Abstract

The space-time properties of the expressions of sub-cycle and single-cycle focused optical pulses with radially polarized electromagnetic field based on the Sink-Source model are studied. The self-induced blue shift of the center frequency of spectrum in the center of the pulse field is found to have an important impact on the electrons acceleration. When the electrons approach to the center of pulse, the electrons will obtain a large kinetic energy gain in a short time. The effect of radiation-reaction force can’t be ignored if the net kinetic energy gain of electrons is more than GeVs. The electrons will deviate from the original acceleration channel and the gain of kinetic energy that electrons may gain will be greatly reduced if the radiation-reaction effect is considered. In contrast to the few-cycle laser pulse accelerating electrons, the gain of kinetic energy obtained by electrons is a few times higher and the corresponding peak optical power is one order of magnitude lower in the case of the sub-cycle laser pulses accelerating electrons. The maximal kinetic energy gain of electrons is robust against the variation of the incident angles.

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

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References

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    [Crossref] [PubMed]

2017 (3)

C. N. Harvey, A. Gonoskov, A. Ilderton, and M. Marklund, “Quantum Quenching of Radiation Losses in Short Laser Pulses,” Phys. Rev. Lett. 118(10), 105004 (2017).
[Crossref] [PubMed]

Z. Zhang, L. Yan, Y. Du, W. Huang, C. Tang, and Z. Huang, “Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam,” Phys. Rev. Accel. Beams 20(5), 050701 (2017).
[Crossref]

A. Vikartofsky, L. W. Pi, and A. F. Starace, “Discontinuities in the electromagnetic fields of vortex beams in the complex source-sink model,” Phys. Rev. A. 95(5), 053826 (2017).
[Crossref]

2016 (2)

X. M. Cai, J. Y. Zhao, Q. Lin, and J. L. Luo, “Electron acceleration by subcycle pulsed focused vector beams,” J. Opt. Soc. Am. B 33(2), 158–164 (2016).
[Crossref]

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

2015 (1)

S. M. Mahajan, F. A. Asenjo, and R. D. Hazeltine, “Comparison of the electron-spin force and radiation reaction force,” Mon. Not. R. Astron. Soc. 446(4), 4112–4115 (2015).
[Crossref]

2014 (1)

F. Terranova, “Particle acceleration in subcycle optical cells,” Phys. Rev. Spec. Top. Accel. Beams 17(7), 071301 (2014).
[Crossref]

2013 (2)

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

A. A. Voronin, J. M. Mikhailova, M. Gorjan, Z. Major, and A. M. Zheltikov, “Pulse compression to subcycle field waveforms with split-dispersion cascaded hollow fibers,” Opt. Lett. 38(21), 4354–4357 (2013).
[Crossref] [PubMed]

2012 (2)

V. Marceau, A. April, and M. Piché, “Electron acceleration driven by ultrashort and nonparaxial radially polarized laser pulses,” Opt. Lett. 37(13), 2442–2444 (2012).
[Crossref] [PubMed]

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

2011 (2)

J. L. Liu, Z. M. Sheng, and J. Zheng, “Exact solution of the vectorial field structure of a light beam,” Opt. Commun. 284(19), 4646–4649 (2011).
[Crossref]

J. Zheng, E. M. Qiu, and Q. Lin, “High harmonic generation with sub-cycle pulses,” J. Opt. 13(7), 075206 (2011).
[Crossref]

2010 (2)

R. Martinez-Herrero, P. M. Mejias, and A. Manjavacas, “On the longitudinal polarization of non-paraxial electromagnetic fields,” Appl. Phys. B 99(3), 579–584 (2010).
[Crossref]

Q. Lin, J. Zheng, J. Dai, I. Chen Ho, and X. C. Zhang, “Intrinsic chirp of single-cycle pulses,” Phys. Rev. A 81(4), 043821 (2010).
[Crossref]

2009 (2)

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

E. N. Nerush and I. Yu. Kostyukov, “Carrier-Envelope Phase Effects in Plasma-Based Electron Acceleration with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 103(3), 035001 (2009).
[Crossref] [PubMed]

