Abstract

By numerically solving the time-dependent Schrödinger equation, we theoretically investigate the dynamics of the low-energy photoelectrons ionized by a single attosecond pulse in the presence of an infrared laser field. The obtained photoelectron momentum distributions exhibit complicated interference structures. With the semiclassical model, the originations for the different types of the interference structures are unambiguously identified. Moreover, by changing the time delay between the attosecond pulse and the infrared laser field, these interferences could be selectively enhanced or suppressed. This enables us to extract information about the ionization dynamics encoded in the interference structures. As an example, we show that the phase of the electron wave-packets ionized by the linearly and circularly polarized attosecond pulses can be extracted from the interference structures of the direct and the near-forward rescattering electrons.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (12)

J. Li, Q. Zhang, L. Li, X. Zhu, T. Huang, P. Lan, and P. Lu, “Orientation dependence of high-order harmonic generation in nanowire,” Phys. Rev. A 99(3), 033421 (2019).
[Crossref]

B. Wang, L. He, Y. He, Y. Zhang, R. Shao, P. Lan, and P. Lu, “All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation,” Opt. Express 27(21), 30172–30181 (2019).
[Crossref]

J. Li, L. Li, Q. Zhang, X. Zhu, T. Huang, P. Lan, and P. Lu, “Channel-closing effects of electronic excitation in solids,” Opt. Express 27, 37224–37235 (2019).
[Crossref]

A. Tong, Q. Li, X. Ma, Y. Zhou, and P. Lu, “Internal collision induced strong-field nonsequential double ionization in molecules,” Opt. Express 27(5), 6415 (2019).
[Crossref]

Y. Zhao, Y. Zhou, J. Liang, Z. Zeng, Q. Ke, Y. Liu, M. Li, and P. Lu, “Frustrated tunneling ionization in the elliptically polarized strong laser fields,” Opt. Express 27(15), 21689–21701 (2019).
[Crossref]

Q. Ke, Y. Zhou, J. Tan, M. He, J. Liang, Y. Zhao, M. Li, and P. Lu, “Two-dimensional photoelectron holography in strong-field tunneling ionization by counter rotating two-color circularly polarized laser pulses,” Opt. Express 27, 32193–32209 (2019).
[Crossref]

Y. Feng, M. Li, S. Luo, K. Lui, B. Du, Y. Zhou, and P. Lu, “Semiclassical analysis of photoelectron interference in a synthesized two-color laser pulses,” Phys. Rev. A 100(6), 063411 (2019).
[Crossref]

M. Li, H. Xie, W. Cao, S. Luo, J. Tan, Y. Feng, B. Du, W. Zhang, Y. Li, Q. Zhang, P. Lan, Y. Zhou, and P. Lu, “Photoelectron holographic interferometry to probe the longitudinal momentum offset at the tunnel exit,” Phys. Rev. Lett. 122(18), 183202 (2019).
[Crossref]

S. Luo, M. Li, W. Xie, K. Liu, Y. Feng, B. Du, Y. Zhou, and P. Lu, “Exit momentum, and instantaneous ionization rate of nonadiabatic tunneling ionization in elliptically polarized laser fields,” Phys. Rev. A 99(5), 053422 (2019).
[Crossref]

W. Xie, M. Li, S. Luo, M. He, K. Liu, Q. Zhang, Y. Zhou, and P. Lu, “Nonadiabaticity-induced ionization time shift in strong-field tunneling ionization,” Phys. Rev. A 100(2), 023414 (2019).
[Crossref]

J. Tan, Y. Zhou, M. He, Q. Ke, J. Liang, Y. Li, M. Li, and P. Lu, “Time-resolving tunneling ionization via strong-field photoelectron holography,” Phys. Rev. A 99(3), 033402 (2019).
[Crossref]

