Abstract

Electron acceleration in vacuum driven by a tightly focused radially polarized Gaussian beam has been studied in detail. Weniger transformation method is used to eliminate the divergence of the radially polarized electromagnetic field derived from the Lax series approach. And, electron dynamics in an intense radially polarized Gaussian beam is analyzed by using the Weniger transformation field. The roles of the initial phase of the electromagnetic field and the injection angle, position and energy of electron in energy gain of electron have been studied in detail.

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  1. M. D. Perry, D. Pennington, B. C. Stuart, G. Tietbohl, J. A. Britten, C. Brown, S. Herman, B. Golick, M. Kartz, J. Miller, H. T. Powell, M. Vergino, and V. Yanovsky, “Petawatt laser pulses,” Opt. Lett. 24(3), 160–162 (1999).
    [CrossRef]
  2. Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
    [CrossRef] [PubMed]
  3. N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
    [CrossRef]
  4. Y. I. Salamin, “Electron acceleration from rest in vacuum by an axicon Gaussian laser beam,” Phys. Rev. A 73(4), 043402 (2006).
    [CrossRef]
  5. J. X. Li, W. P. Zang, and J. G. Tian, “Electron acceleration in vacuum induced by a tightly focused chirped laser pulse,” Appl. Phys. Lett. 96(3), 031103 (2010).
    [CrossRef]
  6. J. X. Li, W. P. Zang, and J. G. Tian, “Analysis of electron capture acceleration channel in an Airy beam,” Opt. Lett. 35(19), 3258–3260 (2010).
    [CrossRef] [PubMed]
  7. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [CrossRef] [PubMed]
  8. S. X. Hu and A. F. Starace, “Laser acceleration of electrons to giga-electron-volt energies using highly charged ions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066502 (2006).
    [CrossRef] [PubMed]
  9. M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11(4), 1365–1370 (1975).
    [CrossRef]
  10. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19(3), 1177–1179 (1979).
    [CrossRef]
  11. Y. I. Salamin, “Fields of a radially polarized Gaussian laser beam beyond the paraxial approximation,” Opt. Lett. 31(17), 2619–2621 (2006).
    [CrossRef] [PubMed]
  12. H. Luo, S. Y. Liu, Z. F. Lin, and C. T. Chan, “Method for accurate description of a radially polarized Gaussian laser beam beyond the paraxial approximation,” Opt. Lett. 32(12), 1692–1694 (2007).
    [CrossRef] [PubMed]
  13. R. Borghi and M. Santarsiero, “Summing Lax series for nonparaxial beam propagation,” Opt. Lett. 28(10), 774–776 (2003).
    [CrossRef] [PubMed]
  14. J. X. Li, W. P. Zang, and J. G. Tian, “Simulation of Gaussian laser beams and electron dynamics by Weniger transformation method,” Opt. Express 17(7), 4959–4969 (2009).
    [CrossRef] [PubMed]
  15. J. X. Li, W. P. Zang, Y.-D. Li, and J. G. Tian, “Acceleration of electrons by a tightly focused intense laser beam,” Opt. Express 17(14), 11850–11859 (2009).
    [CrossRef] [PubMed]
  16. A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136(1-2), 114–124 (1997).
    [CrossRef]
  17. P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152(1-3), 108–118 (1998).
    [CrossRef]
  18. Y. I. Salamin, “Accurate fields of radially polarized Gaussian laser beam,” N. J. Phys. 8(8), 133 (2006).
    [CrossRef]
  19. E. J. Weniger, “Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series,” Comput. Phys. Rep. 10(5-6), 189–371 (1989).
    [CrossRef]
  20. U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, “Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients,” Phys. Rev. Lett. 85(12), 2446–2449 (2000).
    [CrossRef] [PubMed]
  21. E. J. Weniger, “Summation of divergent power series by means of factorial series,” Appl. Numer. Math. 60(12), 1429–1441 (2010).
    [CrossRef]

2010

J. X. Li, W. P. Zang, and J. G. Tian, “Electron acceleration in vacuum induced by a tightly focused chirped laser pulse,” Appl. Phys. Lett. 96(3), 031103 (2010).
[CrossRef]

J. X. Li, W. P. Zang, and J. G. Tian, “Analysis of electron capture acceleration channel in an Airy beam,” Opt. Lett. 35(19), 3258–3260 (2010).
[CrossRef] [PubMed]

E. J. Weniger, “Summation of divergent power series by means of factorial series,” Appl. Numer. Math. 60(12), 1429–1441 (2010).
[CrossRef]

2009

2007

2006

Y. I. Salamin, “Fields of a radially polarized Gaussian laser beam beyond the paraxial approximation,” Opt. Lett. 31(17), 2619–2621 (2006).
[CrossRef] [PubMed]