2006 (1)

Q. Lin, J. Zheng, and W. Becker, “Subcycle Pulsed Focused Vector Beams,” Phys. Rev. Lett. 97(25), 253902 (2006).
[Crossref] [PubMed]

2005 (1)

C. Varin, M. Piché, and M. A. Porras, “Acceleration of electrons from rest to GeV energies by ultrashort transverse magnetic laser pulses in free space,” Phys. Rev. E. 71(2), 026603 (2005).
[Crossref] [PubMed]

2003 (1)

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

2001 (2)

R. Martínez-Herrero, P. M. Mejías, S. Bosch, and A. Carnicer, “Vectorial structure of nonparaxial electromagnetic beams,” J. Opt. Soc. Am. A 18(7), 1678–1680 (2001).
[Crossref] [PubMed]

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

2000 (2)

H. Spohn, “The critical manifold of the Lorentz-Dirac equation,” Europhys. Lett. 50(3), 287–292 (2000).
[Crossref]

Y. I. Salamin and F. H. M. Faisal, “Ultrahigh electron acceleration and Compton emission spectra in a superintense laser pulse and a uniform axial magnetic field,” Phys. Rev. A 61(4), 043801 (2000).
[Crossref]

1999 (1)

C. F. R. Caron and R. M. Potvliege, “Free-space propagation of ultrashort pulses: Space-time couplings in Gaussian pulse beams,” J. Mod. Opt. 46(13), 1881–1891 (1999).
[Crossref]

1998 (1)

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: A scalar treatment,” Phys. Rev. A 57(4), 2971–2979 (1998).
[Crossref]

1997 (1)

B. Rau, T. Tajima, and H. Hojo, “Coherent Electron Acceleration by Subcycle Laser Pulses,” Phys. Rev. Lett. 78(17), 3310–3313 (1997).
[Crossref]

1994 (1)

J. P. Costella and B. H. J. McKellar, “Electromagnetic Deflection of Spinning Particles,” Int. J. Mod. Phys. A 9(3), 461–473 (1994).
[Crossref]

1987 (1)

April, A.

Asenjo, F. A.

S. M. Mahajan, F. A. Asenjo, and R. D. Hazeltine, “Comparison of the electron-spin force and radiation reaction force,” Mon. Not. R. Astron. Soc. 446(4), 4112–4115 (2015).
[Crossref]

Becker, W.

Q. Lin, J. Zheng, and W. Becker, “Subcycle Pulsed Focused Vector Beams,” Phys. Rev. Lett. 97(25), 253902 (2006).
[Crossref] [PubMed]

Benavides, S.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Bochkarev, S. G.

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

Bosch, S.

Buck, A.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Bychenkov, V. Yu.

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

Cai, X. M.

Cao, N.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Carbajo, S.

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

Carnicer, A.

Caron, C. F. R.

C. F. R. Caron and R. M. Potvliege, “Free-space propagation of ultrashort pulses: Space-time couplings in Gaussian pulse beams,” J. Mod. Opt. 46(13), 1881–1891 (1999).
[Crossref]

Chen Ho, I.

Q. Lin, J. Zheng, J. Dai, I. Chen Ho, and X. C. Zhang, “Intrinsic chirp of single-cycle pulses,” Phys. Rev. A 81(4), 043821 (2010).
[Crossref]

Costella, J. P.

J. P. Costella and B. H. J. McKellar, “Electromagnetic Deflection of Spinning Particles,” Int. J. Mod. Phys. A 9(3), 461–473 (1994).
[Crossref]

Dai, J.

Q. Lin, J. Zheng, J. Dai, I. Chen Ho, and X. C. Zhang, “Intrinsic chirp of single-cycle pulses,” Phys. Rev. A 81(4), 043821 (2010).
[Crossref]

Du, Y.

Z. Zhang, L. Yan, Y. Du, W. Huang, C. Tang, and Z. Huang, “Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam,” Phys. Rev. Accel. Beams 20(5), 050701 (2017).
[Crossref]

Dudnikova, G. I.

