-dimensional time-profile analysis of high-order harmonic generation in molecules: Nuclear interferences in H2+,” Phys. Rev. A 71(5), 053407 (2005).
[Crossref]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[Crossref] [PubMed]

A. D. Bandrauk and H. Yu, “High-order harmonic generation by one- and two-electron molecular ions with intense laser pulses,” Phys. Rev. A 59(1), 539–548 (1999).
[Crossref]

Becker, W.

R. Kopold, W. Becker, and M. Kleber, “Model calculations of high-harmonic generation in molecular ions,” Phys. Rev. A 58(5), 4022–4038 (1998).
[Crossref]

Ben-Itzhak, I.

V. Roudnev, B. D. Esry, and I. Ben-Itzhak, “Controlling HD+ and H2+ dissociation with the carrier-envelope phase difference of an intense ultrashort laser pulse,” Phys. Rev. Lett. 93(16), 163601 (2004).
[Crossref] [PubMed]

Biegert, J.

Bleda, E. A.

I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A 85(1), 013416 (2012).
[Crossref]

Brabec, T.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref] [PubMed]

Burnett, K.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45(5), 3347–3349 (1992).
[Crossref] [PubMed]

Cao, X.

X. Cao, S. Jiang, C. Yu, Y. Wang, L. Bai, and R. Lu, “Generation of isolated sub-10-attosecond pulses in spatially inhomogenous two-color fields,” Opt. Express 22(21), 26153–26161 (2014).
[Crossref] [PubMed]

C. Yu, Y. H. Wang, X. Cao, S. C. Jiang, and R. F. Lu, “Isolated few-attosecond emission in a multicycle asymmetrically nonhomogeneous twocolor laser field,” J. Phys. At. Mol. Opt. Phys. 47(22), 225602 (2014).
[Crossref]

Chacón, A.

I. Yavuz, M. F. Ciappina, A. Chacón, Z. Altun, M. F. Kling, and M. Lewenstein, “Controlling electron localization in H2+ by intense plasmon-enhanced laser fields,” Phys. Rev. A 93(3), 033404 (2016).
[Crossref]

Charalambidis, D.

N. A. Papadogiannis, B. Witzel, C. Kalpouzos, and D. Charalambidis, “Observation of attosecond light localization in higher order harmonic generation,” Phys. Rev. Lett. 83(21), 4289–4292 (1999).
[Crossref]

Chen, Y. J.

Y. J. Chen and J. Liu, “High-order harmonic generation from diatomic molecules with large internuclear distance: The effect of two-center interference,” Phys. Rev. A 77(1), 013410 (2008).
[Crossref]

Chirila, C. C.

M. F. Ciappina, C. C. Chirilă, and M. Lein, “Influence of Coulomb continuum wave functions in the description of high-order harmonic generation with H2+,” Phys. Rev. A 75(4), 043405 (2007).
[Crossref]

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[Crossref] [PubMed]

Chou, Y.

Y. Chou, P. C. Li, T. S. Ho, and S. I. Chu, “Generation of an isolated few-attosecond pulse in optimized inhomogeneous two-color fields,” Phys. Rev. A 92(2), 023423 (2015).
[Crossref]

Chu, S. I.

Y. Chou, P. C. Li, T. S. Ho, and S. I. Chu, “Generation of an isolated few-attosecond pulse in optimized inhomogeneous two-color fields,” Phys. Rev. A 92(2), 023423 (2015).
[Crossref]

X. Chu and S. I. Chu, “Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission,” Phys. Rev. A 64(2), 021403(R) (2001).

X. M. Tong and S. I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802(R) (2000).

Chu, X.

X. Chu and S. I. Chu, “Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission,” Phys. Rev. A 64(2), 021403(R) (2001).

Ciappina, M. F.

