Phase of Pendellösung oscillations in X-ray dynamical diffraction for perfect crystals

2020 ◽  
Vol 76 (2) ◽  
pp. 132-136
Author(s):  
Takashi Saka
Keyword(s):  
Phase Shift ◽  
Perfect Crystal ◽  
Dynamical Diffraction ◽  
X Ray ◽  
The Real ◽  
Diffracted Waves

Formulations are given for the intensities of transmitted and diffracted waves in the Laue case of a perfect crystal. This is applicable irrespective of the magnitudes of both the real and imaginary parts of the Fourier components of the crystal polarizability. The phase shift of the Pendellösung oscillations of the transmitted and diffracted waves is analyzed in detail for a symmetrical Laue case. The phase is determined to shift continuously from out of phase to in phase for absorbing crystals.

Investigation of the phase shift in X-ray forward diffraction using an X-ray interferometer

1998 ◽  
Vol 5 (3) ◽  
pp. 967-968 ◽  
Author(s):  
Keiichi Hirano ◽  
Atsushi Momose
Keyword(s):  
Phase Shift ◽  
Silicon Crystal ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Bragg Geometry

The phase shift of forward-diffracted X-rays by a perfect crystal is discussed on the basis of the dynamical theory of X-ray diffraction. By means of a triple Laue-case X-ray interferometer, the phase shift of forward-diffracted X-rays by a silicon crystal in the Bragg geometry was investigated.

Complete determination of polarization state in the hard X-ray region

1991 ◽  
Vol 24 (6) ◽  
pp. 982-986 ◽  
Author(s):  
T. Ishikawa ◽  
K. Hirano ◽  
S. Kikuta
Keyword(s):  
Phase Shift ◽  
Linear Polarization ◽  
Amplitude Ratio ◽  
Polarization State ◽  
Perfect Crystal ◽  
Electric Vector ◽  
X Ray ◽  
Complete Determination ◽  
Unpolarized Radiation

A new method for complete determination of polarization state in the hard X-ray region is described. The system consists of a perfect-crystal phase retarder and a linear polarization analyzer. This method gives not only the amplitude ratio of mutually perpendicular electric vector components and the phase shift between them but also the proportion of unpolarized radiation.

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals

2018 ◽  
Vol 74 (5) ◽  
pp. 586-594 ◽  
Author(s):  
Takashi Saka
Keyword(s):  
Riemann Surface ◽  
Analytical Method ◽  
Bragg Condition ◽  
Approximation Characteristic ◽  
Dynamical Diffraction ◽  
X Ray ◽  
The Real ◽  
Dispersion Surface ◽  
Beam Approximation ◽  
Characteristic Features

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals is analysed using a Riemann surface. In the conventional two-beam approximation, each branch or wing of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities that specify the degree of departure from the exact Bragg condition and the reflection strength. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters with no approximation. Characteristic features of the dispersion surface are also revealed by geometrical considerations with respect to the Riemann surface.

X-ray third-order nonlinear plane-wave Bragg-case dynamical diffraction effects in a perfect crystal

2015 ◽  
Vol 22 (6) ◽  
pp. 1410-1418 ◽  
Author(s):  
Minas K. Balyan
Keyword(s):  
Analytical Solution ◽  
Perfect Crystal ◽  
Total Reflection ◽  
Numerical Calculations ◽  
Third Order ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Infinite Crystal ◽  
Nonlinear Plane ◽  
Diffraction Effects

Two-wave symmetric Bragg-case dynamical diffraction of a plane X-ray wave in a crystal with third-order nonlinear response to the electric field is considered theoretically. For certain diffraction conditions for a non-absorbing perfect semi-infinite crystal in the total reflection region an analytical solution is found. For the width and for the center of the total reflection region expressions on the intensity of the incidence wave are established. It is shown that in the nonlinear case the total reflection region exists below a maximal intensity of the incidence wave. With increasing intensity of the incidence wave the total reflection region's center moves to low angles and the width decreases. Using numerical calculations for an absorbing semi-infinite crystal, the behavior of the reflected wave as a function of the intensity of the incidence wave and of the deviation parameter from the Bragg condition is analyzed. The results of numerical calculations are compared with the obtained analytical solution.

X-Ray Dynamical Diffraction Process Inside a Distorted Crystal

1982 ◽  
Vol 37 (5) ◽  
pp. 460-464
Author(s):  
S. Takagi
Keyword(s):  
Wave Field ◽  
Perfect Crystal ◽  
Primary Wave ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Exit Surface ◽  
Wave Induced ◽  
The Waves ◽  
Resultant Wave

It is shown that the dynamical diffraction process inside a distorted crystal consists of ordinary dynamical progression inside perfect portions of the crystal and scattering at distortions. The scattered waves proceed as in the perfect crystal and can be multiply scattered. The sum of the primary wave induced at the entrance surface and the waves scattered at distorted parts inside the “inverted Borrmann triangle” gives the resultant wave field at the exit surface.

scholarly journals X-ray third-order nonlinear plane-wave Bragg-case dynamical diffraction effects in a perfect crystal. Erratum

2016 ◽  
Vol 23 (5) ◽  
pp. 1272-1272
Author(s):  
Minas K. Balyan
Keyword(s):  
Plane Wave ◽  
Perfect Crystal ◽  
Third Order ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Nonlinear Plane ◽  
Diffraction Effects

Formulae in the paper by Balyan (2015) [J. Synchrotron Rad.22, 1410–1418] are corrected.

X-ray dynamical diffraction analogues of the integer and fractional Talbot effects

2019 ◽  
Vol 26 (5) ◽  
pp. 1650-1659 ◽  
Author(s):  
Minas K. Balyan
Keyword(s):  
Perfect Crystal ◽  
Talbot Effect ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Dispersion Branch ◽  
Talbot Distance ◽  
Rational Multiple ◽  
Talbot Effects ◽  
First Time ◽  
Initial Distributions

The X-ray integer and fractional Talbot effect is studied under two-wave dynamical diffraction conditions in a perfect crystal, for the symmetrical Laue case of diffraction. The fractional dynamical diffraction Talbot effect is studied for the first time. A theory of the dynamical diffraction integer and fractional Talbot effect is given, introducing the dynamical diffraction comb function. An expression for the dynamical diffraction polarization-sensitive Talbot distance is established. At the rational multiple depths of the Talbot depth the wavefield amplitude for each dispersion branch is a coherent sum of the initial distributions, shifted by rational multiples of the object period and having its own phases. The simulated dynamical diffraction Talbot carpet for the Ronchi grating is presented.

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