Abstract

Using semiclassical models with implementing interference effects, we study the low-energy photoelectron intra-half-cycle interferences among nonscattering trajectories and multiple forward scattering trajectories of atoms ionized by a strong mid-infrared laser field. Tracing back to the initial tunneling coordinates, we find that up to three kinds of forward scattering trajectories have substantial contributions to the low-energy photoelectrons. Those multiple forward scattering trajectories depend sensitively on the initial transverse momentum at the tunnel exit and they lead to sign reversal of the transverse momentum of the electrons. We show that the interference of the nonscattering trajectory and the triple-scattered trajectory has the largest contribution to the low-energy structure in mid-infrared laser fields. It is also shown that the long-range Coulomb potential has a significant effect on the low-energy photoelectron interference patterns.

© 2016 Optical Society of America

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2016 (9)

C. Zhai, L. He, P. Lan, X. Zhu, Y. Li, F. Wang, W. Shi, Q. Zhang, and P. Lu, “Coulomb-corrected molecular orbital tomography of nitrogen,” Sci. Rep. 6, 23236 (2016).
[Crossref] [PubMed]

X. Zhu, P. Lan, K. Liu, Y. Li, X. Liu, Q. Zhang, I. Barth, and P. Lu, “Helicity sensitive enhancement of strong-field ionization in circularly polarized laser fields,” Opt. Express 24(4), 4196–4209 (2016).
[Crossref] [PubMed]

X. Ma, Y. Zhou, and P. Lu, “Multiple recollisions in strong-field nonsequential double ionization,” Phys. Rev. A 93(1), 013425 (2016).
[Crossref]

Z. Wang, M. Li, Y. Zhou, Y. Li, P. Lan, and P. Lu, “Counterintuitive energy shifts in joint electron-nuclear-energy spectra of strong-field fragmentation of H2+,” Phys. Rev. A 93(1), 013418 (2016).
[Crossref]

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]

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]

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

M. Haertelt, X.-B. 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]

N. I. Shvetsov-Shilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, and K. Tőkési, “Semiclassical two-step model for strong-field ionization,” Phys. Rev. A 94(1), 013415 (2016).
[Crossref]

2015 (3)

A. Tong, Y. Zhou, and P. Lu, “Resolving subcycle electron emission in strong-field sequential double ionization,” Opt. Express 23(12), 15774–15783 (2015).
[Crossref] [PubMed]

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).
[Crossref]

M. Richter, M. Kunitski, M. Schöffler, T. Jahnke, L. P. H. Schmidt, M. Li, Y. Liu, and R. Dörner, “Streaking temporal double-slit interference by an orthogonal two-color laser field,” Phys. Rev. Lett. 114(14), 143001 (2015).
[Crossref] [PubMed]

2014 (2)

M. Li, J. W. Geng, H. Liu, Y. Deng, C. Wu, L. Y. Peng, Q. Gong, and Y. Liu, “Classical-quantum correspondence for above-threshold ionization,” Phys. Rev. Lett. 112(11), 113002 (2014).
[Crossref] [PubMed]

M. Möller, F. Meyer, A. M. Sayler, G. G. Paulus, M. F. Kling, B. E. Schmidt, W. Becker, and D. B. Milošević, “Off-axis low-energy structures in above-threshold ionization,” Phys. Rev. A 90(2), 023412 (2014).
[Crossref]

2013 (3)

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

J. Dura, N. Camus, A. Thai, A. Britz, M. Hemmer, M. Baudisch, A. Senftleben, C. D. Schröter, J. Ullrich, R. Moshammer, and J. Biegert, “Ionization with low-frequency fields in the tunneling regime,” Sci. Rep. 3, 2675 (2013).
[Crossref] [PubMed]

C. Lemell, J. Burgdörfer, S. Gräfe, K. I. Dimitriou, D. G. Arbó, and X.-M. Tong, “Classical-quantum correspondence in atomic ionization by midinfrared pulses: multiple peak and interference structures,” Phys. Rev. A 87(1), 013421 (2013).
[Crossref]

2012 (5)

X. Xie, S. Roither, D. Kartashov, E. Persson, D. G. Arbó, L. Zhang, S. Gräfe, M. S. Schöffler, J. Burgdörfer, A. Baltuška, and M. Kitzler, “Attosecond probe of valence-electron wave packets by subcycle sculpted laser fields,” Phys. Rev. Lett. 108(19), 193004(2012).
[Crossref] [PubMed]

