Abstract

Accurate determination of laser intensity is of fundamental importance to study various phenomena in intense laser-atom/molecule interactions. We theoretically demonstrate a scheme to measure laser intensity by examining the holographic structure originating from the interference between the direct and near-forward rescattering electrons in strong-field tunneling ionization. By adding a weak second-harmonic field with polarization orthogonal to the strong fundamental driving field, the interference pattern oscillates with the changing relative phases of the two-color fields. Interestingly, the amplitude of this oscillation in the photoelectron momentum spectrum depends on the parallel momentum. With the quantum-orbit analysis, we show that the amplitude of the oscillation minimizes when the time difference between the recollision and ionization of near-forward rescattering electron is half cycle of the fundamental driving field. This enables us to measure accurately the laser intensity by seeking the minimum of the oscillation amplitude. Moreover, we show that this minimum can be determined without scanning the relative phases, instead, by just monitoring the interference patterns for two relative phases. This facilitates the application of our scheme in experiment.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (9)

Y. Chen, Y. Zhou, Y. Li, M. Li, P. Lan, and P. Lu, “Rabi oscillation in few-photon double ionization through doubly excited states,” Phys. Rev. A 97(1), 013428 (2018).
[Crossref]

L. Li, P. Lan, L. He, X. Zhu, J. Chen, and P. Lu, “Scaling law of high harmonic generation in the framework of photon channels,” Phys. Rev. Lett. 120(22), 223203 (2018).
[Crossref] [PubMed]

S. Luo, X. Ma, H. Xie, M. Li, Y. Zhou, W. Cao, and P. Lu, “Controlling nonsequential double ionization of Ne with parallel-polarized two-color laser pulse,” Opt. Express 26(10), 13666–13676 (2018).
[Crossref] [PubMed]

C. Zhai, X. Zhang, X. Zhu, L. He, Y. Zhang, B. Wang, Q. Zhang, P. Lan, and P. Lu, “Single-shot molecular orbit tomography with orthogonal two-color fields,” Opt. Express 26(3), 2775–2784 (2018).
[Crossref] [PubMed]

H. Yuan, L. He, F. Wang, B. Wang, X. Zhu, P. Lan, and P. Lu, “Tomography of asymmetric molecular orbits with a one-color inhomogeneous field,” Opt. Lett. 43(4), 931–934 (2018).
[Crossref] [PubMed]

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamic of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
[Crossref] [PubMed]

M. Li, W. Jiang, H. Xie, S. Luo, Y. Zhou, and P. Lu, “Strong-field photoelectron holography of atoms by bicircular two-color laser pulses,” Phys. Rev. A 97(2), 023415 (2018).
[Crossref]

M. He, Y. Li, Y. Zhou, M. Li, W. Cao, and P. Lu, “Direct visualization of valence electron motion using strong-field photoelectron holography,” Phys. Rev. Lett. 120(13), 133204 (2018).
[Crossref] [PubMed]

J. Tan, Y. Li, Y. Zhou, M. He, Y. Chen, M. Li, and P. Lu, “Identifying the contributions of multiple-returning recollision orbits in strong-field above-threshold ionization,” Opt. Quant. Electron. 50(2), 57 (2018).
[Crossref]

2017 (4)

M. He, Y. Zhou, Y. Li, M. Li, and P. Lu, “Revealing the target structure information encoded in strong-field photoelectron hologram,” Opt. Quant. Electron. 49(6), 232 (2017).
[Crossref]

S. G. Walt, N. B. Ram, M. Atala, N. I. S. Shilovski, A. Conta, D. Baykusheva, M. Lein, and H. J. Wörner, “Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering,” Nat. Commun. 8, 15651 (2017).
[Crossref] [PubMed]

T. Gaumnitz, A. Jain, Y. Pertot, M. Huppert, I. Jordan, F. A. Lamas, and H. J. Wörner, “Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driver,” Opt. Express 25(22), 27506–27518 (2017).
[Crossref] [PubMed]