Y. Liu, J. Tan, M. He, H. Xie, Y. Qin, Y. Zhao, M. Li, Y. Zhou, and P. Lu, “Photoelectron holographic interferences from multiple returning in strong-field tunneling ionization,” Opt. Quantum Electron. 51(5), 145 (2019).
[Crossref]

2018 (5)

X. Yu, M. Li, M. Han, and Y. Liu, “Controlling backward-scattering photoelectron holography by attosecond streaking,” Phys. Rev. A 98(1), 013415 (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]

J. Tan, Y. Zhou, M. He, Y. Chen, Q. Ke, J. Liang, X. Zhu, M. Li, and P. Lu, “Determination of the Ionization Time Using Attosecond Photoelectron Interferometry,” Phys. Rev. Lett. 121(25), 253203 (2018).
[Crossref]

J. Vos, L. Cattaneo, S. Patchkovskii, T. Zimmermann, C. Cirelli, M. Lucchini, A. Kheifets, A. S. Landsman, and U. Keller, “Orientation-dependent stereo Wigner time delay, and electron localization in a small molecule,” Science 360(6395), 1326–1330 (2018).
[Crossref]

D. Kiesewetter, R. R. Jones, A. Camper, S. B. Schoun, P. Agostini, and L. F. DiMauro, “Probing electronic binding potentials with attosecond photoelectron wavepackets,” Nat. Phys. 14(1), 68–73 (2018).
[Crossref]

2016 (1)

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]

2014 (6)

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), 594–600 (2014).
[Crossref]

M. Li, J. Yuan, X. Sun, J. Yu, Q. Gong, and Y. Liu, “Recollision-induced subcycle interference of molecules in strong laser fields,” Phys. Rev. A 89(3), 033425 (2014).
[Crossref]

X.-B. Bian and A. D. Bandrauk, “Orientation-dependent forward-backward photoelectron holography from asymmetric molecules,” Phys. Rev. A 89(3), 033423 (2014).
[Crossref]

Q. Liao and U. Thumm, “Attosecond Time-Resolved Photoelectron Dispersion and Photoemission Time Delays,” Phys. Rev. Lett. 112(2), 023602 (2014).
[Crossref]

Q.-C. Ning, L.-Y. Peng, S.-N. Song, W.-C. Jiang, S. Nagele, R. Pazourek, J. Burgdórfer, and Q. Gong, “Attosecond streaking of Cohen-Fano interferences in the photoionization of H$^+_2$2+,” Phys. Rev. A 90(1), 013423 (2014).
[Crossref]

J. Su, H. Ni, A. Becker, and A. Jaroń-Becker, “Attosecond-streaking time delays: Finite-range property and comparison of classical and quantum approaches,” Phys. Rev. A 89(1), 013404 (2014).
[Crossref]

2013 (5)

R. Pazourek, S. Nagele, and J. Burgdórfer, “Time-resolved photoemission on the attosecond scale: opportunities and challenges,” Faraday Discuss. 163, 353–376 (2013).
[Crossref]

G. Dixit, H. S. Chakraborty, and M.-A. Madjet, “Time Delay in the Recoiling Valence Photoemission of Ar Endohedrally Confined in C60,” Phys. Rev. Lett. 111(20), 203003 (2013).
[Crossref]

V. V. Serov, V. L. Derbov, and T. A. Sergeeva, “Interpretation of time delay in the ionization of two-center systems,” Phys. Rev. A 87(6), 063414 (2013).
[Crossref]

C. Liu, M. Reduzzi, A. Trabattoni, A. Sunilkumar, A. Dubrouil, F. Calegari, M. Nisoli, and G. Sansone, “Carrier-Envelope Phase Effects of a Single Attosecond Pulse in Two-Color Photoionization,” Phys. Rev. Lett. 111(12), 123901 (2013).
[Crossref]

J.-W. Geng, L.-Y. Peng, S.-N. Song, and Q. Gong, “Interference structures in photoelectron spectra of atoms ionized by XUV pulses in the presence of a strong IR field,” Phys. Rev. A 88(5), 053418 (2013).
[Crossref]

