Spherical-wave X-ray dynamical diffraction Talbot effect inside a crystal

Abstract

<jats:p>Two-wave dynamical diffraction of an X-ray spherical wave in a crystal, when the wave passes through an object with a periodic amplitude transmission function, is considered. The behavior of the diffracted wave (spherical-wave Talbot effect) in the crystal is investigated. The Talbot effect inside the crystal is accompanied by the focusing effect and the pendulum effect. Peculiarities of the effect before the focus point, in the focusing plane and in the region after the focus point inside the crystal are revealed. An expression is found for the Talbot depth and the spherical-wave Talbot effect in these three regions is investigated. The spherical-wave dynamical diffraction Talbot effect in a crystal is compared with the classical spherical-wave Talbot effect and also with spherical-wave effects inside the crystal without a periodic object.</jats:p>

X-ray dynamical diffraction Talbot effect behind a crystal in free space

“…The peak intensity of each focal point is proportional to jA n j 2 , but the phase information of each A n is lost. Similar results were obtained for diffraction inside the crystal (Balyan et al, 2020).…”

“…Continuing the theme of the work by Balyan (2019aBalyan ( ,b,c, 2020 and Balyan et al (2020), in this paper the dynamical diffraction Talbot effect for a diffracted wave is studied behind the crystal and the behavior of this wave is investigated. The cases of object illumination with both spherical and plane waves are considered.…”

“…The wave then falls on a crystal at the Bragg angle relative to the reflecting atomic planes RP, which are perpendicular to the entrance surface of the crystal. The dynamical diffraction Talbot effect takes place inside the crystal (Balyan et al, 2020;Balyan, 2019a). We will study the behavior of the diffracted wave emerging from the exit surface of the crystal and propagating in free space.…”

“…Note that at L h ! 0 expression (12) takes the form of the previously obtained expression inside the crystal (Balyan et al, 2020). By representing the amplitude of the diffracted wave (12) as the sum of two modes and separating the phases of each of the harmonics, we have…”

“…The X-ray spherical-wave theory of the dynamical diffraction Talbot effect inside a crystal has been investigated by Balyan et al (2020). In that work it was shown that, in addition to the pendulum effect, the Talbot effect is also accompanied by focusing inside the crystal (Aristov et al, 1980;Levonyan, 1981).…”