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Properties of electron lenses produced by ponderomotive potential with Bessel and Laguerre–Gaussian beams

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 (LG) beam is exploited to produce an electron round lens and a third-order spherical aberration (SA) corrector. Several formulas for the focal length and SA 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 LG beams produce no focusing power and no negative third-order SA; 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.