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nat. Commun. 8(1), 186 (2017).
[Crossref] [PubMed]

2016 (8)

B. Wolter, M. G. Pullen, A. T. Le, M. Baudisch, K. D. Dier, A. Senftleben, M. Hemmer, C. D. Schröter, J. Ullrich, T. Pfeifer, R. Moshammer, S. Gräfe, O. Vendrell, C. D. Lin, and J. Biegert, “Ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene,” Science 354(6310), 308–312 (2016).
[Crossref] [PubMed]

M. Haertelt, X. Bian, M. Spanner, A. Staudte, and P. B. Corkum, “Probing Molecular Dynamics by Laser-Induced Backscattering Holography,” Phys. Rev. Lett. 116(13), 133001 (2016).
[Crossref] [PubMed]

M. He, Y. Li, Y. Zhou, M. Li, and P. Lu, “Temporal and spatial manipulation of the recolliding wave packet in strong-field photoelectron holography,” Phys. Rev. A 93(3), 033406 (2016).
[Crossref]

Y. Li, Y. Zhou, M. He, M. Li, and P. Lu, “Identifying backward-rescattering photoelectron hologram with orthogonal two-color laser fields,” Opt. Express 24(21), 23697–23706 (2016).
[Crossref] [PubMed]

S. Zhao, A. T. Le, C. Jin, X. Wang, and C. D. Lin, “Analytical model for calibrating laser intensity in strong-field-ionization experiment,” Phys. Rev. A 93(2), 023413 (2016).
[Crossref]

C. Hofmann, T. Zimmermann, A. Zielinski, and A. S. Landsman, “Non-adiabatic imprints on the electron wave packet in strong field ionization with circular polarization,” New J. Phys. 18(4), 043001 (2016).
[Crossref]

M. Liu, M. Li, C. Wu, Q. Gong, A. Staudte, and Y. Liu, “Phase structure of strong-field tunneling wave packet from molecules,” Phys. Rev. Lett. 116(16), 163004 (2016).
[Crossref] [PubMed]

Y. Zhou, O. I. Tolstikhin, and T. Morishita, “Near-forward rescattering photoelectron holography in strong-field ionization: extraction of the phase of the scattering amplitude,” Phys. Rev. Lett. 116(17), 173001 (2016).
[Crossref] [PubMed]

2015 (4)

S. Skruszewicz, J. Tiggesbäumker, K. H. M. Broes, M. Arbeiter, T. Fennel, and D. Bauer, “Two-color strong-field photoelectron spectroscopy and the phase of the phase,” Phys. Rev. Lett. 115(4), 043001 (2015).
[Crossref] [PubMed]

P. He, N. Takemoto, and F. He, “Photoelectron momentum distribution of atomic and molecular systems in strong circularly or elliptically polarized laser field,” Phys. Rev. A 91(6), 063413 (2015).
[Crossref]

Y. Shao, M. Li, M. Liu, X. Sun, X. Xie, P. Wang, Y. Deng, C. Wu, Q. Gong, and Y. Liu, “Isolating resonant excitation from above-threshold ionization,” Phys. Rev. A 92(1), 013415 (2015).
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M. Li, P. Zhang, S. Luo, Y. Zhou, Q. Zhang, P. Lan, and P. Lu, “Selective enhancement of resonant multiphoton ionization with strong laser fields,” Phys. Rev. A 92(6), 063404 (2015).
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2014 (1)

M. Meckel, A. Staudte, S. Patchkovskii, D. M. Villeneuve, P. B. Corkum, R. Dörner, and M. Spanner, “Signatures of the continuum electron phase in molecular strong-field photoelectron holography,” Nat. Phys. 10(8), 594 (2014).
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2013 (1)

R. Boge, C. Cirelli, A. S. Landsman, S. Heuser, A. Ludwig, J. Maurer, M. Weger, L. Gallmann, and U. Keller, “Probing nonadiabatic effects in strong-field tunnel ionization,” Phys. Rev. Lett. 111(10), 103003 (2013).
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2012 (8)

