Abstract

We calculate the dynamics and the radiation emitted from free electrons in an ultrashort pulsed laser focus. In a Gaussian focus, at low electron densities for which space charge is negligible, we find that ponderomotive forces limit the effective volume of radiation emission to a region that is much smaller than the focal waist and even significantly smaller than the fundamental wavelength. Constructive interference produces significant enhancements in the radiation emitted by the plasma for the lower harmonics, whereas destructive interference limits the radiation for the higher harmonics. We also investigate the radiation emitted by electrons in the focus of a conical axicon, an optical geometry that was proposed for laser-based electron accelerators [ J. Appl. Phys. 54, 4285 ( 1983)]. This radiation may be a useful diagnostic in such accelerators. These studies are intended as a prelude to experiments with high-intensity ultrashort laser pulses.

© 1992 Optical Society of America

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References

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  1. C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980), p. 225.
  2. L. S. Brown, T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, 3A (1964).
    [CrossRef]
  3. Vachaspati, “Harmonics in the scattering of light by free electrons,” Phys. Rev. 128, 2 (1962).
    [CrossRef]
  4. E. S. Sarachik, G. T. Schappert, “Classical theory of scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
    [CrossRef]
  5. J. N. Bardsley, B. M. Penetrante, M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1989).
    [CrossRef] [PubMed]
  6. X. F. Li, L. A. Lompre, A. L’Huillier, G. Mainfray, M. Ferray, “Multiple harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 4, 5751–5761 (1989).
    [CrossRef]
  7. A. Zavriyev, Columbia University, New York, N.Y 10027 (personal communication, 1990).
  8. B. Wolff, K. H. Welge, H. Rottke, D. Feldman, “Multiphoton-ionization of hydrogen-atoms in intense laser-fields,” Z. Phys. D 10, 35–43 (1988).
    [CrossRef]
  9. P. Sprangle, E. Esarey, A. Ting, “Nonlinear interaction of intense laser pulses in plasmas,” Phys. Rev. A 41, 4463–4469 (1990).
    [CrossRef] [PubMed]
  10. P. Sprangle, Naval Research Laboratory, Washington, D.C. 20375 (personal communication, 1991).
  11. J. F. Seeley, E. G. Harris, “Heating of a plasma by multi-photon inverse bremsstrahlung,” Phys. Rev. A 7, 1064–1067 (1973).
    [CrossRef]
  12. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 657.
  13. P. H. Bucksbaum, M. Bashkansky, T. J. McIlrath, “Scattering of electrons by intense coherent light,” Phys. Rev. Lett. 58, 349–352 (1987).
    [CrossRef] [PubMed]
  14. J. R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cherenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
    [CrossRef]
  15. R. D. Romea, W. D. Kimura, “Modeling of inverse Cerenkov laser acceleration with axicon laser-beam focus ing,” Phys. Rev. D 42, 1807–1818 (1990).
    [CrossRef]

1990 (2)

P. Sprangle, E. Esarey, A. Ting, “Nonlinear interaction of intense laser pulses in plasmas,” Phys. Rev. A 41, 4463–4469 (1990).
[CrossRef] [PubMed]

R. D. Romea, W. D. Kimura, “Modeling of inverse Cerenkov laser acceleration with axicon laser-beam focus ing,” Phys. Rev. D 42, 1807–1818 (1990).
[CrossRef]

1989 (2)

J. N. Bardsley, B. M. Penetrante, M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1989).
[CrossRef] [PubMed]

X. F. Li, L. A. Lompre, A. L’Huillier, G. Mainfray, M. Ferray, “Multiple harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 4, 5751–5761 (1989).
[CrossRef]

1988 (1)

B. Wolff, K. H. Welge, H. Rottke, D. Feldman, “Multiphoton-ionization of hydrogen-atoms in intense laser-fields,” Z. Phys. D 10, 35–43 (1988).
[CrossRef]

1987 (1)

