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

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 propagation through single crystals in an anomalous scattering range and determination of permittivity tensor components by transmission experiments

Simple equations are obtained which enable one to describe x‐ray propagation through single crystals in an anomalous scattering range when Bragg diffraction does not take place and the angle between the initial x‐ray wave and crystal surface significantly exceeds the critical value. Using the results obtained we develop a method for determining the components of the permittivity tensors of non‐gyrotropic crystals of arbitrary symmetry by transmission experiments. Copyright © 2003 John Wiley & Sons, Ltd.     

Development of variable‐magnification X‐ray Bragg optics

A novel X‐ray Bragg optics is proposed for variable‐magnification of an X‐ray beam. This X‐ray Bragg optics is composed of two magnifiers in a crossed arrangement, and the magnification factor, M, is controlled through the azimuth angle of each magnifier. The basic properties of the X‐ray optics such as the magnification factor, image transformation matrix and intrinsic acceptance angle are described based on the dynamical theory of X‐ray diffraction. The feasibility of the variable‐magnification X‐ray Bragg optics was verified at the vertical‐wiggler beamline BL‐14B of the Photon Factory. For X‐ray Bragg magnifiers, Si(220) crystals with an asymmetric angle of 14° were used. The magnification factor was calculated to be tunable between 0.1 and 10.0 at a wavelength of 0.112 nm. At various magnification factors (M≥ 1.0), X‐ray images of a nylon mesh were observed with an air‐cooled X‐ray CCD camera. Image deformation caused by the optics could be corrected by using a 2 × 2 transformation matrix and bilinear interpolation method. Not only absorption‐contrast but also edge‐contrast due to Fresnel diffraction was observed in the magnified images.     

Acoustooptic multiplication of the frequency shift of optical radiation on the basis of bragg polarization splitting

A technique for the acoustooptic multiplication of the frequency shift of an optical beam is proposed. The technique is based on the cascade diffraction of the beam by a single acoustic wave with the use of Bragg polarization splitting in a uniaxial crystal. The fundamental possibility of the practical realization of the technique is confirmed experimentally by using anisotropic acoustooptic diffraction in LiNbO₃.     

X-ray Laue diffraction with allowance for two-dimensional curvature of the wavefront: The concept a locally plane wave

Symmetrical Laue diffraction in a perfect crystal with a plane entance surface is considered. The two dimensional curvature of the wave front of the incident beam is taken into account. Using the corresponding Green function, a general expression for the amplitude of diffracted wave in the crystal is presented. Based on this expression, the concept of a locally plane wave is analyzed taking into account two-dimensional curvature of the wave front. This concept is used for obtaining the rocking curves depending on the angles of deviation from the chosen exact Bragg direction in both the diffraction plane and in perpendicular direction. The obtained result is compared with the result of the standard dynamical diffraction theory.     

Diffraction of X‐ray free‐electron laser femtosecond pulses on single crystals in the Bragg and Laue geometry

A solution of the problem of dynamical diffraction for X‐ray pulses with arbitrary dimensions in the Bragg and Laue cases in a crystal of any thickness and asymmetry coefficient of reflection is presented. Analysis of pulse form and duration transformation in the process of diffraction and propagation in a vacuum is conducted. It is shown that only the symmetrical Bragg case can be used to avoid smearing of reflected pulses.     

Multiplication of optical frequency shift by cascaded electro-optic traveling phase gratings operating above 10 GHz

We propose and demonstrate an electro-optic (EO) multiplication of a frequency shift using 10 GHz order electrical signal. The principle is based on a successive Bragg diffraction from cascaded EO traveling phase gratings in a traveling wave EO phase modulator. We fabricate a shift frequency doubler using simple domain engineering processes in a LiTaO? crystal. Frequency shifting of ±32.5 GHz with an efficiency of 60% is demonstrated using a 16.25 GHz modulation signal.     

Diffraction reflection of x-ray radiation with a two-dimensionally bounded wavefront from perfect crystals

The problem of dynamical diffraction of x-ray radiation with a two-dimensionally bounded wavefront is solved in the Bragg and Laue geometries in a crystal with an arbitrary thickness and an arbitrary reflection asymmetry parameter. An analysis of the wavefront deformation during the diffraction and subsequent propagation is carried out. It is shown that the most favorable conditions for the reflected beam to retain its shape are accomplished in a crystal whose thickness is less than the extinction depth.     

Wave packets in smoothly inhomogeneous dispersive media

In the quasi-optical aberration-free approximation, a parabolic equation for the envelope of an electromagnetic wave packet propagating along a geometric optical ray in a smoothly inhomogeneous isotropic medium with time dispersion is obtained. The corresponding Green’s function is found whose parameters are determined by integrating a system of ordinary differential equations. The effects of the combined influence of the refraction, diffraction, and dispersion on the evolution of the packet are analyzed; in particular, the effects that cause precession of the envelope waves about the binormal to the propagation trajectory are considered.     

A fresh look at diffraction from a nonabsorbing perfect crystal in the Bragg-Laue configuration

The Bragg diffraction from a thick, nonabsorbing perfect crystal theory of dynamical diffraction. The intensities of two beams, one in the incident and the other in the diffracted direction, exciting the side face of the crystal are characterised. The implications of such beams for neutron diffraction experiments are indicated.     