Y. I. Salamin, “Accurate fields of radially polarized Gaussian laser beam,” N. J. Phys. 8(8), 133 (2006).
[CrossRef]

S. X. Hu and A. F. Starace, “Laser acceleration of electrons to giga-electron-volt energies using highly charged ions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066502 (2006).
[CrossRef] [PubMed]

Y. I. Salamin, “Electron acceleration from rest in vacuum by an axicon Gaussian laser beam,” Phys. Rev. A 73(4), 043402 (2006).
[CrossRef]

2003

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

R. Borghi and M. Santarsiero, “Summing Lax series for nonparaxial beam propagation,” Opt. Lett. 28(10), 774–776 (2003).
[CrossRef] [PubMed]

2002

Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
[CrossRef] [PubMed]

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

2000

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, “Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients,” Phys. Rev. Lett. 85(12), 2446–2449 (2000).
[CrossRef] [PubMed]

1999

1998

P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152(1-3), 108–118 (1998).
[CrossRef]

1997

A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136(1-2), 114–124 (1997).
[CrossRef]

1989

E. J. Weniger, “Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series,” Comput. Phys. Rep. 10(5-6), 189–371 (1989).
[CrossRef]

1979

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19(3), 1177–1179 (1979).
[CrossRef]

1975

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11(4), 1365–1370 (1975).
[CrossRef]

Becher, J.

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, “Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients,” Phys. Rev. Lett. 85(12), 2446–2449 (2000).
[CrossRef] [PubMed]

Borghi, R.

Britten, J. A.

Brown, C.

Cao, N.

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Chan, C. T.

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19(3), 1177–1179 (1979).
[CrossRef]

Doicu, A.

A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136(1-2), 114–124 (1997).
[CrossRef]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Golick, B.

Herman, S.

Ho, Y. K.

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Hu, S. X.

S. X. Hu and A. F. Starace, “Laser acceleration of electrons to giga-electron-volt energies using highly charged ions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066502 (2006).
[CrossRef] [PubMed]

Ito, H.

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Jentschura, U. D.

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, “Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients,” Phys. Rev. Lett. 85(12), 2446–2449 (2000).
[CrossRef] [PubMed]

Kartz, M.

Keitel, C. H.

Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
[CrossRef] [PubMed]

Kong, Q.

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11(4), 1365–1370 (1975).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Li, J. X.

Li, Y.-D.

Lin, Z. F.

Liu, S. Y.

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11(4), 1365–1370 (1975).
[CrossRef]

Luo, H.

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11(4), 1365–1370 (1975).
[CrossRef]

Miller, J.

Nishida, Y.

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Pennington, D.

Perry, M. D.

Powell, H. T.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Salamin, Y. I.

Y. I. Salamin, “Electron acceleration from rest in vacuum by an axicon Gaussian laser beam,” Phys. Rev. A 73(4), 043402 (2006).
[CrossRef]

Y. I. Salamin, “Fields of a radially polarized Gaussian laser beam beyond the paraxial approximation,” Opt. Lett. 31(17), 2619–2621 (2006).
[CrossRef] [PubMed]

Y. I. Salamin, “Accurate fields of radially polarized Gaussian laser beam,” N. J. Phys. 8(8), 133 (2006).
[CrossRef]

Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
[CrossRef] [PubMed]

Santarsiero, M.

Soff, G.

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, “Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients,” Phys. Rev. Lett. 85(12), 2446–2449 (2000).
[CrossRef] [PubMed]

Starace, A. F.

S. X. Hu and A. F. Starace, “Laser acceleration of electrons to giga-electron-volt energies using highly charged ions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066502 (2006).
[CrossRef] [PubMed]

Stuart, B. C.

Tian, J. G.

Tietbohl, G.

Török, P.

P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152(1-3), 108–118 (1998).
[CrossRef]

Varga, P.

P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152(1-3), 108–118 (1998).
[CrossRef]

Vergino, M.

Wang, P. X.

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Weniger, E. J.

E. J. Weniger, “Summation of divergent power series by means of factorial series,” Appl. Numer. Math. 60(12), 1429–1441 (2010).
[CrossRef]

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, “Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients,” Phys. Rev. Lett. 85(12), 2446–2449 (2000).
[CrossRef] [PubMed]

E. J. Weniger, “Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series,” Comput. Phys. Rep. 10(5-6), 189–371 (1989).
[CrossRef]

Wriedt, T.

A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136(1-2), 114–124 (1997).
[CrossRef]

Yanovsky, V.

Yuan, X. Q.

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Yugami, N.

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Zang, W. P.

Appl. Numer. Math.

E. J. Weniger, “Summation of divergent power series by means of factorial series,” Appl. Numer. Math. 60(12), 1429–1441 (2010).
[CrossRef]

Appl. Phys. Lett.

