Animation showing the figure-eight motion and the resulting

radiation patterns

animation (avi)
Click to download a zip-compressed avi movie file.

Box 1 (upper right-hand side):  This box shows the time evolution of the
electric and magnetic fields in a linearly-polarized laser beam. Blue lines
indicates the electric field and red lines indicates magnetic fields. The arrow
repesents the direction of propagation of the laser beam. The laser intensity is written
at the bottom of the window. The amplitude of the fields plotted is always
normalized to the viewing window, so you won't be able to see the change of
the amplitude when the laser intensity is changed.

Box 2 (middle upper): This box shows the motion of an electron in the laser beam that is
plotted at the right-hand side.  At low laser
intensities, the electron oscillates up and down in a linear trajectory
along the direction of the electric field. This is becuase that the motion
of electron is dominated by the laser electric field and the effect of the
magnetic field is negligible at such intensities. With increase of the laser
intensity the trajectory of the electron motion becomes a
firgure-of-eight. This is because that at high laser intensities the
velocity of the electron motion becomes comparable to the speed of light so
that the force of the magnetic field  becomes comparable to the force of the
electric field. The maximum offset
(amplitude) of the electron position in the vertical direction is shown at
the bottom of the window.

Box 3 (left upper), 4 (left lower), 5 (middle lower) and 6 (right lower):
These boxes show the angular patterns of the harmonic light radiated by
the motion of the electron in the laser fields at various laser intensities.
Angular pattern means the distribution of intensity of the radiation (light
emitted) as a function of angular direction.

Box 3 shows the the summation of the first to the tenth harmonics.  Box 4,
5 and 6 show the angular patterns of the first (n=1), second (n=2), and
third (n=3) harmonics.  The number at the bottom of each small
window (n=1, n=2, n=3, n=1:10) indicates the magnification of the angular
pattern with respect to the n=1 pattern (for which the magnification is
always unity). As you can see, the radiation pattern of n=1 is a typical dipole
radiation pattern. The hole in the angular pattern is along the direction of
the electric field. We rotate the radiation pattern (with respect to the
plot of the electron motion and laser fields) for ease of viewing.
The intensity of the harmonics (n=2,3) increases rapidly
with increase of laser intensity as a result of the relativistic nonlinear
motion of the electron ( I(n) ~ (laser intensity)^n ), as seen in the
magnification factor. In addition, the angular pattern also becomes
stretched toward the opposite of laser propagation direction, as a result of
relativistic transformation (Lorentz transformation). Each harmonic has its own
unique angular pattern, serving as the unique signatures of such
photon-emitting process.
 

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