Abstract

The harmonics of the scattering of a femtosecond intense laser pulse by an electron has been numerically investigated. The harmonic spectrum shows interesting red shifts and parasitic lines in the blue sides of harmonic lines. The red shift of the lines is found to be caused by the dilation of laser oscillation experienced by an electron due to its relativistic drift motion along the direction of a driving laser propagation and the parasitic lines come from the variation of the laser intensity. The angular distribution of each higher harmonic line shows double peak patterns in the forward direction. The backward scattering has its own distinct pattern: line-shaped nodes perpendicular to the laser electric field, the number of which is the harmonic order number minus one. As the harmonic order increases, the primary peaks of higher harmonics move from the backward to the forward direction of the laser propagation. In the time domain, each radiation pulse in the case of a linearly-polarized laser pulse has a double peak structure due to the disappearance of the acceleration during the half cycle of an electron’s oscillation.

© 2002 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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IEEE Trans. Plasma Sci.

E. Esarey, A. Ting, P. Sprangle, D. Umstadter, and X. Liu, �??Nonlinear analysis of relativistic harmonic generation by intense lasers in plasmas,�?? IEEE Trans. Plasma Sci. 21, 95 (1993).
[CrossRef]

J. Appl. Phys.

P. Sprangle, A. Ting, E. Esarey, and A. Fisher, "Tunable, short pulse hard x-rays from a compact laser synchrotron source,�?? J. Appl. Phys. 72, 5032 (1992).
[CrossRef]

Laser and Particle Beams

Y. Ueshima, Y. Kishimoto, A. Sasaki, and T. Tajima, �??Laser Larmor X-ray radiation from low-Z matter,�?? Laser and Particle Beams 17, 45 (1999).
[CrossRef]

Nature

S.-Y. Chen, A. Maksimchuk, and D. Umstadter, �??Experimental observation of relativistic nonlinear Thomson scattering,�?? Nature (London) 396, 653 (1998).
[CrossRef]

Phys. Plasmas

Wei Yu, M. Y. Yu, J. X. Ma, Z. Xu, �??Strong frequency up-conversion by nonlinear Thomson scattering from relativistic electrons,�?? Phys. Plasmas 5, 406 (1998).
[CrossRef]

F. V. Hartemann, �??High-intensity scattering processes of relativistic electrons in vacuum,�?? Phys. Plasmas 5, 2037 (1998).
[CrossRef]

Phys. Rev.

Vachaspati, �??Harmonics in the Scattering of Light by Free Electrons,�?? Phys. Rev. 128, 664 (1962).
[CrossRef]

L. S. Brown and T. W. B. Kibble, �??Interaction of Intense Laser Beams with Electrons,�?? Phys. Rev. 133, A705 (1964).
[CrossRef]

Phys. Rev. A

E. Esarey and P. Sprangle, �??Generation of stimulated backscattered harmonic radiation from intense-laser interactions with beams and plasmas,�?? Phys. Rev. A 45, 5872 (1992).
[CrossRef] [PubMed]

Dong-Eon Kim, Csaba Toth, and Christopher P. J. Barty, �??Population inversion between atomic inner-shell vacancy states created by electron-impact ionization and Coster-Kronig decay,�?? Phys. Rev. A Rap. Comm. 59, R4129 (1999)

D. Kim, S. H. Son, J. H. Kim, C. Toth, and C. P. J. Barty, �??Gain characteristics of inner-shell photoionization-pumped L23M1 transition in Ca,�?? Phys. Rev. A 63, 023806 (2001).
[CrossRef]

R. E. Wagner, Q. Su, and R. Grobe, �??High-order harmonic generation in relativistic ionization of magnetically dressed atoms,�?? Phys. Rev. A 60, 3233 (1999).
[CrossRef]

Phys. Rev. D

E. S. Sarachik and G. T. Schappert, �??Classical Theory of the Scattering of Intense Laser Radiation by Free Electrons,�?? Phys. Rev. D 1, 2738 (1970).
[CrossRef]

Phys. Rev. E

E. Esarey, S. K. Ride, and P. Sprangle, �??Nonlinear Thomson Scattering of intense laser pulses from beams and plasmas,�?? Phys. Rev. E 48, 3003 (1993).
[CrossRef]

K. Lee, Y. H. Cha, M. S. Shin, B. H. Kim, and D. Kim, �??Relativistic nonlinear Thomson scattering as attosecond x-ray source,�?? in print in Phys. Rev. E 67 2003.
[CrossRef]

Phys. Rev. Lett.