2012 (5)

D. D. Hickstein, P. Ranitovic, S. Witte, X.-M. Tong, Y. Huismans, P. Arpin, X. Zhou, K. Ellen Keister, C. W. Hogle, B. Zhang, C. Ding, P. Johnsson, and N. Toshima, “Direct Visualization of Laser-Driven Electron Multiple Scattering, and Tunneling Distance in Strong-Field Ionization,” Phys. Rev. Lett. 109(7), 073004 (2012).
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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).
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C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, and T. A. Miller, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature 483(7388), 194–197 (2012).
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I. A. Ivanov, A. S. Kheifets, and V. V. Serov, “Attosecond time-delay spectroscopy of the hydrogen molecule,” Phys. Rev. A 86(6), 063422 (2012).
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R. Pazourek, J. Feist, S. Nagele, and J. Burgdórfer, “Attosecond Streaking of Correlated Two-Electron Transitions in Helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
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2011 (5)

M. Ivanov and O. Smirnova, “How Accurate Is the Attosecond Streak Camera?” Phys. Rev. Lett. 107(21), 213605 (2011).
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S. Nagele, R. Pazourek, J. Feist, K. Doblhoff-Dier, C. Lemell, K. Tókési, and J. Burgdórfer, “Time-resolved photoemission by attosecond streaking: extraction of time information,” J. Phys. B 44(8), 081001 (2011).
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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. van der 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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M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
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X.-B. Bian, Y. Huismans, O. Smirnova, K.-J. Yuan, M. J. J. Vrakking, and A. D. Bandrauk, “Subcycle interference dynamics of time-resolved photoelectron holography with midinfrared laser pulses,” Phys. Rev. A 84(4), 043420 (2011).
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2010 (8)

D. G. Arbó, K. L. Ishikawa, K. Schiessl, E. Persson, and J. Burgdórfer, “Intracycle, and intercycle interferences in above-threshold ionization: The time grating,” Phys. Rev. A 81(2), 021403 (2010).
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C.-H. Zhang and U. Thumm, “Electron-ion interaction effects in attosecond time-resolved photoelectron spectra,” Phys. Rev. A 82(4), 043405 (2010).
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M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328(5986), 1658–1662 (2010).
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A. S. Kheifets and I. A. Ivanov, “Delay in Atomic Photoionization,” Phys. Rev. Lett. 105(23), 233002 (2010).
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J. C. Baggesen and L. B. Madsen, “Polarization Effects in Attosecond Photoelectron Spectroscopy,” Phys. Rev. Lett. 104(4), 043602 (2010).
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H. Wang, M. Chini, S. Chen, C.-H. Zhang, F. He, Y. Cheng, Y. Wu, U. Thumm, and Z. Chang, “Attosecond Time-Resolved Autoionization of Argon,” Phys. Rev. Lett. 105(14), 143002 (2010).
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S. Gilbertson, M. Chini, X. Feng, S. Khan, Y. Wu, and Z. Chang, “Monitoring and Controlling the Electron Dynamics in Helium with Isolated Attosecond Pulses,” Phys. Rev. Lett. 105(26), 263003 (2010).
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V. S. Yakovlev, J. Gagnon, N. Karpowicz, and F. Krausz, “Attosecond Streaking Enables the Measurement of Quantum Phase,” Phys. Rev. Lett. 105(7), 073001 (2010).
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2009 (4)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
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C.-H. Zhang and U. Thumm, “Attosecond photoelectron spectroscopy of metal surfaces,” Phys. Rev. Lett. 102(12), 123601 (2009).
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A. K. Kazansky and P. M. Echenique, “One-Electron Model for the Electronic Response of Metal Surfaces to Subfemtosecond Photoexcitation,” Phys. Rev. Lett. 102(17), 177401 (2009).
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C. Lemell, B. Solleder, K. Tókési, and J. Burgdórfer, “Simulation of attosecond streaking of electrons emitted from a tungsten surface,” Phys. Rev. A 79(6), 062901 (2009).
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2008 (3)

