Abstract

Exact closed-form solutions to Maxwell’s equations are used to investigate the acceleration of electrons in vacuum driven by ultrashort and nonparaxial radially polarized laser pulses. We show that the threshold power above which significant acceleration takes place is greatly reduced by using a tighter focus. Moreover, electrons accelerated by tightly focused single-cycle laser pulses may reach around 80% of the theoretical energy gain limit, about twice the value previously reported with few-cycle paraxial pulses. Our results demonstrate that the direct acceleration of electrons in vacuum is well within reach of current laser technology.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
    [CrossRef]
  2. C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
    [CrossRef]
  3. Y. I. Salamin, Phys. Rev. A 73, 043402 (2006).
    [CrossRef]
  4. Y. I. Salamin, Opt. Lett. 32, 90 (2007).
    [CrossRef]
  5. A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
    [CrossRef]
  6. P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
    [CrossRef]
  7. L. J. Wong and F. X. Kärtner, Opt. Express 18, 25035 (2010).
    [CrossRef]
  8. S. G. Bochkarev, K. I. Popov, and V. Y. Bychenkov, Plasma Phys. Rep. 37, 603 (2011).
    [CrossRef]
  9. L. J. Wong and F. X. Kärtner, Appl. Phys. Lett. 99, 211101 (2011).
    [CrossRef]
  10. L. J. Wong and F. X. Kärtner, Opt. Lett. 36, 957 (2011).
    [CrossRef]
  11. A. April, in Coherence and Ultrashort Pulse Laser Emission, F. J. Duarte, ed. (InTech, 2010), pp. 355–382.
  12. C. F. R. Caron and R. M. Potvliege, J. Mod. Opt. 46, 1881 (1999).
    [CrossRef]
  13. A. April and M. Piché, Opt. Express 18, 22128 (2010).
    [CrossRef]
  14. G. Rodríguez-Morales and S. Chávez-Cerda, Opt. Lett. 29, 430 (2004).
    [CrossRef]
  15. S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

2011

S. G. Bochkarev, K. I. Popov, and V. Y. Bychenkov, Plasma Phys. Rep. 37, 603 (2011).
[CrossRef]

L. J. Wong and F. X. Kärtner, Appl. Phys. Lett. 99, 211101 (2011).
[CrossRef]

L. J. Wong and F. X. Kärtner, Opt. Lett. 36, 957 (2011).
[CrossRef]

2010

2008

V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
[CrossRef]

2007

A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
[CrossRef]

Y. I. Salamin, Opt. Lett. 32, 90 (2007).
[CrossRef]

2006

C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
[CrossRef]

Y. I. Salamin, Phys. Rev. A 73, 043402 (2006).
[CrossRef]

2004

1999

C. F. R. Caron and R. M. Potvliege, J. Mod. Opt. 46, 1881 (1999).
[CrossRef]

April, A.

A. April and M. Piché, Opt. Express 18, 22128 (2010).
[CrossRef]

A. April, in Coherence and Ultrashort Pulse Laser Emission, F. J. Duarte, ed. (InTech, 2010), pp. 355–382.

Bochkarev, S. G.

S. G. Bochkarev, K. I. Popov, and V. Y. Bychenkov, Plasma Phys. Rep. 37, 603 (2011).
[CrossRef]

Bychenkov, V. Y.

S. G. Bochkarev, K. I. Popov, and V. Y. Bychenkov, Plasma Phys. Rep. 37, 603 (2011).
[CrossRef]

Caron, C. F. R.

C. F. R. Caron and R. M. Potvliege, J. Mod. Opt. 46, 1881 (1999).
[CrossRef]

Chávez-Cerda, S.

Faure, J.

V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
[CrossRef]

Fortin, P.-L.

P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

Fourmaux, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

Gauduel, Y. A.

V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
[CrossRef]

Karmakar, A.

A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
[CrossRef]

Kärtner, F. X.

Kieffer, J. C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

Lefebvre, E.

