Twisted X-rays: incoming waveforms yielding discrete diffraction patterns for helical structures

TL;DR

This paper introduces twisted X-ray waveforms that produce discrete diffraction patterns for helical structures, enabling direct atomic structure determination without crystallization.

Contribution

The authors theoretically derive twisted wave solutions to Maxwell's equations that generate discrete diffraction patterns for helical structures, expanding X-ray diffraction techniques.

Findings

Twisted waves produce discrete diffraction patterns for helical structures.

Peak locations encode symmetry and helix parameters.

Peak intensities reveal electronic structure.

Abstract

Conventional X-ray methods use incoming plane waves and 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 Maxwell's 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 structure of numerous biomolecules and nanostructures with helical symmetries. This would eliminate the need to crystallize those structures or their subunits.