T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, and W. Sandner, “Strong-Field Tunneling without Ionization,” Phys. Rev. Lett. 101(23), 233001 (2008).
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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).
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J. Mauritsson, P. Johnsson, E. Mansten, M. Swoboda, T. Ruchon, A. L’Huillier, and K. J. Schafer, “Coherent Electron Scattering Captured by an Attosecond Quantum Stroboscope,” Phys. Rev. Lett. 100(7), 073003 (2008).
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2006 (2)

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314(5798), 443–446 (2006).
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T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2(5), 323–326 (2006).
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2005 (1)

M. Wickenhauser, J. Burgdórfer, F. Krausz, and M. Drescher, “Time Resolved Fano Resonances,” Phys. Rev. Lett. 94(2), 023002 (2005).
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2004 (3)

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427(6977), 817–821 (2004).
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E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct Measurement of Light Waves,” Science 305(5688), 1267–1269 (2004).
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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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2003 (1)

F. Quere, J. Itatani, G. L. Yudin, and P. B. Corkum, “Attosecond Spectral Shearing Interferometry,” Phys. Rev. Lett. 90(7), 073902 (2003).
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2001 (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, 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).
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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), 658–661 (2000).
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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), 389–486 (1997).
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1994 (1)

G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72(18), 2851–2854 (1994).
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1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
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1988 (1)

M. R. Hermann and J. A. Fleck, “Split-operator spectral method for solving the time-dependent Schrödinger equation in spherical coordinates,” Phys. Rev. A 38(12), 6000–6012 (1988).
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Agostini, P.

D. Kiesewetter, R. R. Jones, A. Camper, S. B. Schoun, P. Agostini, and L. F. DiMauro, “Probing electronic binding potentials with attosecond photoelectron wavepackets,” Nat. Phys. 14(1), 68–73 (2018).
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C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, and T. A. Miller, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature 483(7388), 194–197 (2012).
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P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, 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).
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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. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314(5798), 443–446 (2006).
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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).
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Arbó, D. G.

D. G. Arbó, K. L. Ishikawa, K. Schiessl, E. Persson, and J. Burgdórfer, “Intracycle, and intercycle interferences in above-threshold ionization: The time grating,” Phys. Rev. A 81(2), 021403 (2010).
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Arpin, P.

D. D. Hickstein, P. Ranitovic, S. Witte, X.-M. Tong, Y. Huismans, P. Arpin, X. Zhou, K. Ellen Keister, C. W. Hogle, B. Zhang, C. Ding, P. Johnsson, and N. Toshima, “Direct Visualization of Laser-Driven Electron Multiple Scattering, and Tunneling Distance in Strong-Field Ionization,” Phys. Rev. Lett. 109(7), 073004 (2012).
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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).
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Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, 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).
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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. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314(5798), 443–446 (2006).
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Azzeer, A. M.

M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328(5986), 1658–1662 (2010).
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Baggesen, J. C.

J. C. Baggesen and L. B. Madsen, “Polarization Effects in Attosecond Photoelectron Spectroscopy,” Phys. Rev. Lett. 104(4), 043602 (2010).
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Bakker, J. M.

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. van der 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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Balcou, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, 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).
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Baltuska, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427(6977), 817–821 (2004).
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E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct Measurement of Light Waves,” Science 305(5688), 1267–1269 (2004).
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Bammer, F.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427(6977), 817–821 (2004).
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Bandrauk, A. D.

