  The properties of electron round lenses produced by the ponderomotive
potential are investigated in geometrical optics. The potential proportional to
the intensity distribution of a focused first-order Bessel or Laguerre-Gaussian
beam is exploited to produce an electron round lens and a third-order spherical
aberration corrector. Several formulas for the focal length and spherical
aberration coefficients in the thin-lens approximation are derived to set the
lens properties and associated light beam parameters. When the mode field of
the optical beam is small, the electron trajectory calculation results show
properties similar to those obtained using the formulas. Alternatively, large
higher-order aberrations are introduced because of the annular distribution of
the potential. The second- and higher-order Bessel and Laguerre-Gaussian beams
produce no focusing power and no negative third-order spherical aberration;
however, they can still be used as circularly symmetric higher-order aberration
correctors. Results show that the ponderomotive potential-based electron lens
or phase plate forms a refractive index medium with a shape that is
considerably more flexible than that achieved in the case of conventional
electrostatic and magnetic electron optics. The formulas presented herein can
serve as guidelines for designing preferred light fields, thus promoting the
advancement of a novel technology in electron optics that exploits the
electron-light interaction.