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

Dunning, M.

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

Dwayne Miller, R. J.

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

Esarey, E.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Faisal, F. H. M.

Y. I. Salamin and F. H. M. Faisal, “Ultrahigh electron acceleration and Compton emission spectra in a superintense laser pulse and a uniform axial magnetic field,” Phys. Rev. A 61(4), 043801 (2000).
[Crossref]

Felsen, L. B.

Fourmaux, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Fu, F.

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

Geissler, M.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Gonoskov, A.

C. N. Harvey, A. Gonoskov, A. Ilderton, and M. Marklund, “Quantum Quenching of Radiation Losses in Short Laser Pulses,” Phys. Rev. Lett. 118(10), 105004 (2017).
[Crossref] [PubMed]

Gorjan, M.

Habs, D.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Harvey, C. N.

C. N. Harvey, A. Gonoskov, A. Ilderton, and M. Marklund, “Quantum Quenching of Radiation Losses in Short Laser Pulses,” Phys. Rev. Lett. 118(10), 105004 (2017).
[Crossref] [PubMed]

Hast, C.

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

Hazeltine, R. D.

S. M. Mahajan, F. A. Asenjo, and R. D. Hazeltine, “Comparison of the electron-spin force and radiation reaction force,” Mon. Not. R. Astron. Soc. 446(4), 4112–4115 (2015).
[Crossref]

Hemsing, E.

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

Herrmann, D.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Heyman, E.

Hidding, B.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Ho, Y. K.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Hojo, H.

B. Rau, T. Tajima, and H. Hojo, “Coherent Electron Acceleration by Subcycle Laser Pulses,” Phys. Rev. Lett. 78(17), 3310–3313 (1997).
[Crossref]

Huang, W.

Z. Zhang, L. Yan, Y. Du, W. Huang, C. Tang, and Z. Huang, “Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam,” Phys. Rev. Accel. Beams 20(5), 050701 (2017).
[Crossref]

Huang, Z.

Z. Zhang, L. Yan, Y. Du, W. Huang, C. Tang, and Z. Huang, “Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam,” Phys. Rev. Accel. Beams 20(5), 050701 (2017).
[Crossref]

Ilderton, A.

C. N. Harvey, A. Gonoskov, A. Ilderton, and M. Marklund, “Quantum Quenching of Radiation Losses in Short Laser Pulses,” Phys. Rev. Lett. 118(10), 105004 (2017).
[Crossref] [PubMed]

Keathley, P. D.

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

Kieffer, J. C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Kong, Q.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Kostyukov, I. Yu.

E. N. Nerush and I. Yu. Kostyukov, “Carrier-Envelope Phase Effects in Plasma-Based Electron Acceleration with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 103(3), 035001 (2009).
[Crossref] [PubMed]

Krausz, F.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Laurent, G.

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

Légaré, F.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Lin, Q.

X. M. Cai, J. Y. Zhao, Q. Lin, and J. L. Luo, “Electron acceleration by subcycle pulsed focused vector beams,” J. Opt. Soc. Am. B 33(2), 158–164 (2016).
[Crossref]

J. Zheng, E. M. Qiu, and Q. Lin, “High harmonic generation with sub-cycle pulses,” J. Opt. 13(7), 075206 (2011).
[Crossref]

Q. Lin, J. Zheng, J. Dai, I. Chen Ho, and X. C. Zhang, “Intrinsic chirp of single-cycle pulses,” Phys. Rev. A 81(4), 043821 (2010).
[Crossref]

Q. Lin, J. Zheng, and W. Becker, “Subcycle Pulsed Focused Vector Beams,” Phys. Rev. Lett. 97(25), 253902 (2006).
[Crossref] [PubMed]

Liu, J. L.

J. L. Liu, Z. M. Sheng, and J. Zheng, “Exact solution of the vectorial field structure of a light beam,” Opt. Commun. 284(19), 4646–4649 (2011).
[Crossref]

Luo, J. L.

MacLean, J. P.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Mahajan, S. M.

