  Free electrons moving in an electromagnetic wave feel the ponderomotive
force, which as an effective potential acts as a refractive-index medium in
electron optics. Emerging technologies involving the effective 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 of electrons with a cylindrically distributed
electromagnetic field has not been studied despite its suitability for
electron-optical imaging systems. Here, we theoretically show that the radial
ponderomotive force can be provided by a tightly focused cylindrically
polarized light beam. The radially and azimuthally polarized beams with an
annular profile are focused using a high-numerical aperture optical lens, and
then the electromagnetic fields at the focus create the divergence and
convergence forces to electrons, respectively. In particular, the divergence
force formed by the azimuthally polarized beam acts as an electron convex lens
with negative (opposite sign) spherical aberration compared to conventional
electron round lenses created by electrodes and magnetic coils. This remarkable
result will contribute to the innovative design of electron optical systems and
also bring new capabilities into matter-wave optics.