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and N. Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature 485(7398), 343 (2012).
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C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, T. A. Miller, L. F. DiMauro, and C. D. Lin, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature 483(7388), 194 (2012).
[Crossref] [PubMed]

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

W. Becker, X. Liu, P. J. Ho, and J. H. Eberly, “Theories of photoelectron correlation in laser-driven multiple atomic ionization,” Rev. Mod. Phys. 84(3), 1011 (2012).
[Crossref]

Y. Huismans, A. Gijsbertsen, A. S. Smolkowska, J. H. Jungmann, A. Rouzée, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. Meer, M. Yu. Ivanov, T. M. Yan, D. Bauer, O. Smirnova, and M. J. J. Vrakking, “Scaling laws for photoelectron holography in the midinfrared wavelength regime,” Phys. Rev. Lett. 109(1), 013002 (2012).
[Crossref] [PubMed]

S. Xu, X. Sun, B. Zeng, W. Chu, J. Zhao, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Simple method of measuring laser peak intensity inside femtosecond laser filament in air,” Opt. Express 20(1), 299–307 (2012).
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D. D. Hickstein, P. Ranitovic, S. Witte, X. Tong, Y. Huismans, P. Arpin, X. Zhou, K. E. Keister, C. W. Hogle, B. Zhang, C. Ding, P. Johnsson, N. Toshima, M. J. J. Vrakking, M. M. Murnane, and H. C. Kapteyn, “Direct visualization of laser-driven electron multiple scattering and tunneling distance in strong-field ionization,” Phys. Rev. Lett. 109(7), 073004 (2012).
[Crossref] [PubMed]

X. Bian and A. D. Bandrauk, “Attosecond Time-Resolved Imaging of Molecular Structure by Photoelectron Holography,” Phys. Rev. Lett. 108(26), 263003 (2012).
[Crossref] [PubMed]

2011 (5)

C. Smeenk, J. Z. Salvail, L. Arissian, P. B. Corkum, C. T. Hebeisen, and A. Staudte, “Precise in-situ measurement of laser pulse intensity using strong field ionization,” Opt. Express 19(10), 9336–9344 (2011).
[Crossref] [PubMed]

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6013), 61–64 (2011).
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T. Marchenko, Y. Huismans, K. J. Schafer, and M. J. J. Vrakking, “Criteria for the observation of strong-field photoelectron holography,” Phys. Rev. A 84(5), 053427 (2011).
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Y. Zhou, C. Huang, and P. Lu, “Coulomb-tail effect of electron-electron interaction on nonsequential double ionizaiton,” Phys. Rev. A 84(2), 023405 (2011).
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Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses,” Opt. Express 19(3), 2301–2308 (2011).
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2010 (2)

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. Wang, H. Liu, Y. Gu, X. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effect in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104(20), 203001 (2010).
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Y. Zhou, Q. Liao, and P. Lu, “Asymmetric electron energy sharing in strong-field double ionization of helium,” Phys. Rev. A 82(5), 053402 (2010).
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2009 (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163 (2009).
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2008 (1)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
[Crossref] [PubMed]

2007 (1)

X. Tong, S. Watahiki, K. Hino, and N. Toshima, “Numerical observation of the rescattering wave packet in laser-atom interaction,” Phys. Rev. Lett. 99(9), 093001 (2007).
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2006 (4)

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39(14), R203 (2006).
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X. Tong, K. Hino, and N. Toshima, “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
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S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, 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).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. D. Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006).
[Crossref] [PubMed]

2004 (3)