S. M. Mahajan, F. A. Asenjo, and R. D. Hazeltine, “Comparison of the electron-spin force and radiation reaction force,” Mon. Not. R. Astron. Soc. 446(4), 4112–4115 (2015).
[Crossref]

Major, Z.

Maksimchuk, A.

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

Manjavacas, A.

R. Martinez-Herrero, P. M. Mejias, and A. Manjavacas, “On the longitudinal polarization of non-paraxial electromagnetic fields,” Appl. Phys. B 99(3), 579–584 (2010).
[Crossref]

Marceau, V.

Marcinkevicius, A.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Marklund, M.

C. N. Harvey, A. Gonoskov, A. Ilderton, and M. Marklund, “Quantum Quenching of Radiation Losses in Short Laser Pulses,” Phys. Rev. Lett. 118(10), 105004 (2017).
[Crossref] [PubMed]

Martinez-Herrero, R.

R. Martinez-Herrero, P. M. Mejias, and A. Manjavacas, “On the longitudinal polarization of non-paraxial electromagnetic fields,” Appl. Phys. B 99(3), 579–584 (2010).
[Crossref]

Martínez-Herrero, R.

McKellar, B. H. J.

J. P. Costella and B. H. J. McKellar, “Electromagnetic Deflection of Spinning Particles,” Int. J. Mod. Phys. A 9(3), 461–473 (1994).
[Crossref]

Mejias, P. M.

R. Martinez-Herrero, P. M. Mejias, and A. Manjavacas, “On the longitudinal polarization of non-paraxial electromagnetic fields,” Appl. Phys. B 99(3), 579–584 (2010).
[Crossref]

Mejías, P. M.

Meyer-Ter-Vehn, J.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Mikhailova, J. M.

Moriena, G.

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

Mourou, G.

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

Nanni, E. A.

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

Nees, J.

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

Nerush, E. N.

E. N. Nerush and I. Yu. Kostyukov, “Carrier-Envelope Phase Effects in Plasma-Based Electron Acceleration with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 103(3), 035001 (2009).
[Crossref] [PubMed]

Nishida, Y.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Payeur, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Pi, L. W.

A. Vikartofsky, L. W. Pi, and A. F. Starace, “Discontinuities in the electromagnetic fields of vortex beams in the complex source-sink model,” Phys. Rev. A. 95(5), 053826 (2017).
[Crossref]

Piche, M.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Piché, M.

V. Marceau, A. April, and M. Piché, “Electron acceleration driven by ultrashort and nonparaxial radially polarized laser pulses,” Opt. Lett. 37(13), 2442–2444 (2012).
[Crossref] [PubMed]

C. Varin, M. Piché, and M. A. Porras, “Acceleration of electrons from rest to GeV energies by ultrashort transverse magnetic laser pulses in free space,” Phys. Rev. E. 71(2), 026603 (2005).
[Crossref] [PubMed]

Porras, M. A.

C. Varin, M. Piché, and M. A. Porras, “Acceleration of electrons from rest to GeV energies by ultrashort transverse magnetic laser pulses in free space,” Phys. Rev. E. 71(2), 026603 (2005).
[Crossref] [PubMed]

Potvliege, R. M.

C. F. R. Caron and R. M. Potvliege, “Free-space propagation of ultrashort pulses: Space-time couplings in Gaussian pulse beams,” J. Mod. Opt. 46(13), 1881–1891 (1999).
[Crossref]

Qiu, E. M.

J. Zheng, E. M. Qiu, and Q. Lin, “High harmonic generation with sub-cycle pulses,” J. Opt. 13(7), 075206 (2011).
[Crossref]

Rau, B.

B. Rau, T. Tajima, and H. Hojo, “Coherent Electron Acceleration by Subcycle Laser Pulses,” Phys. Rev. Lett. 78(17), 3310–3313 (1997).
[Crossref]

Raubenheimer, T. O.

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

Saghafi, S.

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: A scalar treatment,” Phys. Rev. A 57(4), 2971–2979 (1998).
[Crossref]

Salamin, Y. I.