J. Zhou, J. Peatross, M. M. Murnane, and H. C. Kapteyn, �??Enhanced High-Harmonic Generation Using 25 fs Laser Pulses,�?? Phys. Rev. Lett. 76, 752 (1996).
[CrossRef] [PubMed]

A. E. Kaplan and P. L. Shkolnikov, �??Lasetron: A Proposed Source of Powerful Nuclear-Time-Scale Electromagnetic Bursts,�?? Phys. Rev. Lett. 88, 074801 (2002)
[CrossRef] [PubMed]

S.-Y. Chen, A. Maksimchuk, E. Esarey, and D. Umstadter, �??Observation of Phase-Matched Relativistic Harmonic Generation,�?? Phys. Rev. Lett. 84, 5528 (2000).
[CrossRef] [PubMed]

Phys. Today

G.A. Mourou, C. P. J. Barty, and M.D. Perry, �??Ultrahigh-Intensity Lasers: Physics of the Extreme on a Tabletop,�?? Phys. Today 51, 22 (1998).
[CrossRef]

Science

M. D. Perry and G. Mourou, "Terawatt to Petawatt Subpicosecond Lasers,�?? Science 264, 917 (1994)
[CrossRef] [PubMed]

Other

J. Sheffield, Plasma Scattering of Electromagnetic Radiation, (Academic Press, New York, 1975).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Energy spectra integrated over solid angles are plotted for peak laser intensities of 1017 W/cm2 and 1018 W/cm2 and (b) Spectral lines in the forward and backward direction are separately plotted for the case of 1018 W/cm2. The vertical lines denotes unshifted harmonic energies.

Fig. 2.
Fig. 2.

For a laser intensity of 1018 W/cm2, (a) energy spectrum and (b) radiation power are plotted at the direction of θ = 90° and ϕ = 0° (The direction of the laser electric field).

Fig. 3.
Fig. 3.

Theta distributions of the time-integrated radiations on the plane of the electron’s motion (ϕ = 0°) up to 6th order of harmonics are plotted for laser intensities of (a) 1017 W/cm2 and (b) 1018 W/cm2. The directions of the laser propagation and the electric field are also shown for clarity. (c) The directions of the primary peak of the harmonic radiations, θ peak are plotted wherein the horizontal lines indicate the directions of the electron’s velocity at the peak laser intensities.

Fig. 4.
Fig. 4.

(a) The contour plots of the angular distributions of the total radiation for the laser intensity of 1018 W/cm2 are plotted with the linear scale. Those for other harmonics [(b) 1st, (c) 2nd, (d) 3rd, (e) 4th, (f) 5th, and (g) 6th, respectively] are plotted with the logarithmic scale. The directions of the laser field with Cartesian coordinate in parenthesis are shown in (a) for each forward and backward direction. The left and right circle in each sub-figure represents the angular distributions of the forward and backward direction, respectively.

Fig. 5.
Fig. 5.

Schematic diagram to account for the shift of the fundamental frequency on the direction

Fig. 6.
Fig. 6.

For a laser intensity of 1018 W/cm2, (a) the variation of TD and ES on the direction are compared between our simulation result (symbol data) and Esarey et. al.’s formula [4] and (b) the oscillation dynamics of the electron is plotted, which shows the oscillation period is of 3 fs and the same as TD (θ = 90°) in (a).

Equations (8)

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a o = 8.5 × 10 10 λ I 1 2 ,
E s = E o 1 + 1 4 a o 2 ( 1 cos θ ) ,
ω L t k L · r ( t ) = ω L t k L · r ( t ) + 2 π ,
T e = T L + Δ z c ,
T e T L = ( 1 + 1 4 a o 2 ) .
T D = T e Δ l c ,
= T e Δ z c cos θ .
T D = T e ( T e T L ) cos θ ,

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