I. Yavuz, M. F. Ciappina, A. Chacón, Z. Altun, M. F. Kling, and M. Lewenstein, “Controlling electron localization in H2+ by intense plasmon-enhanced laser fields,” Phys. Rev. A 93(3), 033404 (2016).
[Crossref]

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110(5), 053001 (2013).
[Crossref] [PubMed]

M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A 85(3), 033828 (2012).
[Crossref]

M. F. Ciappina, S. S. Aćimović, T. Shaaran, J. Biegert, R. Quidant, and M. Lewenstein, “Enhancement of high harmonic generation by confining electron motion in plasmonic nanostrutures,” Opt. Express 20(24), 26261–26274 (2012).
[Crossref] [PubMed]

M. F. Ciappina, C. C. Chirilă, and M. Lein, “Influence of Coulomb continuum wave functions in the description of high-order harmonic generation with H2+,” Phys. Rev. A 75(4), 043405 (2007).
[Crossref]

Cooper, J.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45(5), 3347–3349 (1992).
[Crossref] [PubMed]

Corkum, P.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Corkum, P. B.

Y. Mairesse, J. Levesque, N. Dudovich, P. B. Corkum, and D. M. Villeneuve, “High harmonic generation from aligned molecules–amplitude and polarization,” J. Mod. Opt. 55(16), 2591–2602 (2008).
[Crossref]

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]

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]

H. Niikura, F. Légaré, R. Hasbani, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Probing molecular dynamics with attosecond resolution using correlated wave packet pairs,” Nature 421(6925), 826–829 (2003).
[Crossref] [PubMed]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[Crossref] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref] [PubMed]

M. Ivanov, P. B. Corkum, T. Zuo, and A. Bandrauk, “Routes to control of intense-field atomic polarizability,” Phys. Rev. Lett. 74(15), 2933–2936 (1995).
[Crossref] [PubMed]

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

M. Y. Ivanov and P. B. Corkum, “Generation of high-order harmonics from inertially confined molecular ions,” Phys. Rev. A 48(1), 580–590 (1993).
[Crossref] [PubMed]

Drescher, M.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref] [PubMed]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Du, H.

X. L. Ge, H. Du, Q. Wang, J. Guo, and X. S. Liu, “Selection of quantum path in high-order harmonics and isolated sub-100 attosecond generation in few-cycle spatially inhomogeneous laser fields,” Chin. Phys. B 24(2), 023201 (2015).
[Crossref]

Dudovich, N.

Y. Mairesse, J. Levesque, N. Dudovich, P. B. Corkum, and D. M. Villeneuve, “High harmonic generation from aligned molecules–amplitude and polarization,” J. Mod. Opt. 55(16), 2591–2602 (2008).
[Crossref]

Durach, M.

S. L. Stebbings, F. Süßmann, Y.-Y. Yang, A. Scrinzi, M. Durach, A. Rusina, M. I. Stockman, and M. F. Kling, “Generation of isolated attosecond extreme ultraviolet pulses employing nanoplasmonic field enhancement: optimization of coupled ellipsoids,” New J. Phys. 13(11), 073010 (2011).
[Crossref]

Esry, B. D.

V. Roudnev, B. D. Esry, and I. Ben-Itzhak, “Controlling HD+ and H2+ dissociation with the carrier-envelope phase difference of an intense ultrashort laser pulse,” Phys. Rev. Lett. 93(16), 163601 (2004).
[Crossref] [PubMed]

Etches, A.

M. D. Śpiewanowski, A. Etches, and L. B. Madsen, “High-order-harmonic generation from field-distorted orbitals,” Phys. Rev. A 89(4), 043407 (2014).
[Crossref]

Feng, L. Q.

L. Q. Feng, “Molecular harmonic extension and enhancement from H2+ ions in the presence of spatially inhomogeneous fields,” Phys. Rev. A 92(5), 053832 (2015).
[Crossref]

Feng, W.

H. Y. Zhong, J. Guo, W. Feng, P. C. Li, and X. S. Liu, “Comparison of high harmonic generation and attosecond pulse from 3D hydrogen atom in three kinds of inhomogeneous fields,” Phys. Lett. A 380(1–2), 188–193 (2016).
[Crossref]

Ge, X. L.

X. L. Ge, H. Du, Q. Wang, J. Guo, and X. S. Liu, “Selection of quantum path in high-order harmonics and isolated sub-100 attosecond generation in few-cycle spatially inhomogeneous laser fields,” Chin. Phys. B 24(2), 023201 (2015).
[Crossref]

Gerber, G.

