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Conventional X-ray methods use incoming plane waves which result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered at helical structures. As examples we present simulated diffraction patterns of carbon nanotubes and tobacco mosaic virus. The new incoming waveforms, which we call twisted waves due to their geometric shape, are found theoretically as closed-form solutions to Maxwellu0027s equations. The theory of the ensuing diffraction patterns is developed in detail. A twisted analogue of the Von Laue condition is seen to hold, with the peak locations encoding the symmetry and the helix parameters, and the peak intensities indicating the electronic structure in the unit cell. If suitable twisted X-ray sources can in the future be realized experimentally, it appears from our mathematical results that they will provide a powerful tool for directly determining the detailed atomic structu...

Twisted X-Rays: Incoming Waveforms Yielding Discrete Diffraction Patterns for Helical Structures