Fine structure of the diffraction image of an edge dislocation in high-resolution section topography

The propagation of an x-ray wave field in an elastic field of an edge dislocation crossing a scattering triangle exactly along the bisector of the scattering angle has been considered. The scattering of the x-ray wave field by a complex elastic field of the edge dislocation has been analyzed using the methods of geometrical optics. It has been established that the fine structure of a diffraction image of defects in thick crystals is determined by the differences in scattering of the normal and anomalous modes of the x-ray wave field in the vicinity of the Bragg reflection. In the case of thick crystals, the x-ray diffraction image of defects can have a symmetry different from the symmetry of the function of local misorientations of the crystal lattice. X-ray wave scattering by local distortions of the crystal lattice can occur according to two different mechanisms depending on the gradient of space changes in the deformation field. In the crystal regions where the elastic field varies slowly with a change in the distance, the x-ray wave field has had time to adjust itself to follow the course of deviations of the crystal lattice from the exact Bragg condition. In the crystal region where the elastic field changes significantly at distances of the order of the extinction length, this region leaves the reflecting position and interference scattering occurs at the interface of the region. It is important that the form of the deformation field in this case is of no significance.     

Acousto-optic interaction in crystals with large acoustic anisotropy

The Bragg diffraction of light from a sinusoidal phase grating induced in an anisotropic medium by an acoustic wave has been studied theoretically for the case of a large acoustic energy walk-off. Based on the modified coupled-wave equations, the frequency and angular characteristics of an anisotropic diffraction in a paratellurite crystal have been calculated. It is shown that the acoustic beam walk-off significantly changes the angular and frequency ranges of acousto-optic interactions.     

Direct measurement of the delay time for a neutron in a crystal in the case of the Laue diffraction

The dynamical Laue diffraction has been studied for a direct beam diffracted from a thin (～3.5 cm) α-quartz crystal at the Bragg angles close to 90°. It is shown that diffraction occurs at Bragg angles up to 87°. The time-of-flight method is used to measure the time of the neutron presence in the crystal under the diffraction conditions. The time delay for a scattered neutron inside the crystal predicted earlier for the Bragg angles close to 90° confirmed experimentally. The effective velocity of the neutron propagation in a crystal measured at the incident-neutron velocity of 810 m/s and the diffraction angle of 87° equals (43±1) m/s. The result obtained confirms the possibility of increasing, by an order of magnitude, the sensitivity of the diffraction method of determining the dipole moment of a neutron at Bragg angles close to 90° predicted earlier theoretically.     

Effect of crystal structure on the background intensity in XRF

A new model for the origin of diffraction peaks in x‐ray fluorescence was developed, using the concept of a virtual primary radiation source. The method offers the possibility of calculating the background intensity formed by characteristic radiation and bremsstrahlung. Bragg diffraction may significantly modify the intensity of primary radiation reflected by crystal planes of a polycrystalline material. Copyright © 2005 John Wiley & Sons, Ltd.     

Aperture (slit) effects on the dynamical diffraction of X-rays and thermal neutrons

With increasing accuracy of perfect crystal methods, the effects of apertures (slits) on angular and spacial intensity distributions in dynamical perfect crystal diffraction have become quite important. We present an analytical treatment of such effects. The results are first applied to the diffraction of rays delivered by a source of given lateral extension, i.e. where the critical size of the source as such is essentially influencing the dynamical diffraction phenomena. Both the Laue and the Bragg geometry are considered. Next we calculate the change which a rocking curve measured in either geometry suffers from a slit with varying width and position in front of or between the crystals. Finally we report a pertinent experiment which we have performed in the Laue geometry. We find good agreement with the calculations. It follows that whenever dynamical diffraction is used in quantitative measurement the possible influence of diffraction from diaphragms requires special attention and analysis. For the latter the theory presented here is very well suited.     

反常氧化碲声光偏转器控制理论研究

根据晶体的声光特性以及反常布喇格衍射的Dixon方程,得出了氧化碲声光偏转器在反常布拉格衍射条件下的参量矢量关系.分析了超声波方向、入射光角度、衍射光角度与声波频率之间的关系.针对卫星光通信中衍射角固定的应用情况,通过数值求解和参量拟合,建立了一个基于平面方程的简单控制模型.利用该模型可以很快得到超声控制频率,使衍射角固定不变.     

0.5 mm金刚石X射线相位延迟板及偏振度的标定

在利用步辐射光源的偏振特性进行自旋相关X射线散射及吸收谱实验来研究材料的磁学性质时，需要应用圆偏振光，这就提出了对具有高通量、高偏振度' 长连续可调的圆偏振X射线的需求；另一方面标定实验所用X射线的圆偏振度也成为这一研究领域的关键技术。由于X射线多光束衍射强度与σ场和π场的光程差δ相关，通过测量圆偏振分析晶体的多光束衍射的强度分布，可以获得入射X射线的圆偏振度。实验在美国国家同步辐射光源实验室X25光束线实验站进行，光子能量为7．1keV的圆偏振X射线由线偏振X射线经过一厚度为0．5mm、晶面为[111]的金刚石晶体产生。通过测量多光束衍射强度，确定了斯托克斯参量。实验值与X射线动力学理论计算结果能较好地吻合。     

169Tm-A new candidate for monochromatization of synchrotron radiation by nuclear Bragg diffraction

Thulium containing crystals with appropriate structure should be feasible for monochromatizing synchrotron radiation by nuclear Bragg diffraction. Thulium iron garnet and thulium gallium garnet were investigated by MB-transmission spectroscopy. The evaluated hyperfine interactions are discussed with respect to the crystal structure. The occurrence of pure nuclear reflections is predicted and theoretical time spectra are calculated by the dynamical theory of MB-optics.     

X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

Coulomb crystals in the harmonic lattice approximation

The dynamic structure factor &Stilde;(k,omega) and the two-particle distribution function g(r,t) of ions in a Coulomb crystal are obtained in a closed analytic form using the harmonic lattice (HL) approximation which takes into account all processes of multiphonon excitation and absorption. The static radial two-particle distribution function g(r) is calculated for classical (T greater, similarPlanck's over 2piomega(p), where omega(p) is the ion plasma frequency) and quantum (T相似文献