G. Winterfeldt, C. Spielmann, and G. Gerber, “Colloquium: Optimal control of high-harmonic generation,” Rev. Mod. Phys. 80(1), 117–140 (2008).
[Crossref]

Golubev, N. V.

N. V. Golubev and A. I. Kuleff, “Control of charge migration in molecules by ultrashort laser pulses,” Phys. Rev. A 91(5), 051401(R) (2015).

Gong, S.

Guo, J.

H. Y. Zhong, J. Guo, W. Feng, P. C. Li, and X. S. Liu, “Comparison of high harmonic generation and attosecond pulse from 3D hydrogen atom in three kinds of inhomogeneous fields,” Phys. Lett. A 380(1–2), 188–193 (2016).
[Crossref]

X. L. Ge, H. Du, Q. Wang, J. Guo, and X. S. Liu, “Selection of quantum path in high-order harmonics and isolated sub-100 attosecond generation in few-cycle spatially inhomogeneous laser fields,” Chin. Phys. B 24(2), 023201 (2015).
[Crossref]

Guo, Y. H.

H. X. He, R. F. Lu, P. Y. Zhang, Y. H. Guo, K. L. Han, and G. Z. He, “Theoretical investigation of the origin of the multipeak structure of kinetic-energy-release spectra from charge-resonance-enhanced ionization of H2+ in intense laser fields,” Phys. Rev. A 84(3), 033418 (2011).
[Crossref]

Han, K. L.

H. X. He, R. F. Lu, P. Y. Zhang, K. L. Han, and G. Z. He, “Direct multi-photon ionizations of H2+ in intense laser fields,” J. Phys. At. Mol. Opt. Phys. 45(12), 085103 (2012).
[Crossref]

H. X. He, R. F. Lu, P. Y. Zhang, Y. H. Guo, K. L. Han, and G. Z. He, “Theoretical investigation of the origin of the multipeak structure of kinetic-energy-release spectra from charge-resonance-enhanced ionization of H2+ in intense laser fields,” Phys. Rev. A 84(3), 033418 (2011).
[Crossref]

R. F. Lu, P. Y. Zhang, and K. L. Han, “Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6), 066701 (2008).
[Crossref] [PubMed]

J. Hu, K. L. Han, and G. Z. He, “Correlation quantum dynamics between an electron and D2+ molecule with attosecond resolution,” Phys. Rev. Lett. 95(12), 123001 (2005).
[Crossref] [PubMed]

Han, Y. C.

Y. C. Han and L. B. Madsen, “Minimum in the high-order harmonic generation spectrum from molecules: role of excited states,” J. Phys. At. Mol. Opt. Phys. 43(10), 225601 (2010).
[Crossref]

Hasbani, R.

H. Niikura, F. Légaré, R. Hasbani, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Probing molecular dynamics with attosecond resolution using correlated wave packet pairs,” Nature 421(6925), 826–829 (2003).
[Crossref] [PubMed]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[Crossref] [PubMed]

Haworth, C. A.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[Crossref] [PubMed]

Hay, N.

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]

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]

He, G. Z.

H. X. He, R. F. Lu, P. Y. Zhang, K. L. Han, and G. Z. He, “Direct multi-photon ionizations of H2+ in intense laser fields,” J. Phys. At. Mol. Opt. Phys. 45(12), 085103 (2012).
[Crossref]

H. X. He, R. F. Lu, P. Y. Zhang, Y. H. Guo, K. L. Han, and G. Z. He, “Theoretical investigation of the origin of the multipeak structure of kinetic-energy-release spectra from charge-resonance-enhanced ionization of H2+ in intense laser fields,” Phys. Rev. A 84(3), 033418 (2011).
[Crossref]

J. Hu, K. L. Han, and G. Z. He, “Correlation quantum dynamics between an electron and D2+ molecule with attosecond resolution,” Phys. Rev. Lett. 95(12), 123001 (2005).
[Crossref] [PubMed]

He, H. X.