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 (2004).
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A. S. Alnaser, X. Tong, T. Osipov, S. Voss, C. M. Maharjan, B. Shan, Z. Chang, and C. L. Cocke, “Laser peak intensity calibration using recoil-ion momentum imaging,” Phys. Rev. A 70(2), 023413 (2004).
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V. L. B. Jesus, B. Feuerstein, K. Zrost, D. Fischer, A. Rudenko, F. Afaneh, C. D. Schröter, R. Moshammer, and J. Ullrich, “Atomic structure dependence of nonsequential double ionization of He, Ne and Ar in strong laser pulses,” J. Phys. B 37(8) L161 (2004).
[Crossref]

2002 (2)

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 (2002).
[Crossref] [PubMed]

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effect,” Adv. At. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

2001 (1)

P. Salières, B. Carré, L. L. Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[Crossref] [PubMed]

2000 (1)

T. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emission in multiphoton double ionization,” Nature 405(6787), 658 (2000).
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1999 (1)

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. L. Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: Model and experiment,” Phys. Rev. Lett. 82(8), 1668 (1999).
[Crossref]

1998 (1)

S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H2+ dissociative ionization intense laser fields,” Phys. Rev. A 57(2), 1176 (1998).
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1997 (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60(4), 389 (1997).
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1994 (2)

B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionization of helium,” Phys. Rev. Lett. 73(9), 1227 (1994).
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G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72(18), 2851 (1994).
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1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994 (1993).
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1992 (1)

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68(24), 3535 (1992).
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1989 (1)

M. D. Perry, O. L. Landen, and A. Szöke, “Measurement of the local laser intensity by photoelectron energy shifts in multiphoto ionization,” J. Opt. Sco. Am. B 6(3), 344–349 (1989).
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1988 (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31 (1988).
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1987 (1)

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59(10), 1092 (1987).
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1983 (1)

A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 μm,” Phys. Rev. A 27(5), 2503 (1983).
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1982 (1)

M. D. Feit, J. A. Fleck, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys. 47(3), 412–433 (1982).
[Crossref]

Afaneh, F.

V. L. B. Jesus, B. Feuerstein, K. Zrost, D. Fischer, A. Rudenko, F. Afaneh, C. D. Schröter, R. Moshammer, and J. Ullrich, “Atomic structure dependence of nonsequential double ionization of He, Ne and Ar in strong laser pulses,” J. Phys. B 37(8) L161 (2004).
[Crossref]

Agostini, P.

C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, T. A. Miller, L. F. DiMauro, and C. D. Lin, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature 483(7388), 194 (2012).
[Crossref] [PubMed]

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. L. Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: Model and experiment,” Phys. Rev. Lett. 82(8), 1668 (1999).
[Crossref]

B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionization of helium,” Phys. Rev. Lett. 73(9), 1227 (1994).
[Crossref] [PubMed]

Alnaser, A. S.

A. S. Alnaser, X. Tong, T. Osipov, S. Voss, C. M. Maharjan, B. Shan, Z. Chang, and C. L. Cocke, “Laser peak intensity calibration using recoil-ion momentum imaging,” Phys. Rev. A 70(2), 023413 (2004).
[Crossref]

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. D. Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006).
[Crossref] [PubMed]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
[Crossref] [PubMed]

Arbeiter, M.

S. Skruszewicz, J. Tiggesbäumker, K. H. M. Broes, M. Arbeiter, T. Fennel, and D. Bauer, “Two-color strong-field photoelectron spectroscopy and the phase of the phase,” Phys. Rev. Lett. 115(4), 043001 (2015).
[Crossref] [PubMed]

Arissian, L.

Arpin, P.

D. D. Hickstein, P. Ranitovic, S. Witte, X. Tong, Y. Huismans, P. Arpin, X. Zhou, K. E. Keister, C. W. Hogle, B. Zhang, C. Ding, P. Johnsson, N. Toshima, M. J. J. Vrakking, M. M. Murnane, and H. C. Kapteyn, “Direct visualization of laser-driven electron multiple scattering and tunneling distance in strong-field ionization,” Phys. Rev. Lett. 109(7), 073004 (2012).
[Crossref] [PubMed]

Atala, M.

