Ponderomotive Achromat for Electron Optics: Radially Polarized Annular Focusing and a Round-Lens Corrector Regime

TL;DR

This paper explores how ponderomotive electron lenses can be engineered for achromatization by analyzing their energy dispersion properties, leading to novel round-lens functionalities including negative aberrations.

Contribution

It demonstrates the energy-dependent dispersion of ponderomotive lenses and derives a condition for achromatization, introducing a new approach to electron-optical element design.

Findings

Distinct energy dispersion for longitudinal and transverse components due to polarization mixing.

Derived a geometry condition for achromatization using a local Abbe number.

Identified parameter regimes for negative chromatic aberration and a compact lens corrector regime.

Abstract

Ponderomotive electron optics has recently attracted attention because structured optical fields can provide round-lens operation with functionalities that are difficult to achieve using conventional electron-optical elements, including negative lens power and negative spherical aberration. A largely unexplored aspect is how ponderomotive lenses disperse with electron energy and whether that dispersion can be engineered for achromatization. Here we show that, for relativistic electrons, longitudinal and transverse optical components exhibit distinct energy dispersion because Lorentz-boost-induced polarization mixing modifies the effective lens action. Focusing a radially polarized annular beam produces two co-located Bessel-like components near focus, a transverse $J_1^2$ lens and a longitudinal component with relativistic mixing, forming a zero-separation doublet. Using a local Abbe number defined in the energy domain, we derive a single geometry condition for achromatization and evaluate the spot-size performance in a thin-lens model. We also identify parameter regions where the same element yields negative on-axis chromatic aberration, indicating a compact round-lens corrector regime.