X-ray two-wave dynamical diffraction analogue of Talbot effect

Abstract

Imaging of periodic objects in free space brings us to the Talbot effect in optics, for x-rays and for matter waves. X-ray dynamical diffraction imaging of periodic objects inside a crystal has scientific and applied interest. Thus, we arrive at the concept of the dynamical diffraction Talbot effect in a crystal. This work is the first attempt to investigate the Talbot effect inside a medium. Using the Green function formalism, an exact formula for the diffracted wave amplitude is found. By means of ‘paraxial’ approximation, which is an analogue of the paraxial approximation in optics, it is shown that the dynamical diffraction Talbot effect takes place. Expressions for polarization sensitive Talbot and corrected Talbot distances are obtained. We analyse the influences of absorption, Bragg filtration of harmonics and polarization on the dynamical diffraction Talbot effect. For the first time, simulated Talbot carpets inside the crystal are obtained, which show that the predictions, obtained by ‘paraxial’ approximation, are true. We present the dynamical diffraction Talbot carpets observation method by means of a wedge-shaped crystal. The dynamical diffraction Talbot effect can be used for investigation of objects and crystal defects and deformations. Dynamical diffraction Talbot effect investigations in optics, for electrons and neutrons, are possible.