P. H. Bucksbaum, M. Bashkansky, T. J. McIlrath, “Scattering of electrons by intense coherent light,” Phys. Rev. Lett. 58, 349–352 (1987).
[CrossRef] [PubMed]

1983 (1)

J. R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cherenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

1973 (1)

J. F. Seeley, E. G. Harris, “Heating of a plasma by multi-photon inverse bremsstrahlung,” Phys. Rev. A 7, 1064–1067 (1973).
[CrossRef]

1970 (1)

E. S. Sarachik, G. T. Schappert, “Classical theory of scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
[CrossRef]

1964 (1)

L. S. Brown, T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, 3A (1964).
[CrossRef]

1962 (1)

Vachaspati, “Harmonics in the scattering of light by free electrons,” Phys. Rev. 128, 2 (1962).
[CrossRef]

Bardsley, J. N.

J. N. Bardsley, B. M. Penetrante, M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1989).
[CrossRef] [PubMed]

Bashkansky, M.

P. H. Bucksbaum, M. Bashkansky, T. J. McIlrath, “Scattering of electrons by intense coherent light,” Phys. Rev. Lett. 58, 349–352 (1987).
[CrossRef] [PubMed]

Brown, L. S.

L. S. Brown, T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, 3A (1964).
[CrossRef]

Bucksbaum, P. H.

P. H. Bucksbaum, M. Bashkansky, T. J. McIlrath, “Scattering of electrons by intense coherent light,” Phys. Rev. Lett. 58, 349–352 (1987).
[CrossRef] [PubMed]

Esarey, E.

P. Sprangle, E. Esarey, A. Ting, “Nonlinear interaction of intense laser pulses in plasmas,” Phys. Rev. A 41, 4463–4469 (1990).
[CrossRef] [PubMed]

Feldman, D.

B. Wolff, K. H. Welge, H. Rottke, D. Feldman, “Multiphoton-ionization of hydrogen-atoms in intense laser-fields,” Z. Phys. D 10, 35–43 (1988).
[CrossRef]

Ferray, M.

X. F. Li, L. A. Lompre, A. L’Huillier, G. Mainfray, M. Ferray, “Multiple harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 4, 5751–5761 (1989).
[CrossRef]

Fontana, J. R.

J. R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cherenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

Harris, E. G.

J. F. Seeley, E. G. Harris, “Heating of a plasma by multi-photon inverse bremsstrahlung,” Phys. Rev. A 7, 1064–1067 (1973).
[CrossRef]

Itzykson, C.

C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980), p. 225.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 657.

Kibble, T. W. B.

L. S. Brown, T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, 3A (1964).
[CrossRef]

Kimura, W. D.

R. D. Romea, W. D. Kimura, “Modeling of inverse Cerenkov laser acceleration with axicon laser-beam focus ing,” Phys. Rev. D 42, 1807–1818 (1990).
[CrossRef]

L’Huillier, A.

X. F. Li, L. A. Lompre, A. L’Huillier, G. Mainfray, M. Ferray, “Multiple harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 4, 5751–5761 (1989).
[CrossRef]

Li, X. F.

X. F. Li, L. A. Lompre, A. L’Huillier, G. Mainfray, M. Ferray, “Multiple harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 4, 5751–5761 (1989).
[CrossRef]

Lompre, L. A.

X. F. Li, L. A. Lompre, A. L’Huillier, G. Mainfray, M. Ferray, “Multiple harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 4, 5751–5761 (1989).
[CrossRef]

Mainfray, G.

X. F. Li, L. A. Lompre, A. L’Huillier, G. Mainfray, M. Ferray, “Multiple harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 4, 5751–5761 (1989).
[CrossRef]

McIlrath, T. J.

P. H. Bucksbaum, M. Bashkansky, T. J. McIlrath, “Scattering of electrons by intense coherent light,” Phys. Rev. Lett. 58, 349–352 (1987).
[CrossRef] [PubMed]

Mittleman, M. H.