X.-B. Bian and A. D. Bandrauk, “Orientation-dependent forward-backward photoelectron holography from asymmetric molecules,” Phys. Rev. A 89(3), 033423 (2014).
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X.-B. Bian, Y. Huismans, O. Smirnova, K.-J. Yuan, M. J. J. Vrakking, and A. D. Bandrauk, “Subcycle interference dynamics of time-resolved photoelectron holography with midinfrared laser pulses,” Phys. Rev. A 84(4), 043420 (2011).
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Bauer, D.

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. van der 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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Becker, A.

J. Su, H. Ni, A. Becker, and A. Jaroń-Becker, “Attosecond-streaking time delays: Finite-range property and comparison of classical and quantum approaches,” Phys. Rev. A 89(1), 013404 (2014).
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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. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314(5798), 443–446 (2006).
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Berden, G.

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. van der 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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Bian, X.-B.

X.-B. Bian and A. D. Bandrauk, “Orientation-dependent forward-backward photoelectron holography from asymmetric molecules,” Phys. Rev. A 89(3), 033423 (2014).
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X.-B. Bian, Y. Huismans, O. Smirnova, K.-J. Yuan, M. J. J. Vrakking, and A. D. Bandrauk, “Subcycle interference dynamics of time-resolved photoelectron holography with midinfrared laser pulses,” Phys. Rev. A 84(4), 043420 (2011).
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Blaga, C. I.

C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, and T. A. Miller, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature 483(7388), 194–197 (2012).
[Crossref]

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, 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).
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Burgdórfer, J.

Q.-C. Ning, L.-Y. Peng, S.-N. Song, W.-C. Jiang, S. Nagele, R. Pazourek, J. Burgdórfer, and Q. Gong, “Attosecond streaking of Cohen-Fano interferences in the photoionization of H$^+_2$2+,” Phys. Rev. A 90(1), 013423 (2014).
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R. Pazourek, S. Nagele, and J. Burgdórfer, “Time-resolved photoemission on the attosecond scale: opportunities and challenges,” Faraday Discuss. 163, 353–376 (2013).
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R. Pazourek, J. Feist, S. Nagele, and J. Burgdórfer, “Attosecond Streaking of Correlated Two-Electron Transitions in Helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
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S. Nagele, R. Pazourek, J. Feist, K. Doblhoff-Dier, C. Lemell, K. Tókési, and J. Burgdórfer, “Time-resolved photoemission by attosecond streaking: extraction of time information,” J. Phys. B 44(8), 081001 (2011).
[Crossref]

D. G. Arbó, K. L. Ishikawa, K. Schiessl, E. Persson, and J. Burgdórfer, “Intracycle, and intercycle interferences in above-threshold ionization: The time grating,” Phys. Rev. A 81(2), 021403 (2010).
[Crossref]

C. Lemell, B. Solleder, K. Tókési, and J. Burgdórfer, “Simulation of attosecond streaking of electrons emitted from a tungsten surface,” Phys. Rev. A 79(6), 062901 (2009).
[Crossref]

M. Wickenhauser, J. Burgdórfer, F. Krausz, and M. Drescher, “Time Resolved Fano Resonances,” Phys. Rev. Lett. 94(2), 023002 (2005).
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Burgdörfer, J.

M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328(5986), 1658–1662 (2010).
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Calegari, F.

C. Liu, M. Reduzzi, A. Trabattoni, A. Sunilkumar, A. Dubrouil, F. Calegari, M. Nisoli, and G. Sansone, “Carrier-Envelope Phase Effects of a Single Attosecond Pulse in Two-Color Photoionization,” Phys. Rev. Lett. 111(12), 123901 (2013).
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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. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314(5798), 443–446 (2006).
[Crossref]

Camper, A.

D. Kiesewetter, R. R. Jones, A. Camper, S. B. Schoun, P. Agostini, and L. F. DiMauro, “Probing electronic binding potentials with attosecond photoelectron wavepackets,” Nat. Phys. 14(1), 68–73 (2018).
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Cao, W.