C. Y. Wu, Y. D. Yang, Y. Q. Liu, Q. H. Gong, M. Y. Wu, X. Liu, X. L. Hao, W. D. Li, X. T. He, and J. Chen, “Characteristic spectrum of very low-energy photoelectron from above-threshold ionization in the tunneling regime,” Phys. Rev. lett. 109(4), 043001 (2012).
[Crossref] [PubMed]

A. Kästner, U. Saalmann, and J. M. Rost, “Electron-energy bunching in laser-driven soft recollisions,” Phys. Rev. Lett. 108(3), 033201 (2012).
[Crossref] [PubMed]

D. D. Hickstein, P. Ranitovic, S. Witte, X. M. 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.-B. 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 (3)

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).
[Crossref]

D. A. Telnov and S.-I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: Role of the Coulomb threshold effect,” Phys. Rev. A 83(6), 063406 (2011).
[Crossref]

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).
[Crossref]

2010 (4)

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

C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by midinfrared strong laser fields,” Phys. Rev. Lett. 105(11), 113003 (2010).
[Crossref] [PubMed]

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105(25), 253002 (2010).
[Crossref]

D. B. Milošević, W. Becker, M. Okunishi, G. Prümper, K. Shimada, and K. Ueda, “Strong-field electron spectra of rare-gas atoms in the rescattering regime: enhanced spectral regions and a simulation of the experiment,” J. Phys. B: At. Mol. Opt. Phys. 43(1), 015401 (2010).
[Crossref]

2009 (6)

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5(5), 335–338 (2009).
[Crossref]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
[Crossref] [PubMed]

F. H. M. Faisal, “Strong-field physics: ionization surprise,” Nat. Phys. 5(5), 319–320 (2009).
[Crossref]

M. Okunishi, R. Itaya, K. Shimada, G. Prumper, K. Ueda, M. Busuladzic, A. G. Busuladzic, D. B. Milosevic, and W. Becker, “Two-source double-slit interference in angle-resolved high-energy above-threshold ionization spectra of diatoms,” Phys. Rev. Lett. 103(4), 043001 (2009).
[Crossref] [PubMed]

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

R. Gopal, K. Simeonidis, R. Moshammer, T. Ergler, M. Dürr, M. Kurka, K. U. Kühnel, S. Tschuch, C.-D. Schröter, D. Bauer, J. Ullrich, A. Rudenko, O. Herrwerth, T. Uphues, M. Schultze, E. Goulielmakis, M. Uiberacker, M. Lezius, and M. F. Kling, “Three-dimensional momentum imaging of electron wave packet interference in few-cycle laser pulses,” Phys. Rev. Lett. 103(5), 053001 (2009).
[Crossref] [PubMed]

2008 (1)

T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, and W. Sandner, “Strong-field tunneling without ionization,” Phys. Rev. Lett. 101(23), 233001 (2008).
[Crossref] [PubMed]

2007 (1)

P. B. Corkum and F. Krausz, “Attosecond science,” Nature Phys. 3(6), 381–387 (2007).
[Crossref]

2006 (3)

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

C. C. Chirilǎ and M. Lein, “High-order above-threshold ionization in stretched molecules,” Phys. Rev. A 74(5), 051401 (2006).
[Crossref]

D. G. Arbó, E. Persson, and J. Burgdörfer, “Time double-slit interferences in strong-field tunneling ionization,” Phys. Rev. A 74(6), 063407 (2006).
[Crossref]

2005 (1)

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95(4), 040401 (2005).
[Crossref] [PubMed]

2004 (1)

C. Altucci, V. Tosa, R. Velotta, and C. H. Nam, “Dynamical medium depletion in high-order above-threshold ionization with few-cycle laser pulses,” Phys. Rev. A 70(6), 065402 (2004).
[Crossref]

2002 (1)

M. B. Gaarde and K. J. Schafer, “Quantum path distributions for high-order harmonics in rare gas atoms,” Phys. Rev. A 65(3), 031406 (2002).
[Crossref]

1993 (1)

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

1991 (1)

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Zh. Eksp. Teor. Fiz. 91(6), 2008(1986), [Sov. Phys. JETP 64(6), 1191–1194 (1986)].

1979 (1)

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42(11), 1127 (1979).
[Crossref]

Agostini, P.

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5(5), 335–338 (2009).
[Crossref]

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42(11), 1127 (1979).
[Crossref]

Altucci, C.