Y. I. Salamin and F. H. M. Faisal, “Ultrahigh electron acceleration and Compton emission spectra in a superintense laser pulse and a uniform axial magnetic field,” Phys. Rev. A 61(4), 043801 (2000).
[Crossref]

Schmid, K.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Schmidt, B. E.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Schramm, U.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Sessler, A. M.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Sheng, Z. M.

J. L. Liu, Z. M. Sheng, and J. Zheng, “Exact solution of the vectorial field structure of a light beam,” Opt. Commun. 284(19), 4646–4649 (2011).
[Crossref]

Sheppard, C. J. R.

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: A scalar treatment,” Phys. Rev. A 57(4), 2971–2979 (1998).
[Crossref]

Spohn, H.

H. Spohn, “The critical manifold of the Lorentz-Dirac equation,” Europhys. Lett. 50(3), 287–292 (2000).
[Crossref]

Starace, A. F.

A. Vikartofsky, L. W. Pi, and A. F. Starace, “Discontinuities in the electromagnetic fields of vortex beams in the complex source-sink model,” Phys. Rev. A. 95(5), 053826 (2017).
[Crossref]

Steinberg, B. Z.

Tajima, T.

B. Rau, T. Tajima, and H. Hojo, “Coherent Electron Acceleration by Subcycle Laser Pulses,” Phys. Rev. Lett. 78(17), 3310–3313 (1997).
[Crossref]

Tang, C.

Z. Zhang, L. Yan, Y. Du, W. Huang, C. Tang, and Z. Huang, “Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam,” Phys. Rev. Accel. Beams 20(5), 050701 (2017).
[Crossref]

Tautz, R.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Tavella, F.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Tchervenkov, C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Terranova, F.

F. Terranova, “Particle acceleration in subcycle optical cells,” Phys. Rev. Spec. Top. Accel. Beams 17(7), 071301 (2014).
[Crossref]

Varin, C.

C. Varin, M. Piché, and M. A. Porras, “Acceleration of electrons from rest to GeV energies by ultrashort transverse magnetic laser pulses in free space,” Phys. Rev. E. 71(2), 026603 (2005).
[Crossref] [PubMed]

Veisz, L.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

Vikartofsky, A.

A. Vikartofsky, L. W. Pi, and A. F. Starace, “Discontinuities in the electromagnetic fields of vortex beams in the complex source-sink model,” Phys. Rev. A. 95(5), 053826 (2017).
[Crossref]

Voronin, A. A.

Vshivkov, V. A.

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

Wang, P. X.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Weathersby, S.

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

Wong, L. J.

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

Xiang, D.

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

Yan, L.

Z. Zhang, L. Yan, Y. Du, W. Huang, C. Tang, and Z. Huang, “Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam,” Phys. Rev. Accel. Beams 20(5), 050701 (2017).
[Crossref]

Yuan, X. Q.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Zhang, X. C.

Q. Lin, J. Zheng, J. Dai, I. Chen Ho, and X. C. Zhang, “Intrinsic chirp of single-cycle pulses,” Phys. Rev. A 81(4), 043821 (2010).
[Crossref]

Zhang, Z.

Z. Zhang, L. Yan, Y. Du, W. Huang, C. Tang, and Z. Huang, “Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam,” Phys. Rev. Accel. Beams 20(5), 050701 (2017).
[Crossref]

Zhao, J. Y.

Zheltikov, A. M.

Zheng, J.

J. L. Liu, Z. M. Sheng, and J. Zheng, “Exact solution of the vectorial field structure of a light beam,” Opt. Commun. 284(19), 4646–4649 (2011).
[Crossref]

J. Zheng, E. M. Qiu, and Q. Lin, “High harmonic generation with sub-cycle pulses,” J. Opt. 13(7), 075206 (2011).
[Crossref]

Q. Lin, J. Zheng, J. Dai, I. Chen Ho, and X. C. Zhang, “Intrinsic chirp of single-cycle pulses,” Phys. Rev. A 81(4), 043821 (2010).
[Crossref]

Q. Lin, J. Zheng, and W. Becker, “Subcycle Pulsed Focused Vector Beams,” Phys. Rev. Lett. 97(25), 253902 (2006).
[Crossref] [PubMed]