J. N. Bardsley, B. M. Penetrante, M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1989).
[CrossRef] [PubMed]

Pantell, R. H.

J. R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cherenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

Penetrante, B. M.

J. N. Bardsley, B. M. Penetrante, M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1989).
[CrossRef] [PubMed]

Romea, R. D.

R. D. Romea, W. D. Kimura, “Modeling of inverse Cerenkov laser acceleration with axicon laser-beam focus ing,” Phys. Rev. D 42, 1807–1818 (1990).
[CrossRef]

Rottke, H.

B. Wolff, K. H. Welge, H. Rottke, D. Feldman, “Multiphoton-ionization of hydrogen-atoms in intense laser-fields,” Z. Phys. D 10, 35–43 (1988).
[CrossRef]

Sarachik, E. S.

E. S. Sarachik, G. T. Schappert, “Classical theory of scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
[CrossRef]

Schappert, G. T.

E. S. Sarachik, G. T. Schappert, “Classical theory of scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
[CrossRef]

Seeley, J. F.

J. F. Seeley, E. G. Harris, “Heating of a plasma by multi-photon inverse bremsstrahlung,” Phys. Rev. A 7, 1064–1067 (1973).
[CrossRef]

Sprangle, P.

P. Sprangle, E. Esarey, A. Ting, “Nonlinear interaction of intense laser pulses in plasmas,” Phys. Rev. A 41, 4463–4469 (1990).
[CrossRef] [PubMed]

P. Sprangle, Naval Research Laboratory, Washington, D.C. 20375 (personal communication, 1991).

Ting, A.

P. Sprangle, E. Esarey, A. Ting, “Nonlinear interaction of intense laser pulses in plasmas,” Phys. Rev. A 41, 4463–4469 (1990).
[CrossRef] [PubMed]

Vachaspati,

Vachaspati, “Harmonics in the scattering of light by free electrons,” Phys. Rev. 128, 2 (1962).
[CrossRef]

Welge, K. H.

B. Wolff, K. H. Welge, H. Rottke, D. Feldman, “Multiphoton-ionization of hydrogen-atoms in intense laser-fields,” Z. Phys. D 10, 35–43 (1988).
[CrossRef]

Wolff, B.

B. Wolff, K. H. Welge, H. Rottke, D. Feldman, “Multiphoton-ionization of hydrogen-atoms in intense laser-fields,” Z. Phys. D 10, 35–43 (1988).
[CrossRef]

Zavriyev, A.

A. Zavriyev, Columbia University, New York, N.Y 10027 (personal communication, 1990).

Zuber, J.-B.

C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980), p. 225.

J. Appl. Phys. (1)

J. R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cherenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

Phys. Rev. (2)

L. S. Brown, T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, 3A (1964).
[CrossRef]

Vachaspati, “Harmonics in the scattering of light by free electrons,” Phys. Rev. 128, 2 (1962).
[CrossRef]

Phys. Rev. A (4)

J. N. Bardsley, B. M. Penetrante, M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1989).
[CrossRef] [PubMed]

X. F. Li, L. A. Lompre, A. L’Huillier, G. Mainfray, M. Ferray, “Multiple harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 4, 5751–5761 (1989).
[CrossRef]

P. Sprangle, E. Esarey, A. Ting, “Nonlinear interaction of intense laser pulses in plasmas,” Phys. Rev. A 41, 4463–4469 (1990).
[CrossRef] [PubMed]

J. F. Seeley, E. G. Harris, “Heating of a plasma by multi-photon inverse bremsstrahlung,” Phys. Rev. A 7, 1064–1067 (1973).
[CrossRef]

Phys. Rev. D (2)

R. D. Romea, W. D. Kimura, “Modeling of inverse Cerenkov laser acceleration with axicon laser-beam focus ing,” Phys. Rev. D 42, 1807–1818 (1990).
[CrossRef]

E. S. Sarachik, G. T. Schappert, “Classical theory of scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
[CrossRef]

Phys. Rev. Lett. (1)

P. H. Bucksbaum, M. Bashkansky, T. J. McIlrath, “Scattering of electrons by intense coherent light,” Phys. Rev. Lett. 58, 349–352 (1987).
[CrossRef] [PubMed]

Z. Phys. D (1)

B. Wolff, K. H. Welge, H. Rottke, D. Feldman, “Multiphoton-ionization of hydrogen-atoms in intense laser-fields,” Z. Phys. D 10, 35–43 (1988).
[CrossRef]

Other (4)

C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980), p. 225.