C. Altucci, V. Tosa, R. Velotta, and C. H. Nam, “Dynamical medium depletion in high-order above-threshold ionization with few-cycle laser pulses,” Phys. Rev. A 70(6), 065402 (2004).
[Crossref]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Zh. Eksp. Teor. Fiz. 91(6), 2008(1986), [Sov. Phys. JETP 64(6), 1191–1194 (1986)].

Arbó, D. G.

N. I. Shvetsov-Shilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, and K. Tőkési, “Semiclassical two-step model for strong-field ionization,” Phys. Rev. A 94(1), 013415 (2016).
[Crossref]

C. Lemell, J. Burgdörfer, S. Gräfe, K. I. Dimitriou, D. G. Arbó, and X.-M. Tong, “Classical-quantum correspondence in atomic ionization by midinfrared pulses: multiple peak and interference structures,” Phys. Rev. A 87(1), 013421 (2013).
[Crossref]

X. Xie, S. Roither, D. Kartashov, E. Persson, D. G. Arbó, L. Zhang, S. Gräfe, M. S. Schöffler, J. Burgdörfer, A. Baltuška, and M. Kitzler, “Attosecond probe of valence-electron wave packets by subcycle sculpted laser fields,” Phys. Rev. Lett. 108(19), 193004(2012).
[Crossref] [PubMed]

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

D. G. Arbó, E. Persson, and J. Burgdörfer, “Time double-slit interferences in strong-field tunneling ionization,” Phys. Rev. A 74(6), 063407 (2006).
[Crossref]

Arpin, P.

D. D. Hickstein, P. Ranitovic, S. Witte, X. M. 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]

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).
[Crossref]

Baltuška, A.

X. Xie, S. Roither, D. Kartashov, E. Persson, D. G. Arbó, L. Zhang, S. Gräfe, M. S. Schöffler, J. Burgdörfer, A. Baltuška, and M. Kitzler, “Attosecond probe of valence-electron wave packets by subcycle sculpted laser fields,” Phys. Rev. Lett. 108(19), 193004(2012).
[Crossref] [PubMed]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95(4), 040401 (2005).
[Crossref] [PubMed]

Bandrauk, A. D.

X.-B. Bian and A. D. Bandrauk, “Attosecond time-resolved imaging of molecular structure by photoelectron holography,” Phys. Rev. Lett. 108(26), 263003 (2012).
[Crossref] [PubMed]

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).
[Crossref]

Barth, I.

Baudisch, M.

J. Dura, N. Camus, A. Thai, A. Britz, M. Hemmer, M. Baudisch, A. Senftleben, C. D. Schröter, J. Ullrich, R. Moshammer, and J. Biegert, “Ionization with low-frequency fields in the tunneling regime,” Sci. Rep. 3, 2675 (2013).
[Crossref] [PubMed]

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).
[Crossref]

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105(25), 253002 (2010).
[Crossref]

R. Gopal, K. Simeonidis, R. Moshammer, T. Ergler, M. Dürr, M. Kurka, K. U. Kühnel, S. Tschuch, C.-D. Schröter, D. Bauer, J. Ullrich, A. Rudenko, O. Herrwerth, T. Uphues, M. Schultze, E. Goulielmakis, M. Uiberacker, M. Lezius, and M. F. Kling, “Three-dimensional momentum imaging of electron wave packet interference in few-cycle laser pulses,” Phys. Rev. Lett. 103(5), 053001 (2009).
[Crossref] [PubMed]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95(4), 040401 (2005).
[Crossref] [PubMed]

Becker, W.

M. Möller, F. Meyer, A. M. Sayler, G. G. Paulus, M. F. Kling, B. E. Schmidt, W. Becker, and D. B. Milošević, “Off-axis low-energy structures in above-threshold ionization,” Phys. Rev. A 90(2), 023412 (2014).
[Crossref]

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

D. B. Milošević, W. Becker, M. Okunishi, G. Prümper, K. Shimada, and K. Ueda, “Strong-field electron spectra of rare-gas atoms in the rescattering regime: enhanced spectral regions and a simulation of the experiment,” J. Phys. B: At. Mol. Opt. Phys. 43(1), 015401 (2010).
[Crossref]

M. Okunishi, R. Itaya, K. Shimada, G. Prumper, K. Ueda, M. Busuladzic, A. G. Busuladzic, D. B. Milosevic, and W. Becker, “Two-source double-slit interference in angle-resolved high-energy above-threshold ionization spectra of diatoms,” Phys. Rev. Lett. 103(4), 043001 (2009).
[Crossref] [PubMed]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95(4), 040401 (2005).
[Crossref] [PubMed]

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).
[Crossref]

Bian, X.-B.

