Super-oscillating Electron Wave Functions with Sub-diffraction Spots

TL;DR

This paper demonstrates how to create super-oscillating electron wave functions with sub-diffraction-limited spots, surpassing traditional diffraction limits, and introduces structured vortex beams with smaller dark cores for high-resolution electron-matter interaction studies.

Contribution

It extends super-oscillation concepts from optics to electron wave functions, experimentally producing sub-diffraction electron spots and structured vortex beams.

Findings

Achieved an electron central spot of 106 pm radius, below the diffraction limit.

Demonstrated structured vortex beams with smaller dark cores.

Showed potential for sub-atomic resolution in electron-matter interactions.

Abstract

Almost one and a half centuries ago, Ernst Abbe [1] and shortly after Lord Rayleigh [2] showed that when an optical lens is illuminated by a plane wave, a diffraction-limited spot with a radius 0.61*lambda/sin(alpha) is obtained, where lambda is the wavelength and alpha is the semi-angle of the beam's convergence cone. However, spots with much smaller features can be obtained at the focal plane when the lens is illuminated by an appropriately structured beam. Whereas this concept is known for light beam, here, we show how to realize it for massive-particle wave function of a free electron. We experimentally demonstrate an electron central spot of radius 106 pm, which is more than two times smaller than the diffraction limit of the experimental setup used. In addition, we demonstrate that this central spot can be structured by adding orbital angular momentum to it. The resulting super-oscillating vortex beam has a smaller dark core with respect to the regular vortex beam. This new family of electron beams having hot-spots with arbitrarily small features and tailored structure can be useful for studying electron-matter interactions with sub-atomic resolution.