Graphene Nanopore Arrays for Electron Focusing and Antifocusing

We have shown, via numerical simulations, that a symmetric array of nanopores with appropriately designed shapes and sizes arranged along an arc of a circle in a graphene nanoribbon can focus or antifocus an incident ballistic electron wavefunction. The position of the focal/antifocal region depends on the electron energy. This effect, which takes place in the energy interval of one-transverse-mode propagation in the nanoribbon, highlights the similarities with plasmonic focusing by an array of holes in a metallic sheet, while emphasizing the differences between the propagation and excitation of electrons and electromagnetic fields. In particular, the electronic antilens has no counterpart in classical optics.