V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
[CrossRef]

Légaré, F.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

MacLean, J. P.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

Malka, V.

V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
[CrossRef]

Payeur, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

Phuoc, K. Y.

V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
[CrossRef]

Piché, M.

P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

A. April and M. Piché, Opt. Express 18, 22128 (2010).
[CrossRef]

C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
[CrossRef]

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

Popov, K. I.

S. G. Bochkarev, K. I. Popov, and V. Y. Bychenkov, Plasma Phys. Rep. 37, 603 (2011).
[CrossRef]

Potvliege, R. M.

C. F. R. Caron and R. M. Potvliege, J. Mod. Opt. 46, 1881 (1999).
[CrossRef]

Pukhov, A.

A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
[CrossRef]

Rodríguez-Morales, G.

Rousse, A.

V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
[CrossRef]

Salamin, Y. I.

Y. I. Salamin, Opt. Lett. 32, 90 (2007).
[CrossRef]

Y. I. Salamin, Phys. Rev. A 73, 043402 (2006).
[CrossRef]

Schmidt, B. E.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

Tchervenkov, C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

Varin, C.

P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
[CrossRef]

Wong, L. J.

Appl. Phys. Lett.

L. J. Wong and F. X. Kärtner, Appl. Phys. Lett. 99, 211101 (2011).
[CrossRef]

J. Mod. Opt.

C. F. R. Caron and R. M. Potvliege, J. Mod. Opt. 46, 1881 (1999).
[CrossRef]

J. Phys. B

P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

Laser Part. Beams

A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
[CrossRef]

Nat. Phys.

V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Y. Phuoc, Nat. Phys. 4, 447 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

Y. I. Salamin, Phys. Rev. A 73, 043402 (2006).
[CrossRef]

Phys. Rev. E

C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
[CrossRef]

Plasma Phys. Rep.

S. G. Bochkarev, K. I. Popov, and V. Y. Bychenkov, Plasma Phys. Rep. 37, 603 (2011).
[CrossRef]

Other

A. April, in Coherence and Ultrashort Pulse Laser Emission, F. J. Duarte, ed. (InTech, 2010), pp. 355–382.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” submitted to Appl. Phys. Lett.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Maximum (a) normalized and (b) absolute energy gain of an electron initially at rest on the optical axis versus the laser pulse peak power for different values of k0a and s. The values of s used represent single-cycle (s=1), two-cycle (s=10), and five-cycle (s=60) pulses. The gray dashed curve (k0a=124, s=155) corresponds to the limit of the paraxial regime investigated in [7]. The energy gain is evaluated 20 ps after the passage of the pulse at z=0.

Fig. 2.
Fig. 2.

Longitudinal on-axis electric field at pulse peak t=z/c (computed for λ0=800nm) versus distance from beam waist for different values of k0a. The other parameters are ϕ0=0, s=10, and Ppeak=1012W.

Fig. 3.
Fig. 3.

(a) Energy gain versus distance from beam waist for an electron accelerated by pulses of various durations with k0a=5, Ppeak=5PW. For each pulse, a snapshot of the longitudinal electric field Ez (computed for λ0=800nm) was taken at the position indicated by the dotted vertical line and is shown in (b)–(d). The filled circle in (b)–(d) indicates the position of the electron on the optical axis. The z0 and ϕ0 parameters are chosen to obtain the maximum energy gain with each pulse.

Equations (4)

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

Er(r,t)={3E0sin2θ˜2R˜(G(0)R˜2G+(1)cR˜+G(2)3c2)},
Ez(r,t)={E0R˜[(3cos2θ˜1)R˜(G(0)R˜G+(1)c)sin2θ˜c2G(2)]},
Hϕ(r,t)={E0sinθ˜η0R˜(G(1)cR˜G+(2)c2)}.
F(ω)=2πejϕ0(sω0)s+1ωsesω/ω0Γ(s+1)H(ω),

Metrics