  Free electrons moving in an optical standing wave field feel the
ponderomotive potential, acting as a refractive-index medium in electron
optics. Emerging technologies involving this potential have been proposed and
realized in electron microscopy, such as electron phase-contrast imaging using
a laser standing wave in an optical enhancement cavity. However, the
interaction between electrons with a cylindrically distributed optical field
has not been investigated although its suitability for electron-optical imaging
systems. In this study, we theoretically show that the divergence and
convergence forces are provided by tightly focused cylindrically polarized
light beams. The radially and azimuthally polarized beams with an annular
profile are focused using a high numerical aperture optical lens. The intensity
distributions at the focus function are concave and convex electron round
lenses, respectively. The convex lens formed by the azimuthally polarized beam
possesses negative (opposite sign) spherical aberration compared with
conventional electron round lenses created by electrodes and magnetic coils.
This remarkable result will contribute to the innovative design of
electron-optical imaging systems and bring new capabilities into matter-wave
optics.