M. Li, H. Xie, W. Cao, S. Luo, J. Tan, Y. Feng, B. Du, W. Zhang, Y. Li, Q. Zhang, P. Lan, Y. Zhou, and P. Lu, “Photoelectron holographic interferometry to probe the longitudinal momentum offset at the tunnel exit,” Phys. Rev. Lett. 122(18), 183202 (2019).
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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).
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Z. Yang, W. Cao, X. Chen, J. Zhang, Y. Mo, H. Xu, K. Mi, Q. Zhang, P. Lan, and P. Lu, “All-optical frequency resolved optical gating for isolated attosecond pulse reconstruction,” arXiv:1911.06427.

X. Huang, Q. Zhang, S. Xu, X. Fu, X. Han, W. Cao, and P. Lu, “Coulomb focusing in retrapped ionization with near-circularly polarized laser field,” arXiv:1911.09805.

Cattaneo, L.

J. Vos, L. Cattaneo, S. Patchkovskii, T. Zimmermann, C. Cirelli, M. Lucchini, A. Kheifets, A. S. Landsman, and U. Keller, “Orientation-dependent stereo Wigner time delay, and electron localization in a small molecule,” Science 360(6395), 1326–1330 (2018).
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Cauchy, C.

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. van der 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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Chakraborty, H. S.

G. Dixit, H. S. Chakraborty, and M.-A. Madjet, “Time Delay in the Recoiling Valence Photoemission of Ar Endohedrally Confined in C60,” Phys. Rev. Lett. 111(20), 203003 (2013).
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Chang, Z.

H. Wang, M. Chini, S. Chen, C.-H. Zhang, F. He, Y. Cheng, Y. Wu, U. Thumm, and Z. Chang, “Attosecond Time-Resolved Autoionization of Argon,” Phys. Rev. Lett. 105(14), 143002 (2010).
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S. Gilbertson, M. Chini, X. Feng, S. Khan, Y. Wu, and Z. Chang, “Monitoring and Controlling the Electron Dynamics in Helium with Isolated Attosecond Pulses,” Phys. Rev. Lett. 105(26), 263003 (2010).
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Chen, S.

H. Wang, M. Chini, S. Chen, C.-H. Zhang, F. He, Y. Cheng, Y. Wu, U. Thumm, and Z. Chang, “Attosecond Time-Resolved Autoionization of Argon,” Phys. Rev. Lett. 105(14), 143002 (2010).
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Chen, X.

Z. Yang, W. Cao, X. Chen, J. Zhang, Y. Mo, H. Xu, K. Mi, Q. Zhang, P. Lan, and P. Lu, “All-optical frequency resolved optical gating for isolated attosecond pulse reconstruction,” arXiv:1911.06427.

Chen, Y.

J. Tan, Y. Zhou, M. He, Y. Chen, Q. Ke, J. Liang, X. Zhu, M. Li, and P. Lu, “Determination of the Ionization Time Using Attosecond Photoelectron Interferometry,” Phys. Rev. Lett. 121(25), 253203 (2018).
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Figures (10)