M. Haertelt, X.-B. 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.-B. Bian and A. D. Bandrauk, “Attosecond time-resolved imaging of molecular structure by photoelectron holography,” Phys. Rev. Lett. 108(26), 263003 (2012).
[Crossref] [PubMed]

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).
[Crossref]

Biegert, J.

J. Dura, N. Camus, A. Thai, A. Britz, M. Hemmer, M. Baudisch, A. Senftleben, C. D. Schröter, J. Ullrich, R. Moshammer, and J. Biegert, “Ionization with low-frequency fields in the tunneling regime,” Sci. Rep. 3, 2675 (2013).
[Crossref] [PubMed]

Blaga, C. I.

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5(5), 335–338 (2009).
[Crossref]

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

Britz, A.

J. Dura, N. Camus, A. Thai, A. Britz, M. Hemmer, M. Baudisch, A. Senftleben, C. D. Schröter, J. Ullrich, R. Moshammer, and J. Biegert, “Ionization with low-frequency fields in the tunneling regime,” Sci. Rep. 3, 2675 (2013).
[Crossref] [PubMed]

Burgdörfer, J.

N. I. Shvetsov-Shilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, and K. Tőkési, “Semiclassical two-step model for strong-field ionization,” Phys. Rev. A 94(1), 013415 (2016).
[Crossref]

C. Lemell, J. Burgdörfer, S. Gräfe, K. I. Dimitriou, D. G. Arbó, and X.-M. Tong, “Classical-quantum correspondence in atomic ionization by midinfrared pulses: multiple peak and interference structures,” Phys. Rev. A 87(1), 013421 (2013).
[Crossref]

X. Xie, S. Roither, D. Kartashov, E. Persson, D. G. Arbó, L. Zhang, S. Gräfe, M. S. Schöffler, J. Burgdörfer, A. Baltuška, and M. Kitzler, “Attosecond probe of valence-electron wave packets by subcycle sculpted laser fields,” Phys. Rev. Lett. 108(19), 193004(2012).
[Crossref] [PubMed]

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

D. G. Arbó, E. Persson, and J. Burgdörfer, “Time double-slit interferences in strong-field tunneling ionization,” Phys. Rev. A 74(6), 063407 (2006).
[Crossref]

Busuladzic, A. G.

M. Okunishi, R. Itaya, K. Shimada, G. Prumper, K. Ueda, M. Busuladzic, A. G. Busuladzic, D. B. Milosevic, and W. Becker, “Two-source double-slit interference in angle-resolved high-energy above-threshold ionization spectra of diatoms,” Phys. Rev. Lett. 103(4), 043001 (2009).
[Crossref] [PubMed]

Busuladzic, M.

M. Okunishi, R. Itaya, K. Shimada, G. Prumper, K. Ueda, M. Busuladzic, A. G. Busuladzic, D. B. Milosevic, and W. Becker, “Two-source double-slit interference in angle-resolved high-energy above-threshold ionization spectra of diatoms,” Phys. Rev. Lett. 103(4), 043001 (2009).
[Crossref] [PubMed]

Camus, N.

J. Dura, N. Camus, A. Thai, A. Britz, M. Hemmer, M. Baudisch, A. Senftleben, C. D. Schröter, J. Ullrich, R. Moshammer, and J. Biegert, “Ionization with low-frequency fields in the tunneling regime,” Sci. Rep. 3, 2675 (2013).
[Crossref] [PubMed]

Catoire, F.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5(5), 335–338 (2009).
[Crossref]

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).
[Crossref]

Chen, J.

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

C. Y. Wu, Y. D. Yang, Y. Q. Liu, Q. H. Gong, M. Y. Wu, X. Liu, X. L. Hao, W. D. Li, X. T. He, and J. Chen, “Characteristic spectrum of very low-energy photoelectron from above-threshold ionization in the tunneling regime,” Phys. Rev. lett. 109(4), 043001 (2012).
[Crossref] [PubMed]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
[Crossref] [PubMed]

Chen, S. G.

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
[Crossref] [PubMed]

Cheng, Y.

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
[Crossref] [PubMed]

Chirila, C. C.

C. C. Chirilǎ and M. Lein, “High-order above-threshold ionization in stretched molecules,” Phys. Rev. A 74(5), 051401 (2006).
[Crossref]

Chu, S.-I.

