Observation of the relativistic reversal of the ponderomotive potential

The interaction between a non-relativistic charged particle and a free-space electromagnetic wave can be described by the ponderomotive potential. Although ponderomotive electron-laser interactions at relativistic velocities are important for emerging technologies from laser-based particle accelerators to laser-enhanced electron microscopy, the effects of special relativity on the interaction have only been studied theoretically. We use a transmission electron microscope (beam energy $\le $ 300 keV) to measure the position-dependent phase shift imparted to a relativistic electron wave function when it traverses a standing laser wave (continuous-wave intensity $=$ 175 GW/cm$^{\mathrm{2}})$. In contrast to the non-relativistic case, we demonstrate that the phase shift depends on both the electron velocity and the wave polarization. Remarkably, if the electron's speed is greater than 1/$\surd $2 of the speed of light, the phase shift at the electric field nodes of the wave can exceed that at the antinodes. In this case there exists a polarization such that the phase shifts at the nodes and antinodes are equal, and the electron does not experience Kapitza-Dirac diffraction.