Fig. 1.
Fig. 1. Schematic illustration of interference trajectories in attosecond streaking. The blue and red lines are the electric field of the SAP and IR pulses, respectively. A represents the direct electron ionized at the center of the SAP. B is the direct electron ionized by the IR field between $0.25T_1$ and $0.5T_1$. C and D are the rescattering electrons ionized at the center of the SAP and scatter from the ion on the first and second returning, respectively. $T_1$ is the optical cycle of IR field. The insert shows the electric field of the laser pulse when the time delay between the SAP and IR pulse is zero. The blue and orange solid lines are the electric field and the vector potential of the laser field, respectively. The black dotted line is the envelope of the IR field.
Fig. 2.
Fig. 2. PEMDs for ionization of model He atom ($I_p=-0.9$ a.u.) by numerically solving TDSE. The center frequencies of the SAP for (a) and (b) are $\omega _2=1.02$ a.u. and $\omega _2=1.55$ a.u., respectively. The intensities of the 1600-nm IR field and the SAP are $6\times 10^{13}$ W/cm$^2$ and $2\times 10^{14}$ W/cm$^2$. The time delay between the IR pulse and SAP is zero. The IR field and SAP are both polarized along the $x-$axis. I$-$VI represent six types of interference structures in the PEMDs.
Fig. 3.
Fig. 3. Interference structures calculated by the semiclassical model. (a) and (b) show the interference between the direct electrons ionized by the SAP and the electrons rescattering with the ions at the first returning. (a) and (b) are for the forward-rescattering and backward-rescattering, respectively. (c) shows the interference between the electrons ionized from the excited state by the IR field and the direct electrons ionized by the SAP. (d) is the interference structures originating from the interference between the forward-rescattering electrons ionized by the SAP and the electrons ionized from excited state by the IR field.
Fig. 4.
Fig. 4. (a) and (b) show the relationships between the final longitudinal momentum $p_x$ and the initial momentum $p_{0}$ for the rescattering occurring at the first (type C, Fig. 1) and the second (type D, Fig. 1) returning. The blue and red lines correspond to the forward-rescattering ($\theta _{0}=0$) and backward-rescattering electrons ($\theta =\pi$), respectively. The dash lines separate the different initial momenta for the same final backward-rescattering momentum which correspond to the short and long trajectories. (c) and (d) show the interference between the backward-rescattering electrons from short and long trajectories for the rescattering occurring at the first (type C) and the second (type D) returning.
Fig. 5.
Fig. 5. The PEMDs in the log scale for the ionization of the H atom by linearly polarized SAP in a linearly polarized IR field. The time delays $\tau$ between the SAP and the IR field for (a)-(d) are $0$, $T_1/12$, $T_1/6$ and $T_1/4$, respectively. Here, $T_1$ is the optical cycle of the IR field. The intensities of the 1600-nm IR field and the SAP are $1\times 10^{13}$ W/cm$^2$ and $2\times 10^{14}$ W/cm$^2$, respectively. The center frequency of the SAP is $0.54$ a.u.. The SAP and IR field are both polarized along $x-$axis.
Fig. 6.
Fig. 6. The PEMDs for ionization of the model H atom by SAP. (a) and (b) are the PEMDs for the linearly polarized SAP. The angles between the $x-$axis and the polarization direction of SAP are $0$ and $\pi /3$ for (a) and (b). (c) and (d) are the PEMDs for the right-hand circularly and left-hand circularly polarized SAP, respectively. The center frequency and the intensity of SAP are $0.54$ a.u. and $2\times 10^{14}$ W/cm$^2$. $\alpha$ is the angle between the direction of the electric final momentum and $x-$axis.
Fig. 7.
Fig. 7. The phase of the continuous electric wave packet calculated by SFA. $\alpha$ is the angle between the direction of the final momentum and $x-$axis as shown in Fig. 6(a). $\phi$ is the phase of the continuous EWPs ionized by the SAP which is calculated by SFA. (a) is the relationship of the phase of the initial EWPs and the direction of the final momentum for the linearly polarized SAP. (b) is the relationship for circularly polarized SAP. The blue solid and red dotted lines correspond to the left-hand and right-hand circularly polarized SAP, respectively.
Fig. 8.
Fig. 8. The PEMDs from ionization of H atom by a linearly polarized SAP in a linearly polarized IR field. The angles between the polarization direction of SAP and $x-$axis in (a)-(d) are $0$, $\pi /9$, $2\pi /9$ and $\pi /3$, respectively. The IR field is polarized at $x-$axis. The intensity of the 1600-nm IR field and the SAP is $1\times 10^{13}$ W/cm$^2$ and $2\times 10^{14}$ W/cm$^2$, respectively. The center frequency of the SAP is $0.54$ a.u.. The PEMD in black dotted box shows the interference minima change to the interference maxima.
Fig. 9.
Fig. 9. The PEMD from ionization of H atom by the right-hand circularly polarized SAP in an IR field linearly polarized along $x-$axis. The intensity of the 1600-nm IR field and the SAP is $1\times 10^{13}$ W/cm$^2$ and $2\times 10^{14}$ W/cm$^2$, respectively. The center frequency of the SAP is $0.54$ a.u..
Fig. 10.
Fig. 10. Analysis of the forward-rescattering hologram in right-hand circularly polarized SAP. (a) Cuts of the PEMDs at $p_x=0.3$ a.u. from Fig. 9 (right hand circularly polarized SAP) and Fig. 8(a) (linearly polarized SAP), as presented by the blue solid and red dashed lines, respectively. (b) The interference term $\cos \delta \phi$ extracted from the cuts in (a). (c) The phase difference $\delta \phi _{+,-}$ for $p_y>0$ (blue dash line) and $p_y<0$ (red solid line) obtained from the cuts in (a). (d) The phase difference $\Delta \phi =\delta \phi _+-\delta \phi _-$ as a function of $|p_y|$ extracted from (a) (the blue circle line) and calculated by SFA (the red solid line), respectively.