S. G. Walt, N. B. Ram, M. Atala, N. I. S. Shilovski, A. Conta, D. Baykusheva, M. Lein, and H. J. Wörner, “Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering,” Nat. Commun. 8, 15651 (2017).
[Crossref] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
[Crossref] [PubMed]

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. D. Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006).
[Crossref] [PubMed]

Baker, S.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, 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]

Bakker, J. M.

Y. Huismans, A. Gijsbertsen, A. S. Smolkowska, J. H. Jungmann, A. Rouzée, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. Meer, M. Yu. Ivanov, T. M. Yan, D. Bauer, O. Smirnova, and M. J. J. Vrakking, “Scaling laws for photoelectron holography in the midinfrared wavelength regime,” Phys. Rev. Lett. 109(1), 013002 (2012).
[Crossref] [PubMed]

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6013), 61–64 (2011).
[Crossref]

Bandrauk, A. D.

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamic of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
[Crossref] [PubMed]

X. Bian and A. D. Bandrauk, “Attosecond Time-Resolved Imaging of Molecular Structure by Photoelectron Holography,” Phys. Rev. Lett. 108(26), 263003 (2012).
[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 (2002).
[Crossref] [PubMed]

S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H2+ dissociative ionization intense laser fields,” Phys. Rev. A 57(2), 1176 (1998).
[Crossref]

Baudisch, M.

B. Wolter, M. G. Pullen, A. T. Le, M. Baudisch, K. D. Dier, A. Senftleben, M. Hemmer, C. D. Schröter, J. Ullrich, T. Pfeifer, R. Moshammer, S. Gräfe, O. Vendrell, C. D. Lin, and J. Biegert, “Ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene,” Science 354(6310), 308–312 (2016).
[Crossref] [PubMed]

Bauer, D.

S. Skruszewicz, J. Tiggesbäumker, K. H. M. Broes, M. Arbeiter, T. Fennel, and D. Bauer, “Two-color strong-field photoelectron spectroscopy and the phase of the phase,” Phys. Rev. Lett. 115(4), 043001 (2015).
[Crossref] [PubMed]

Y. Huismans, A. Gijsbertsen, A. S. Smolkowska, J. H. Jungmann, A. Rouzée, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. Meer, M. Yu. Ivanov, T. M. Yan, D. Bauer, O. Smirnova, and M. J. J. Vrakking, “Scaling laws for photoelectron holography in the midinfrared wavelength regime,” Phys. Rev. Lett. 109(1), 013002 (2012).
[Crossref] [PubMed]

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6013), 61–64 (2011).
[Crossref]

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39(14), R203 (2006).
[Crossref]

Baykusheva, D.

S. G. Walt, N. B. Ram, M. Atala, N. I. S. Shilovski, A. Conta, D. Baykusheva, M. Lein, and H. J. Wörner, “Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering,” Nat. Commun. 8, 15651 (2017).
[Crossref] [PubMed]

Becker, W.

W. Becker, X. Liu, P. J. Ho, and J. H. Eberly, “Theories of photoelectron correlation in laser-driven multiple atomic ionization,” Rev. Mod. Phys. 84(3), 1011 (2012).
[Crossref]

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39(14), R203 (2006).
[Crossref]

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effect,” Adv. At. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

P. Salières, B. Carré, L. L. Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[Crossref] [PubMed]

Benedetti, E.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. D. Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006).
[Crossref] [PubMed]

Berden, G.

Y. Huismans, A. Gijsbertsen, A. S. Smolkowska, J. H. Jungmann, A. Rouzée, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. Meer, M. Yu. Ivanov, T. M. Yan, D. Bauer, O. Smirnova, and M. J. J. Vrakking, “Scaling laws for photoelectron holography in the midinfrared wavelength regime,” Phys. Rev. Lett. 109(1), 013002 (2012).
[Crossref] [PubMed]

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6013), 61–64 (2011).
[Crossref]

Bian, X.

