# Design of electrostatic phase elements for sorting the orbital angular momentum of electrons

## TL;DR

This paper proposes a design for an electron OAM sorter using electrostatic phase elements, analyzes imperfections via simulations, and introduces a three-needle setup to mitigate aberrations and improve measurement accuracy.

## Contribution

It introduces a novel electrostatic phase element design for electron OAM sorting and demonstrates a method to compensate for imperfections using multiple charged needles.

## Key findings

- Finite needle length causes astigmatism and cross-talk.
- A three-needle setup effectively compensates aberrations.
- The improved design achieves near-ideal OAM spectrum measurements.

## Abstract

The orbital angular momentum (OAM) sorter is a new electron optical device for measuring an electron s OAM. It is based on two phase elements, which are referred to as the unwrapper and corrector and are placed in Fourier conjugate planes in an electron microscope. The most convenient implementation of this concept is based on the use of electrostatic phase elements, such as a charged needle as the unwrapper and a set of electrodes with alternating charges as the corrector. Here, we use simulations to assess the role of imperfections in such a device, in comparison to an ideal sorter. We show that the finite length of the needle and the boundary conditions introduce astigmatism, which leads to detrimental cross-talk in the OAM spectrum. We demonstrate that an improved setup comprising three charged needles can be used to compensate for this aberration, allowing measurements with a level of cross-talk in the OAM spectrum that is comparable to the ideal case.