The surprising message of Allen
et al.
(Allen
et al.
1992
Phys. Rev. A
45
, 8185 (
doi:10.1103/PhysRevA.45.8185
)) was that photons could possess orbital angular momentum in free space, which subsequently launched advancements in optical manipulation, microscopy, quantum optics, communications, many more fields. It has recently been shown that this result also applies to quantum mechanical wave functions describing massive particles (matter waves). This article discusses how electron wave functions can be imprinted with quantized phase vortices in analogous ways to twisted light, demonstrating that charged particles with non-zero rest mass can possess orbital angular momentum in free space. With Allen
et al.
as a bridge, connections are made between this recent work in electron vortex wave functions and much earlier works, extending a 175 year old tradition in matter wave vortices.
This article is part of the themed issue ‘Optical orbital angular momentum’.
Perspectives on advances in high-capacity, free-space communications using multiplexing of orbital-angular-momentum beams