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamic of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
[Crossref] [PubMed]

M. Haertelt, X. Bian, M. Spanner, A. Staudte, and P. B. Corkum, “Probing Molecular Dynamics by Laser-Induced Backscattering Holography,” Phys. Rev. Lett. 116(13), 133001 (2016).
[Crossref] [PubMed]

X. Bian and A. D. Bandrauk, “Attosecond Time-Resolved Imaging of Molecular Structure by Photoelectron Holography,” Phys. Rev. Lett. 108(26), 263003 (2012).
[Crossref] [PubMed]

Biegert, J.

B. Wolter, M. G. Pullen, A. T. Le, M. Baudisch, K. D. Dier, A. Senftleben, M. Hemmer, C. D. Schröter, J. Ullrich, T. Pfeifer, R. Moshammer, S. Gräfe, O. Vendrell, C. D. Lin, and J. Biegert, “Ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene,” Science 354(6310), 308–312 (2016).
[Crossref] [PubMed]

Blaga, C. I.

C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, T. A. Miller, L. F. DiMauro, and C. D. Lin, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature 483(7388), 194 (2012).
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Supplementary Material (1)

NameDescription
» Visualization 1       This video shows a sequence of PEMDs in the OTC laser fields for varying relative phases.

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Figures (7)

Fig. 1
Fig. 1 (a) The TDSE results of PEMD for strong-field tunneling ionization of Xe in a single-color laser field with wavelength 1600 nm. (b)–(d) The PEMDs in the OTC laser fields with relative phases Φ = 0.5π, 1π and 1.5π, respectively. The OTC laser fields are combined by a 1600-nm fundamental pulse and weak SH pulse. The 1600-nm field is polarized along the x axis with intensity 1.5 × 1014 W/cm2 and the 800-nm field is polarized along y axis with intensity 1 × 1012 W/cm2. A sequence of PEMDs in the OTC laser fields for varying relative phases are shown in Visualization 1.
Fig. 2
Fig. 2 (a) The interference term cos(Δφ) as a function of py at px = 1.9 a.u. The blue dashed line represents the result extracted from the PEMD of single-color field. The yellow and green solid lines are the results extracted from the PEMDs in the OTC laser fields with relative phases Φ = 0.5π and 1.5π, respectively. The black dashed lines indicate the position of the first minimum of the interference term at py > 0. (b) The shift Δpy of the first minimum of the interference term at py > 0 as a function of relative phase at px = 1.0 a.u. (the yellow solid line), 1.3 a.u. (the green solid line), 1.6 a.u. (the purple solid line) and 1.9 a.u (the blue solid line). (c) The shift Δpy extracted from the TDSE results as a function of relative phase for px ranging from 0.75 a.u. to 1.95 a.u. (d) The shift Δpy obtained from Eq. (8) as a function of relative phase for px ranging from 0.75 a.u. to 1.95 a.u. The black solid lines in (c) and (d) indicate the maximum of the shift Δpy.
Fig. 3
Fig. 3 (a) The amplitude Pm as a function of px. The solid line and dashed line represent the TDSE results extracted from Fig. 2(c) and the results obtained from Fig. 2(d), respectively. The black dashed line indicates the position where Pm gets minimum. (b) The same as (a) but for the quantity Φm.
Fig. 4
Fig. 4 (a) Δpy calculated by Eq. (16) as a function of relative phase for px ranging from 0.75 a.u. to 1.95 a.u. The laser intensity is 1.5I0 (I0 = 1.0 × 1014 W/cm2). The black solid line indicates the maximum of Δpy. (b) The amplitude Pm of the oscillating Δpy as a function of px at laser intensities I = 0.75I0 (the blue lines), 1.0I0 (the green lines), 1.5I0 (the yellow lines) and 2.0I0 (the red lines), respectively. The solid lines represent the TDSE results and dashed lines stand for the results calculated by Eq. (16). (c) Left axis (the blue solid line): Pm as a function of traveling time Δt. Here T1 is the period of the fundamental field. Right axis (the green solid line): the parallel momentum px as a function of the traveling time Δt. A1 is the amplitude of the vector potential of the fundamental field. The laser intensity is 1.5I0. The black dashed lines stand for the position where the amplitude Pm minimizes. (d) The same as (b) but with px scaled by A1.
Fig. 5
Fig. 5 (a) Δt as a function of px at different laser intensities ranging from 0.5I0 to 3.0I0. The black solid line represents Δt = 0.5T1. The vertical axis in (a) is scaled by A1. (b) The black solid line shows the parallel momentum corresponding to Δt = 0.5T1, as marked in (a). The red circles stand for the TDSE results of the position where Pm minimizes.
Fig. 6
Fig. 6 (a) Δpy calculated by Eq. (16) as a function of px at relative phases Φ = 0.1π (the green solid line) and 0.6π (the purple solid line). The red circles represent the amplitude Pm obtained by Eq. (17). The yellow dashed line is the same as that in Fig. 4(b). Here the laser intensity of fundamental field is 1.5I0. (b) The same as (a) but for another pair of relative phases Φ = 1.3π and Φ = 1.8π. (c) The black solid line is the same as that in Fig. 5(a). The red circles stand for the position where the Pm extracted from the TDSE results by Eq. (17) minimizes.
Fig. 7
Fig. 7 The amplitude Pm as a function of the parallel momentum px. Here laser focal volume effect has been taken into account by considering a Gaussian beam profile. The peak laser intensity is 2.25 ×1014 W/cm2. The vertical dashed line indicates the minimum of Pm.

