To generate an Airy beam using electrons, the team massaged the wave function of an electron beam by shooting it through a specially designed hologram—its pattern was designed specifically to cause the desired result….

This is interesting; unfortunately the problem is that we cannot visualize how the 'abstract' wave function of electron beam could generate the Airy beam? Understand its mechanism would make it more interesting, as below…
http://www.vacuum...19〈=en

Major error here in this article."...researchers in 2007 discovered a way to actually create Airy beams based on light". Blew it by 25 yrs. Optical physicists have been routinely making optical & microwave Airy beams since the early `80s.

Physics Review Letters
"Observation of Accelerating Airy Beams"
(Received 15 August 2007; published 20 November 2007)

We report the first observation of Airy optical beams. This intriguing class of wave packets, initially
predicted by Berry and Balazs in 1979, has been realized in both one- and two-dimensional configurations.

Optical << based on light. The preparation of Airy beams requires curved gratings, which are easier to manufacture for microwaves. But the optical ( = visible light) beams are of much later origin.

(from the article)

when it's sent through an aperture, such as is done with a common flashlight, diffraction occurs, causing the beam to widen and lose its intensity.

No, common flashlights don't send their light through apertures. They use approximately paraboloid reflectors, so as to produce a mostly straight beam. Some spreading is desirable, actually, so the reflectors are made to allow that. Loss of intensity is inescapable with any non-colllimated or non-coherent emission; diffraction is not necessary to cause it.