We report the first direct observation of electron inelastic scattering from the ponderomotive potential of an intense laser pulse in vacuum. Electrons gained up to 0.2 eV when scattered from the temporal leading edge of a 1064-nm (1.165 eV), 140-psec laser pulse, and lost comparable amounts of energy when scattered from the trailing edge. When directed to the most intense part of the pulse, they were deflected out of the beam.PACS numbers: 42.50.Vk At very high light intensities electron-photon scattering is dominated by stimulated photon interactions known as ponderomotive effects. This was first recognized by Kaptiza and Dirac, x who suggested that an optical standing wave could cause Bragg scattering of electrons by stimulated Thomson scattering. After the advent of lasers, Kibble, Eberly, and others reexamined the problem, concluding that a continuous laser beam could form a repulsive potential for free electrons. 2 " 6 Kibble pointed out that for a short laser pulse, electrons may exchange energy with light in nonquantized amounts, 2 just as a surfer gains potential energy when lifted by a wave.We have observed for the first time electron acceleration and deceleration produced by "surfing" on the leading and trailing temporal edge of a laser pulse in vacuum. A unique pulsed beam of electrons (80 psec duration) was used to study the ponderomotive potential of a short (140 psec), tightly focused, 1064-nm laser pulse at four electron energies between 0.54 and 4.18 eV. These observations agree with calculations based on the predictions of Kibble and others. 2 " 4 Kapitza and Dirac adopted scattering formalism to derive the probability for the stimulated Thomson effect. However, in the regime of very high light intensity, the scattering rate is so great that a classical treatment is possible. In the classical limit, stimulated photon scattering is most easily understood by consideration of the change in the total energy of an electron that takes place in a coherent light field. 3 The classical wiggling motion of the electron in response to the electromagnetic field produces a time-averaged kinetic energy of
(7 (r,f) = 2ne 2 I(r,t )/m e c(o 2 .(1)Here e is the electron charge, m e its mass, and /, co, and c are the intensity, angular frequency, and speed of the light, respectively. In the full quantum theory, U(r,t) is the increase in the electron self-energy due to stimulated scattering of photons. 5 In a classical relativistic theory, U(r>t)/c 2 is the relativistic increase in the mass of an electron with speed v =[2£/(r,f )/mJ 1/2 , and the scattering can be shown to be the motion of a particle with a position-and time-dependent variable rest mass m =m e /
(I -v 2 /c 2 ) l/2~ m e + U(r,t)/c 2 . 4For our purposes, however, it suffices to consider a nonrelativistic free electron, in the presence of a nearly monochromatic classical radiation field described by a vector potential A(r,/). The Hamiltonian for this particle is
H _ lp-(e/c)A] 2 _ p 2 _ e 2m e 2m e 2m e c (p-A + Ap) 2m e c A (2)The A 2 term is a posi...