Appl. Phys. B (1)

R. Martinez-Herrero, P. M. Mejias, and A. Manjavacas, “On the longitudinal polarization of non-paraxial electromagnetic fields,” Appl. Phys. B 99(3), 579–584 (2010).
[Crossref]

Appl. Phys. Lett. (2)

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piche, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78(15), 2253–2255 (2001).
[Crossref]

Europhys. Lett. (1)

H. Spohn, “The critical manifold of the Lorentz-Dirac equation,” Europhys. Lett. 50(3), 287–292 (2000).
[Crossref]

Int. J. Mod. Phys. A (1)

J. P. Costella and B. H. J. McKellar, “Electromagnetic Deflection of Spinning Particles,” Int. J. Mod. Phys. A 9(3), 461–473 (1994).
[Crossref]

J. Mod. Opt. (1)

C. F. R. Caron and R. M. Potvliege, “Free-space propagation of ultrashort pulses: Space-time couplings in Gaussian pulse beams,” J. Mod. Opt. 46(13), 1881–1891 (1999).
[Crossref]

J. Opt. (1)

J. Zheng, E. M. Qiu, and Q. Lin, “High harmonic generation with sub-cycle pulses,” J. Opt. 13(7), 075206 (2011).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

Mon. Not. R. Astron. Soc. (1)

S. M. Mahajan, F. A. Asenjo, and R. D. Hazeltine, “Comparison of the electron-spin force and radiation reaction force,” Mon. Not. R. Astron. Soc. 446(4), 4112–4115 (2015).
[Crossref]

Opt. Commun. (1)

J. L. Liu, Z. M. Sheng, and J. Zheng, “Exact solution of the vectorial field structure of a light beam,” Opt. Commun. 284(19), 4646–4649 (2011).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (3)

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: A scalar treatment,” Phys. Rev. A 57(4), 2971–2979 (1998).
[Crossref]

Q. Lin, J. Zheng, J. Dai, I. Chen Ho, and X. C. Zhang, “Intrinsic chirp of single-cycle pulses,” Phys. Rev. A 81(4), 043821 (2010).
[Crossref]

Y. I. Salamin and F. H. M. Faisal, “Ultrahigh electron acceleration and Compton emission spectra in a superintense laser pulse and a uniform axial magnetic field,” Phys. Rev. A 61(4), 043801 (2000).
[Crossref]

Phys. Rev. A. (1)

A. Vikartofsky, L. W. Pi, and A. F. Starace, “Discontinuities in the electromagnetic fields of vortex beams in the complex source-sink model,” Phys. Rev. A. 95(5), 053826 (2017).
[Crossref]

Phys. Rev. Accel. Beams (2)

Z. Zhang, L. Yan, Y. Du, W. Huang, C. Tang, and Z. Huang, “Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam,” Phys. Rev. Accel. Beams 20(5), 050701 (2017).
[Crossref]

S. Carbajo, E. A. Nanni, L. J. Wong, G. Moriena, P. D. Keathley, G. Laurent, and R. J. Dwayne Miller, “Direct longitudinal laser acceleration of electrons in free space,” Phys. Rev. Accel. Beams 19(2), 021303 (2016).
[Crossref]

Phys. Rev. E. (2)

G. I. Dudnikova, V. Yu. Bychenkov, A. Maksimchuk, G. Mourou, J. Nees, S. G. Bochkarev, and V. A. Vshivkov, “Electron acceleration by few-cycle laser pulses with single-wavelength spot size,” Phys. Rev. E. 67(2), 026416 (2003).
[Crossref] [PubMed]

C. Varin, M. Piché, and M. A. Porras, “Acceleration of electrons from rest to GeV energies by ultrashort transverse magnetic laser pulses in free space,” Phys. Rev. E. 71(2), 026603 (2005).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

C. N. Harvey, A. Gonoskov, A. Ilderton, and M. Marklund, “Quantum Quenching of Radiation Losses in Short Laser Pulses,” Phys. Rev. Lett. 118(10), 105004 (2017).
[Crossref] [PubMed]

