  A century ago, J. J. Thomson showed that the scattering of low-intensity
light by electrons was a linear process (i.e., the scattered light frequency
was identical to that of the incident light) and that light's magnetic field
played no role. Today, with the recent invention of ultra-high-peak-power
lasers it is now possible to create a sufficient photon density to study
Thomson scattering in the relativistic regime. With increasing light intensity,
electrons quiver during the scattering process with increasing velocity,
approaching the speed of light when the laser intensity approaches 10^18
W/cm^2. In this limit, the effect of light's magnetic field on electron motion
should become comparable to that of its electric field, and the electron mass
should increase because of the relativistic correction. Consequently, electrons
in such high fields are predicted to quiver nonlinearly, moving in figure-eight
patterns, rather than in straight lines, and thus to radiate photons at
harmonics of the frequency of the incident laser light, with each harmonic
having its own unique angular distribution. In this letter, we report the first
ever direct experimental confirmation of these predictions, a topic that has
previously been referred to as nonlinear Thomson scattering. Extension of these
results to coherent relativistic harmonic generation may eventually lead to
novel table-top x-ray sources.
