Electromagnetic lensing using the Aharonov-Bohm effect

We demonstrate theoretically and experimentally a new electromagnetic lensing concept using the magnetic vector potential - in a region free of classical electromagnetic fields - via the Aharonov-Bohm effect. This toroid-shaped lens with poloidal current flow allows for electromagnetic lensing which can be tuned to be convex or concave with a spherical aberration coefficient of opposite polarity to its focal length. This new lens combines the advantages of traditional electromagnetic and electrostatic field-based lenses and opens up new possibilities for the optical design of charged-particle systems. More generally, these results demonstrate that the Aharonov-Bohm effect can shape charged particle wavefronts beyond simple step shifts if topologies beyond simple flux lines are considered and supports the physical significance of the magnetic vector potential.