The secular dynamics of a nonrelativistic charged particle in an 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. Here, we use a transmission electron microscope to measure the position-dependent phase shift imparted to a relativistic electron wave function when it traverses a standing laser wave. The kinetic energy of the electrons is varied between 80 and 300 keV, and the laser standing wave has a continuous-wave intensity of 175  GW/cm^{2}. In contrast to the nonrelativistic case, we demonstrate that the phase shift depends on both the electron velocity and the wave polarization, confirming the predictions of a quasiclassical theory of the interaction. Remarkably, if the electron's speed is greater than 1/sqrt[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. Our results thus provide new capabilities for coherent electron beam manipulation.

Transmission electron microscopy (TEM) of rapidly frozen biological specimens, or cryo-EM, would benefit from the development of a phase plate for in-focus phase contrast imaging. Several types of phase plates have been investigated, but rapid electrostatic charging of all such devices has hindered these efforts. Here, we demonstrate electron phase manipulation with a high-intensity continuous-wave laser beam, and use it as a phase plate for TEM. We demonstrate the laser phase plate by imaging an amorphous carbon film. The laser phase plate provides a stable and tunable phase shift without electrostatic charging or unwanted electron scattering. These results suggest the possibility for dose-efficient imaging of unstained biological macromolecules and cells.

Transmission electron microscopy (TEM) of vitrified biological macromolecules (cryo-EM) is limited by the weak phase contrast signal that is available from such samples. Using a phase plate would thus substantially improve the signal-to-noise ratio. We have previously demonstrated the use of a high-power Fabry-Perot cavity as a phase plate for TEM. We now report improvements to our laser cavity that allow us to achieve record continuous wave intensities of over 450 GW/cm², sufficient to produce the optimal 90° phase shift for 300 keV electrons. In addition, we have performed the first cryo-EM reconstruction using a laser phase plate, demonstrating that the stability of this laser phase plate is sufficient for use during standard cryo-EM data collection.