Equations (17)

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i Ψ ( r , t ) t = H ( r , t ) Ψ ( r , t ) ,
H ( r , t ) = 1 2 2 + V C ( r ) + V L ( r , t ) ,
F ( t ) = f ( t ) [ F x ( t ) e ^ x + F y ( t ) e ^ y ] = f ( t ) [ F 1 cos ( ω t ) e ^ x + F 1 cos ( 2 ω t + Φ ) e ^ y ] .
Ψ ( τ ) = Ψ ( τ ) [ 1 F s ( R s ) ] + Ψ ( τ ) F s ( R s ) = Ψ 1 ( τ ) + Ψ 2 ( τ ) .
Ψ 2 ( , τ ) = C ¯ ( p , τ ) e i p τ 2 π d 2 p ,
d P ( p ) d E d θ = 2 E | τ C ¯ ( p , τ ) | 2 ,
| M | 2 = | M d | 2 + | M r | 2 + 2 | M d | | M r | cos ( Δ φ ) ,
Δ φ = φ r φ d = 1 2 t i d t r [ p y + A y ( t ) ] 2 d t + 1 2 t i d t r [ p x + A x ( t ) ] 2 d t 1 2 t i r t r [ k y + A y ( t ) ] 2 d t 1 2 t i r t r [ k x + A x ( t ) ] 2 d t + I p ( t i r t i d ) .
1 2 [ p + A x ( t i d ) ] 2 + I p = 0 ,
1 2 [ k x + A x ( t i r ) ] 2 + I p = 0 ,
1 2 [ k x + A x ( t r ) ] 2 = 1 2 [ p + A x ( t r ) ] 2 ,
t r t i r [ k x + A x ( t ) ] d t = 0 ,
t r t i r [ k y + A y ( t ) ] d t = 0 ,
Δ p y = P m cos ( Φ Φ m ) ,
Δ φ 1 2 t i t r { [ p y + A y ( t ) ] 2 [ k y + A y ( t ) ] 2 } d t .
Δ p y = p y O T C p y S = t i t r A y ( t ) d t t r t i = F 2 2 ω t i t r sin ( 2 ω t + Φ ) d t t r t i .
Δ p y ( Φ ; p x ) 2 + Δ p y ( Φ + 0.5 π ; p x ) 2 = P m 2 ( p x ) .

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