H. X. He, R. F. Lu, P. Y. Zhang, K. L. Han, and G. Z. He, “Direct multi-photon ionizations of H2+ in intense laser fields,” J. Phys. At. Mol. Opt. Phys. 45(12), 085103 (2012).
[Crossref]

H. X. He, R. F. Lu, P. Y. Zhang, Y. H. Guo, K. L. Han, and G. Z. He, “Theoretical investigation of the origin of the multipeak structure of kinetic-energy-release spectra from charge-resonance-enhanced ionization of H2+ in intense laser fields,” Phys. Rev. A 84(3), 033418 (2011).
[Crossref]

Heinzmann, U.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Hentschel, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref] [PubMed]

Herrmann, J.

Hiskes, J. R.

J. R. Hiskes, “Dissociation of molecular ions by electric and magnetic fields,” Phys. Rev. 122(4), 1207–1217 (1961).
[Crossref]

Ho, T. S.

Y. Chou, P. C. Li, T. S. Ho, and S. I. Chu, “Generation of an isolated few-attosecond pulse in optimized inhomogeneous two-color fields,” Phys. Rev. A 92(2), 023423 (2015).
[Crossref]

Hong, W.

Hu, J.

J. Hu, K. L. Han, and G. Z. He, “Correlation quantum dynamics between an electron and D2+ molecule with attosecond resolution,” Phys. Rev. Lett. 95(12), 123001 (2005).
[Crossref] [PubMed]

Hu, P.

Husakou, A.

Itatani, J.

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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).
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Figures (5)

Fig. 1
Fig. 1 The nonhomogeneous fields for the input laser intensify of 1.0 × 1014 W/cm2 and β = 0.004. (a) Asymmetric case (ANLF), and (b) symmetric case (SNLF).
Fig. 2
Fig. 2 Harmonic spectra from 3D calculations for H2+ in (a) ANLF and (b) SNLF, where the solid lines give the smoothed spectra, and the yellow and dark green arrows indicate the location of the minima for m = 5 and 6 respectively according to Eq. (1). (c) Harmonic spectra from | G 1 (ω) | 2 + | G 2 (ω) | 2 of H2+ without interferences at R = 13 a.u. (red line for SNLF, black line for ANLF). (d) The time-frequency distribution for HHG in SNLF at R = 13 a.u., where the white dashed line corresponds to the minima. The harmonic spectra for R = 12 a.u. in (a), (b), and the harmonic spectra for ANLF in (c) are the raw data, whereas the harmonic spectra for R = 13, 14, 15, and 16 a.u. in (a), (b), and the harmonic spectra for SNLF in (c) are shifted up vertically for clarity.
Fig. 3
Fig. 3 Relationship between the location of interference minimnum and internuclear distance.
Fig. 4
Fig. 4 Time-dependent electronic density for R = 15 a.u. in (a) ANLF and (b) SNLF. Recollision flux of the electronic wavepacket in the case of (c) ANLF and (d) SNLF.
Fig. 5
Fig. 5 (a) The time-frequency distribution for HHG in ANLF at R = 13 a.u.. (b) Harmonic spectra of H2+ at R = 13 a.u. in ANLF and SNLF.

Equations (10)

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Rcosθ= (2m+1)λ/2,m=0, 1, 2,. . . .
i t ψ(z;t)=[ 1 2 2 z 2 +V(z)+zE(z;t) ]ψ(z;t),
i t ψ(z,ρ;t)=[ T R + T z + T ρ + V c (R,z,ρ)+kzE(z;t) ]ψ(z,ρ;t),
a(t)= ψ(z,ρ;t) | V(R,z,ρ) z +E(t) | ψ(z,ρ;t) ,
P(ω)= | 1 2π 0 T a(t) e iwt dt | 2 .
A(t,ω)= a( t ) ω W(ω( t t))d t ,
P smooth (ω)= P(ω' )exp( (ω'ω) 2 / σ 2 )dω'.
P(ω)= | G 1 (ω) | 2 + | G 2 (ω) | 2 +2Re[ G 1 (ω) G 2 * (ω)],
F(t)= Im[ ψ * δ(z z 0 ) z ψ]ρdρ ,
Δ N exp[iΘ( t f , t 0 )]exp[iΘ( t f ', t 0 ')],

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