D. A. Telnov and S.-I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: Role of the Coulomb threshold effect,” Phys. Rev. A 83(6), 063406 (2011).
[Crossref]

Colosimo, P.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5(5), 335–338 (2009).
[Crossref]

Corkum, P.

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

Corkum, P. B.

M. Haertelt, X.-B. 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]

P. B. Corkum and F. Krausz, “Attosecond science,” Nature Phys. 3(6), 381–387 (2007).
[Crossref]

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

Delone, N. B.

N. B. Delone and V. P. Krainov, “Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation,” J. Opt. Soc. Am. B 8(6), 1207–1211 (1991).
[Crossref]

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Zh. Eksp. Teor. Fiz. 91(6), 2008(1986), [Sov. Phys. JETP 64(6), 1191–1194 (1986)].

Deng, Y.

M. Li, J. W. Geng, H. Liu, Y. Deng, C. Wu, L. Y. Peng, Q. Gong, and Y. Liu, “Classical-quantum correspondence for above-threshold ionization,” Phys. Rev. Lett. 112(11), 113002 (2014).
[Crossref] [PubMed]

DiChiara, A. D.

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

DiMauro, L. F.

L. Guo, S. S. Han, X. Liu, Y. Cheng, Z. Z. Xu, J. Fan, J. Chen, S. G. Chen, W. Becker, C. I. Blaga, A. D. DiChiara, E. Sistrunk, P. Agostini, and L. F. DiMauro, “Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment,” Phys. Rev. Lett. 110 (1), 013001 (2013).
[Crossref] [PubMed]

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5(5), 335–338 (2009).
[Crossref]

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

Dimitriou, K. I.

C. Lemell, J. Burgdörfer, S. Gräfe, K. I. Dimitriou, D. G. Arbó, and X.-M. Tong, “Classical-quantum correspondence in atomic ionization by midinfrared pulses: multiple peak and interference structures,” Phys. Rev. A 87(1), 013421 (2013).
[Crossref]

Ding, C.

D. D. Hickstein, P. Ranitovic, S. Witte, X. M. 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]

Doherty, B. J. S.

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

Dörner, R.

M. Richter, M. Kunitski, M. Schöffler, T. Jahnke, L. P. H. Schmidt, M. Li, Y. Liu, and R. Dörner, “Streaking temporal double-slit interference by an orthogonal two-color laser field,” Phys. Rev. Lett. 114(14), 143001 (2015).
[Crossref] [PubMed]

Dudovich, N.

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

Dura, J.

J. Dura, N. Camus, A. Thai, A. Britz, M. Hemmer, M. Baudisch, A. Senftleben, C. D. Schröter, J. Ullrich, R. Moshammer, and J. Biegert, “Ionization with low-frequency fields in the tunneling regime,” Sci. Rep. 3, 2675 (2013).
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Dürr, M.

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Yan, T. M.

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105(25), 253002 (2010).
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Yuan, K.-J.

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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Zamith, S.

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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Zhai, C.

C. Zhai, L. He, P. Lan, X. Zhu, Y. Li, F. Wang, W. Shi, Q. Zhang, and P. Lu, “Coulomb-corrected molecular orbital tomography of nitrogen,” Sci. Rep. 6, 23236 (2016).
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Zhang, B.

D. D. Hickstein, P. Ranitovic, S. Witte, X. M. 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).
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Zhang, L.

X. Xie, S. Roither, D. Kartashov, E. Persson, D. G. Arbó, L. Zhang, S. Gräfe, M. S. Schöffler, J. Burgdörfer, A. Baltuška, and M. Kitzler, “Attosecond probe of valence-electron wave packets by subcycle sculpted laser fields,” Phys. Rev. Lett. 108(19), 193004(2012).
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Zhang, P.

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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Zhang, Q.

C. Zhai, L. He, P. Lan, X. Zhu, Y. Li, F. Wang, W. Shi, Q. Zhang, and P. Lu, “Coulomb-corrected molecular orbital tomography of nitrogen,” Sci. Rep. 6, 23236 (2016).
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X. Zhu, P. Lan, K. Liu, Y. Li, X. Liu, Q. Zhang, I. Barth, and P. Lu, “Helicity sensitive enhancement of strong-field ionization in circularly polarized laser fields,” Opt. Express 24(4), 4196–4209 (2016).
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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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Zhou, X.

D. D. Hickstein, P. Ranitovic, S. Witte, X. M. 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).
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Zhou, Y.