J. X. Li, W. P. Zang, and J. G. Tian, “Electron acceleration in vacuum induced by a tightly focused chirped laser pulse,” Appl. Phys. Lett. 96(3), 031103 (2010).
[CrossRef]

Comput. Phys. Rep.

E. J. Weniger, “Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series,” Comput. Phys. Rep. 10(5-6), 189–371 (1989).
[CrossRef]

N. J. Phys.

Y. I. Salamin, “Accurate fields of radially polarized Gaussian laser beam,” N. J. Phys. 8(8), 133 (2006).
[CrossRef]

Opt. Commun.

A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136(1-2), 114–124 (1997).
[CrossRef]

P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152(1-3), 108–118 (1998).
[CrossRef]

N. Cao, Y. K. Ho, Q. Kong, P. X. Wang, X. Q. Yuan, Y. Nishida, N. Yugami, and H. Ito, “Accurate description of Gaussian laser beams and electron dynamics,” Opt. Commun. 204(1-6), 7–15 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11(4), 1365–1370 (1975).
[CrossRef]

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19(3), 1177–1179 (1979).
[CrossRef]

Y. I. Salamin, “Electron acceleration from rest in vacuum by an axicon Gaussian laser beam,” Phys. Rev. A 73(4), 043402 (2006).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

S. X. Hu and A. F. Starace, “Laser acceleration of electrons to giga-electron-volt energies using highly charged ions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066502 (2006).
[CrossRef] [PubMed]

Phys. Rev. Lett.

Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, “Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients,” Phys. Rev. Lett. 85(12), 2446–2449 (2000).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(Color online) (a) and (b) Propagation dynamics of Ez , accurate up to ε 10, of LSF and WTF, respectively. w 0 = λ.

Fig. 2
Fig. 2

(Color online) (a)–(c) Cross sections of electromagnetic field components Ez , Er , and Bθ , respectively. w 0 = λ, and z = 5zr . Red, blue and grey curves represent the components of LSF accurate up to ε 2, ε 8, and ε 24, respectively. Green solid and black dash-dot curves represent the components of WTF and PWSF, both accurate up to ε 24, respectively.

Fig. 3
Fig. 3

(Color online) (a)–(e) Electron trajectories, energy gains, and electromagnetic field components Ez , Er , and Bθ , sensed by electron along its trajectory, respectively. An electron is initially set at the origin and injected in x-z plane, with injection angle θ 0 = 25°, γ 0 = 100, w 0 = λ, q = 150, and φ 0 = π. Integration limit takes ηf = 103 π. Black curves present the beam boundaries.

Fig. 4
Fig. 4

(Color online) (a)-(d) Variation of the energy gain with ϕ 0 , θ 0, γ 0, and r. q = 150. In (a) γ 0 = 100, θ 0 = 15°, and ηf = 35π. In (b) γ 0 = 100, φ 0 = π, and ηf = 2.2×103 π. In (c) φ 0 = π, γ 0 = 10, θ 0 = 0° and ηf = 40π. In (d) ϕ 0 = π, θ 0 = 15°, and ηf = 103 π. Other parameters are same as those of Fig. 3.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

A ( r , θ , z , t ) = z ^ A 0 ψ ( r , z ) e i η ,
ψ ( r , z ) = n = 0 ε 2 n ψ 2 n ( r , z ) .
E = i k A i k ( A ) ,     B = × A .
E r = E n = 0 m ε 2 n + 1 E 2 n + 1 ( f , ρ ) ,
E z = i E n = 0 m ε 2 n + 2 E 2 n + 2 ( f , ρ ) ,
B θ = E n = 0 m ε 2 n + 1 B 2 n + 1 ( f , ρ ) ,
E z = j = 0 n ( 1 ) j ( n j ) ( 1 + j ) n 1 ( S 2 j / E 2 j + 2 ) j = 0 n ( 1 ) j ( n j ) ( 1 + j ) n 1 ( 1 / E 2 j + 2 )
A ( r , z ) = 1 2 π P ( k x , k y ) e i ( k x x + k y y + k z z ) d k x d k y ,
P ( k x , k y ) = 1 2 π A ( r , 0 ) e i ( k x x + k y y ) d x d y .
k x = κ cos θ ,   k y = κ sin θ ,   x = r cos θ ,   y = r sin θ .
A ( r , z ) = 1 2 π 0 P ( κ ) e i z k 2 κ 2 J 0 ( κ r ) κ d κ ,
E r = 1 k 0 κ 2 k 2 κ 2 P ( κ ) e i z k 2 κ 2 J 1 ( κ r ) d κ ,
E z = i k 0 κ 3 P ( κ ) e i z k 2 κ 2 J 0 ( κ r ) d κ ,
B θ = 0 κ 2 P ( κ ) e i z k 2 κ 2 J 1 ( κ r ) d κ .
0 ... = 0 k ... + k ...

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