Q. Lin, J. Zheng, and W. Becker, “Subcycle Pulsed Focused Vector Beams,” Phys. Rev. Lett. 97(25), 253902 (2006).
[Crossref] [PubMed]

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-Cycle Laser-Driven Electron Acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[Crossref] [PubMed]

B. Rau, T. Tajima, and H. Hojo, “Coherent Electron Acceleration by Subcycle Laser Pulses,” Phys. Rev. Lett. 78(17), 3310–3313 (1997).
[Crossref]

M. Dunning, E. Hemsing, C. Hast, T. O. Raubenheimer, S. Weathersby, D. Xiang, and F. Fu, “Demonstration of Cascaded Optical Inverse Free-Electron Laser Accelerator,” Phys. Rev. Lett. 110(24), 244801 (2013).
[Crossref] [PubMed]

E. N. Nerush and I. Yu. Kostyukov, “Carrier-Envelope Phase Effects in Plasma-Based Electron Acceleration with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 103(3), 035001 (2009).
[Crossref] [PubMed]

Phys. Rev. Spec. Top. Accel. Beams (1)

F. Terranova, “Particle acceleration in subcycle optical cells,” Phys. Rev. Spec. Top. Accel. Beams 17(7), 071301 (2014).
[Crossref]

Other (2)

A. April, Coherence and Ultrashort Pulse Laser Emission (InTech, pp.355–382, 2010).

L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th ed. (Pergamon Oxford, 1989).

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Figures (9)

Fig. 1
Fig. 1 (a) The 0.45-cycle waveforms versus time. (b) The frequency spectrum of the pulse.
Fig. 2
Fig. 2 The power distribution of the focus spots of different wavelength components of the tightly focused sub-cycle radially polarized EM field on the waist plane.
Fig. 3
Fig. 3 (a), (b) The exit kinetic energy of the electron versus the CEP and the beam waist. The radiation-reaction force is considered in (a) and is neglected in (b). (c) The kinetic energy of the electron versus time, the CEP and beam waist of the pulse are 0.62π and 15.1μm.(d) Trajectory of the electron, the parameters are the same as (c).
Fig. 4
Fig. 4 The exit kinetic energy of electrons for the 0.45-cycle pulse. (a), (b)The case of the Poisson type pulse. The incidence angle of electrons is 90 degrees in (a). (c), (d) The case of the Lorentz type pulse. The incidence angle of electrons is 10 degrees in (c). (b), (d)The maximal kinetic energy of an electron versus the incidence angle.
Fig. 5
Fig. 5 (a), (b) The exit kinetic energy of the electron versus the CEP and the beam waist. The incidence angle of electrons is 10 degrees in (a) and is 90 degrees in (b). (c) The maximal kinetic energy of the electron versus the incidence angle.
Fig. 6
Fig. 6 (a), (c) The exit kinetic energy of the electron versus the CEP and the beam waist. The incidence angle of electrons is 10 degrees in (a) and is 90 degrees in (c).(b) The kinetic energy of the electron versus time, the CEP and beam waist of the pulse are 0.32πand 15.1μm.(d) The maximal kinetic energy of the electron versus the incidence angle.
Fig. 7
Fig. 7 (a), (b) The exit kinetic energy of the electron versus the CEP and the beam waist. The incidence angle of electrons is 10 degrees in (a) and is 90 degrees in (b). (c) The maximal kinetic energy of the electron versus the incidence angle.
Fig. 8
Fig. 8 The exit kinetic energy of the electron versus the CEP and the beam waist. (a), (b) The 0.45-cycle pulse cases. (c), (d)The 1.37-cycle pulse cases. (a), (c) v 0 =0.01c. (b), (d) v 0 =0.1c v 0 is 0.01c in (a), (c) and is 0.1c in (b), (d). Figure 8 shows that the electron acceleration cases are almost the same as Fig. 3-7. This illustrates that the initial different interaction times t 0 have little effect on the electron acceleration. The reason can be attributed to the ultra-short duration of the sub-cycle and single-cycle pulses and the fringe electric fields of the pulses disappear quickly. The second case is shown in Fig. 9. The incidence angle θ 0 is 80 degrees.
Fig. 9
Fig. 9 The exit kinetic energy of the electron versus the CEP and the beam waist, v 0 =0.1c, θ 0 =80 o . (a) The 0.45-cycle pulse cases. (b) The 1.37-cycle pulse cases.