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).
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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).
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Z. Wang, M. Li, Y. Zhou, Y. Li, P. Lan, and P. Lu, “Counterintuitive energy shifts in joint electron-nuclear-energy spectra of strong-field fragmentation of H2+,” Phys. Rev. A 93(1), 013418 (2016).
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X. Ma, Y. Zhou, and P. Lu, “Multiple recollisions in strong-field nonsequential double ionization,” Phys. Rev. A 93(1), 013425 (2016).
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A. Tong, Y. Zhou, and P. Lu, “Resolving subcycle electron emission in strong-field sequential double ionization,” Opt. Express 23(12), 15774–15783 (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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Zhu, X.

C. Zhai, L. He, P. Lan, X. Zhu, Y. Li, F. Wang, W. Shi, Q. Zhang, and P. Lu, “Coulomb-corrected molecular orbital tomography of nitrogen,” Sci. Rep. 6, 23236 (2016).
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X. Zhu, P. Lan, K. Liu, Y. Li, X. Liu, Q. Zhang, I. Barth, and P. Lu, “Helicity sensitive enhancement of strong-field ionization in circularly polarized laser fields,” Opt. Express 24(4), 4196–4209 (2016).
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Z. Wang, M. Li, Y. Zhou, Y. Li, P. Lan, and P. Lu, “Counterintuitive energy shifts in joint electron-nuclear-energy spectra of strong-field fragmentation of H2+,” Phys. Rev. A 93(1), 013418 (2016).
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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).
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Figures (5)

Fig. 1
Fig. 1 Two-dimensional PADs of H atoms ionized by an eight-cycle pulses as shown by the top panel using the QTMC model. Red area in electric fields on the top of PADs are the electron ionization time windows for (a) four cycles pulse (b) half-cycle pulse. The dash lines in (b) are used to guide the inner spider structure and the solid lines are used to guide the primary spider structure. The structures A and B show parts of electrons in the lower-energy region (0 < pz < 0.32 a.u.) and higher-energy region (pz > 0.32 a.u.), respectively.
Fig. 2
Fig. 2 (a) The electron final transverse momentum with respect to initial transverse momentum and the electron ionization time. Red color represents positive final transverse momentum, blue color represents negative final transverse momentum, and gray color represents unionized electrons (frustrated tunneling ionization). The ionization probability is not included in (a). Panels (b) and (c) show the density plots of the ionization probability with respect to the initial transverse momentum and the ionization time corresponding to the area A and area B in Fig. 1(b), respectively. I represents the indirect trajectory, and II–IV represent different forward scattering trajectories (see text for details).
Fig. 3
Fig. 3 Panels (a) and (b) show the typical trajectories of I–IV in Fig. 2(b) using the QTMC model. (c) The electrons transverse momenta evolution corresponding to the four trajectories in (a) and (b). I is the indirect electron and II III and IV stand for the single, double and triple forward scattering electrons, respectively. z is the laser polarization direction and x is the transverse direction. All the trajectories have the same final momentum.
Fig. 4
Fig. 4 (a)–(c) are the interference patterns from the interference between indirect trajectory and the single, double and triple-scattered trajectory using the semi-classical recollision model, respectively. The relative contributions of each interference pattern are not included. The schematic diagrams on the bottom row illustrate the indirect trajectory (ID) and the forward rescattering trajectories (S).
Fig. 5
Fig. 5 The time difference between the rescattering and the ionization with respect to the final momentum pz, for the single (solid), double (dashed) and triple (dot dashed) forward scattering trajectories, respectively.

Equations (8)

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S i = v 0 r ( t 0 ) + I p t 0 + t 0 { v i 2 ( t ) / 2 2 Z / | r ( t ) | } d t ,
E ( t ) = E 0 sin ( ω t + φ ) f ( t ) z ^ ,
f ( t ) = { t 2 T , 0 < t 2 T , 1 , 2 T < t 6 T , 8 T t 2 T , 6 T < t 8 T ,
v z = E 0 ω [ cos ( ω t ) cos ( ω t 0 ) ] .
sin ( ω t c ) sin ( ω t 0 sig ) ω ( t c t 0 sig ) cos ( ω t 0 sig ) = 0 .
p z = E 0 ω cos ( ω t c ) + v c cos ( θ c ) , p x = v c sin ( θ c ) ,
t 0 ref = 1 ω [ π cos 1 ( ω p z / E 0 ) ] , v x = p x .
Δ S 0 = 1 2 t 0 sig t c v z 2 d t 1 2 t 0 ref t c v z 2 d t 1 2 v x 2 ( t c t 0 ref ) I p ( t 0 sig t 0 ref )

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