Equations (20)

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i Ψ ( r , t ) t = [ 2 2 + V ( r ) r E ( t ) ] Ψ ( r , t ) ,
E ( t ) = E IR ( t ) + E SAP ( t + τ ) ,
E SAP ( t + τ ) = E SAP f 2 ( t + τ ) ( cos [ ω 2 ( t + τ ) ] 1 1 + η 2 e x + sin [ ω 2 ( t + τ ) ] η 1 + η 2 e y ) .
E SAP ( t + τ ) = E SAP f 2 ( t + τ ) ( cos [ ω 2 ( t + τ ) ] cos θ e x + cos [ ω 2 ( t + τ ) ] sin θ e y ) .
d p ( t ) d t = E IR ( t ) .
p ( t ) = A ( t ) A ( t 0 ) + p 0 ,
r ( t ) = t 0 t p ( t ) d t + r 0 ,
p f = p 0 A ( t 0 ) .
r ( t s ) = E IR ω 1 2 cos ( ω t s ) E IR ω 1 2 cos ( ω t 0 ) + [ p 0 A ( t 0 ) ] ( t s t 0 ) = 0 ,
p s = A ( t s ) A ( t 0 ) + p 0 .
p f = [ p s cos θ 0 A ( t s ) ] e x + p s sin θ 0 e y .
S d SAP = t 0 t [ p x + A ( t ) 2 ] 2 d t + I p ( t t 0 ) + p y 2 2 ( t t 0 ) ,
S s SAP = t 0 t s [ A ( t ) A ( t 0 ) + p 0 2 ] 2 d t + t s t [ p x + A ( t ) 2 ] 2 d t + I p ( t t 0 ) + p y 2 2 ( t t s ) ,
S d IR = 1 2 t i IR t [ p x + A ( t ) ] 2 d t + I p ( t t i I R ) + p y 2 2 ( t t i IR ) ,
1 2 [ p x + A ( t i IR ) ] 2 + 1 2 p y 2 + I p = 0.
M 2 ( p ) = | M i ( p ) + M j ( p ) | 2 = | M i ( p ) | 2 + | M j ( p ) | 2 + 2 | M i ( p ) | | M j ( p ) | cos ( S i S j ) .
M ( p ) = ψ c r E | ψ 0 = | M ( p ) | e i ϕ ,
δ ϕ = 1 2 p y 2 ( t s t 0 ) + ϕ s + [ ϕ ( 0 ; t 0 ) ϕ ( p y ; t 0 ) ] ,
e f ( p y ) [ 1 + g ( p y ) c o s δ ϕ ] .
Δ ϕ = δ ϕ + δ ϕ = ϕ ( | p y | ) ϕ ( | p y | ) .

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