P. Sprangle, Naval Research Laboratory, Washington, D.C. 20375 (personal communication, 1991).

A. Zavriyev, Columbia University, New York, N.Y 10027 (personal communication, 1990).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 657.

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Figures (10)

Fig. 1
Fig. 1

Feynman diagram for calculating the cross section for radiation into the second harmonic for the electron. The probability amplitudes of all combinations of absorption of the incident photons and reradiation into the second harmonic must be summed.

Fig. 2
Fig. 2

Trajectory of the electron along the polarization direction in an f/5, 100-mJ, 100-fs focus for three different initial radial positions. The time axis is in inverse frequency units.

Fig. 3
Fig. 3

Maximum intensity seen by the electrons versus their initial radial positions in an f/5, 100-mJ, 100-fs Gaussian focus.

Fig. 4
Fig. 4

a, Dipole radiation pattern in the nonrelativistic Thomson scattering regime, b, Radiation pattern at relativistic velocities around the instantaneous velocity vector.

Fig. 5
Fig. 5

Typical electron trajectory in a plane wave with an intensity of 3.6 × 1019 W/cm2 in the laboratory frame.

Fig. 6
Fig. 6

Radiated spectrum from an electron in a plane wave with an intensity of 3.6 × 1019 W/cm2 observed at an angle of 30° to the beam direction in the plane of polarization.

Fig. 7
Fig. 7

Radiated spectrum at an angle of 30° from the beam direction in the plane of polarization for only 10 electrons randomly distributed in the center of a 4-J, 800-nm, 100-fs, f/10 pulsed laser focus.

Fig. 8
Fig. 8

Radiated spectrum at an angle of 30° from the beam direction in the plane of polarization from 100 randomly distributed electrons in the center of a 4-J, 800-nm, 100-fs, f/10 pulsed laser focus.

Fig. 9
Fig. 9

Range of initial velocities that lead to trapping of the electron in an axicon focus formed by 100-fs pulses of different energies with a waist of 2.5 cm.

Fig. 10
Fig. 10

Radiated spectrum from an electron with an initial γ of 25 in the axicon focus formed by a 10-J, 100-fs pulse with a waist of 2.5 cm.

Equations (6)

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d 2 x μ d τ 2 = ( e m c ) F μ ν d x ν d τ
q = λ 2 π ( e E 0 m c 2 ) .
E x = E 0 ( 1 + i ξ ) exp [ ( x 2 + y 2 ) ω 0 2 ( 1 + i ξ ) + i ( k z ω t ) ( ( k z ω t ) ω T ) 2 ] , E z = i E 0 ( 1 + i ξ ) 2 2 x k ω 0 2 exp [ ( x 2 + y 2 ) ω 0 2 ( 1 + i ξ ) + i ( k z ω t ) ( ( k z ω t ) ω T ) 2 ] , ξ = 2 x k ω 0 2 .
E ( x , t ) = ( e c ) { n × ( [ n β ] × β ˙ ) ( 1 β n ) 3 R } ret .
E z ( r , z , t ) = E o J 0 ( n k r sin θ ) exp [ i ( ω t n k z cos θ ) ] , E x ( r , z , t ) = i cot θ E o J 1 ( n k r sin θ ) exp [ i ( ω t n k z cos θ ) ] , H ϕ = i n E o sin θ J 1 ( n k r sin θ ) exp [ i ( ω t n k z cos θ ) ] .
n β cos ( θ ) = 1 ,

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