Tables (1)

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Table 1 Parameters of Figures

Equations (12)

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P(r,t)= p 0 f(t) e z δ( r )
zz= z ' +ia,t t ' =t t 0 +i a c
R ' = x 2 + y 2 + (z+ia) 2
D( R ' , t ' )= c 2 μ 0 4π δ( t ' R ' /c)δ( t ' + R ' /c) R '
E x 1 = c 2 μ 0 p 0 4π real{ z ' R ' 2 ( f .. 1 f .. 2 c 2 R ' + 3( f . 1 + f . 2 ) c R ' 2 + 3( f 1 f 2 ) R ' 3 ) }x e x E y 1 = c 2 μ 0 p 0 4π real{ z ' R ' 2 { f .. 1 f .. 2 c 2 R ' + 3( f . 1 + f . 2 ) c R ' 2 + 3( f 1 f 2 ) R ' 3 } }y e y E z 1 = c 2 μ 0 p 0 4π real{ z ' 2 R ' 2 [ f .. 1 f .. 2 c 2 R ' + 3( f . 1 + f . 2 ) c R ' 2 + 3( f 1 f 2 ) R ' 3 ] [ f .. 1 f .. 2 c 2 R ' + ( f . 1 + f . 2 ) c R ' 2 + ( f 1 f 2 ) R ' 3 ]} e z B x =- c μ 0 y p 0 4π real{ ( f .. 1 + f .. 2 c 2 R ' 2 + ( f . 1 f . 2 ) c R ' 3 ) } e x B y = c μ 0 x p 0 4π real{ ( f .. 1 + f .. 2 c 2 R ' 2 + ( f . 1 f . 2 ) c R ' 3 ) } e y
E 0 =max{ E z } | x,y,z=0
E 0 = p 0 c 2 μ 0 4π [ 2 (ia) 2 ( f . 1 (0)+ f . 2 (2ia/c) c + ( f 1 (0) f 2 (2ia/c) ia ) ]
d β dt = 1 γmc [ e( β ( β E )( E +c β × B ) )+ f ]
d β x dt = e γmc [ β x ( β x E x + β y E y + β z E z )( E x +c( β y B z β z B y ) e x ) ]+ f x γmc d β y dt = e γmc [ β y ( β x E x + β y E y + β z E z )( E y +c( β z B x β x B z ) e y ) ]+ f y γmc d β z dt = e γmc [ β z ( β x E x + β y E y + β z E z )( E z +c( β x B y β y B x ) e z ) ]+ f z γmc d x dt =c βx , d y dt =c βy , d z dt =c βz
f γmc = 1 3× 10 7 2 e 3 m 2 { 1 c [ ct +( β ) ] E +[ β ×( ct +( β ) ) B ] } + 1 3× 10 7 2 e 4 m 3 γc { E × B c +[ B ×( B × β ) ]+ E c 2 ( β E ) } 1 3× 10 7 2 e 4 β γ m 3 c { ( E c + β × B ) 2 1 c 2 ( β E ) 2 }
P( t ' )= e 2 16 π 2 ε 0 c 3 | e r ×[( e r v /c)× v . ] | 2 (1 e r v /c) 5 dΩ = e 2 16 π 2 ε 0 c 3 [ a θ ( a θ v r a r v θ )/c] 2 + [ a ϕ ( a ϕ v r a r v ϕ )/c] 2 (1 v r /c) 5 sinθdθdϕ
a r = a x sinθcosϕ+ a y sinθsinϕ+ a z cosθ a θ = a x cosθcosϕ+ a y cosθsinϕ a z sinθ a ϕ = a x sinϕ+ a y cosϕ

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