Inelastic effect on the resonance lineshapes in he-graphite scattering

A multiple Debye—Waller effect for bound state resonances in atom scattering was recently proposed to explain the observed width and strength of measured resonances. The model was applied with success to measurement of the specular intensity for He-graphite at low incident energies, and to measurement of the diffracted intensities for D-LiF(001) at grazing incidence. We present new calculations for He-graphite at intermediate incident energy, by which the multiple Debye-Waller attenuation appears completely inadequate to describe experimental the inelastic effect on the resonance lineshapes.     

RHEED from stepped surfaces and its relation to RHEED intensity oscillations observed during MBE

Multiple scattering theory is used to calculate the intensities of reflection high energy electron diffraction from periodic arrays of surface steps. The intensities are found to depend strongly on the direction of the incident beam azimuth. When the incident beam azimuth is parallel to the step edges, both the specular and diffracted beam intensities are diminished with respect to the intensities from a flat surface. When the incident beam azimuth is perpendicular to the edges, the intensities of all the beams are of the same order of magnitude as for a flat surface but some of the peak heights are oscillatory functions of the number of atoms in the topmost layer. These peak intensity oscillations are very similar to the intensity oscillations observed during molecular beam epitaxial film growth.     

Elastic and inelastic scattering of slow positrons from a LiF(100) surface

The intensity profile for the elastic specular reflection of 5–100 eV positrons from a LiF(100) surface (ang1e of incidence 45°) has been measured using a simple time-of-flight spectrometer. The profile exhibits strong maxima below 25 eV and a smaller peak at 57 eV. Positron energy loss spectra have also been measured for a range of incident energies by retarding field analysis of the scattered beam. The mean energy loss appears to increase with increasing incident beam energy. Both the elastic and inelastic results are compared with similar data for slow-electron scattering obtained with the same apparatus.     

Adsorbate induced changes of Debye-Waller factors

The scattering of a molecular beam by a solid surface is sensitive to the vibrational properties of the surface which are changed by the presence of adsorbed molecules. In particular light adsorbates with discrete localized vibrational modes lead to discrete structures in the energy distribution of scattered particles and corresponding structures in the intensities of specular scattering as measured by the Debye-Waller factor. We investigate the dependence of the Debye-Waller factor on various parameters characterizing the adsorbate as well as the scattered particle. It turns out that the intensity of discrete structures in the Debye-Waller factor usually is small. Only in a very restricted range of parameter values one may be able to find observable effects.     

Atom-solid scattering: He + graphite basal plane

Theoretical studies of scattering of atoms by solid surfaces and calculations of atomic band structure of adsorbed atoms are presented. Inelastic effects on the intensities of diffracted beams are considered within the framework of the optical model potential. The atom-solid potential used for carrying out the numerical calculation is the sum of Lennard-Jones 12-6 pair potentials for the He-graphite system. Resonances with bound states of adsorbed atoms are shown to enhance the diffraction into some of the open channels and inelastic scattering. The degree of enhancement for a certain process depends on the coupling between that process and the resonant bound state and the coupling between the bound state and the incident beam. For first order bound state resonances, minima in the specular intensity may result from a large increase in some of the diffracted intensities or enhancement of inelastic scattering.     

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by a “fork” hologram from an incident circular Laguerre-Gaussian beam whose axis differs from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the “proper” topological charge m of the incident vortex beam and the topological charge l of the singularity “imparted” by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical vortex beam generation and optical measurements are discussed.     

Transformation of optical-vortex beams by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by the “fork” holograms from incident circular Laguerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most cases its structure is formed under the influence of the divergent spherical wave originating from the discontinuity caused by the hologram’s groove bifurcation. Presence of this wave is manifested by the ripple structure in the near-field beam pattern and by the power-law amplitude decay at the beam periphery. Conditions when the divergent wave is not excited are discussed.The diffracted beam carries a screw wavefront dislocation (optical vortex) whose order equals to algebraic sum of the incident beam azimuthal index and the topological charge of the singularity imparted by the hologram. The input beam singularity can be healed when the above sum is zero. In such cases the diffracted beam can provide better energy concentration in the central intensity peak than the Gaussian beam whose initial distribution coincides with the Gaussian envelope of the incident beam. Applications are possible for generation of optical-vortex beams with prescribed properties and for analyzing the optical-vortex beams in problems of information processing.     

On-line beam diagnostics based on single-shot beam splitting phase retrieval

We propose a novel on-line beam diagnostic method based on single-shot beam splitting phase retrieval. The incident beam to be measured is diffracted into many replicas by a Dammann grating and then propagates through a weakly scattering phase plate with a known structure; the exiting beams propagate along their original direction and form an array of diffraction patterns on the detector plane. By applying the intensity of diffraction patterns into an iterative algorithm and calculating between the grating plane, weakly scattering plane, and detector plane, the complex field of the incident beam can be reconstructed rapidly; the feasibility of this method is verified experimentally with wavelengths of 1053 and 632.8 nm.     

Theoretical studies of atom-solid elastic scattering by iterative integration using the Green function

The elastic scattering of low-energy light atoms from a perfect crystalline surface is studied by an iterative integration scheme using the Green function. The atom-solid interaction is represented by the often used Morse type surface potential. A varying number of closed and open channels is included in the calculation, according to necessicity. For a beam incident along the cyrstal symmetry directions, a scheme to utilize the symmetry condition for efficient computation is proposed. The diffraction intensities at a bound state resonance (selective adsorption) are calculated by properly selecting a reference potential for the calculation of the Green function. The calculations yield the resonant diffraction intensity patterns in agreement with previous calculations using a different numerical technique and with the experimental observations for the HeLiF and HeNaF systems. A calculation including 69 allowed diffracted beams (open channels) for the HeLiF system at normal incidence is also presented and comparison with experimental results is made to estimate the periodic potential parameter.     

A study of the (00) LEED beam intensity at normal incidence from CdS(0001), Cu(001), Cu(111), and Ni(111)

A Faraday cage apparatus is used for the measurement of the (00) LEED beam intensity, I₍₀₀₎, and the total secondary emission coefficient, δ(E_k), for angles of incidence from 0° ± 2° to 8° ± 2°, with an energy resolution of ± 0.037 of the incident beam energy, in the energy range 1 to 200 eV. The data are normalized and expressed as a fraction of the incident beam intensity. The basic principle of operation is the separation of the incident and specularly diffracted beams in a uniform magnetic field. Monolayer, or in-plane, resonances associated with the emergence of nonspecular beams, as well as beam threshold minima, are observed in I₍₀₀₎ at normal incidence from clean CdS(0001), Cu(111), and Ni(111). Some major differences are observed in the I₍₀₀₎ profiles for the clean (111) surfaces of nickel and copper. All secondary Bragg peaks, except the 2$\text{2}\text{3}$ order, have greater intensities for Ni(111) in the energy range 50–150 eV, thus indicating that the atomic scattering cross-section for electrons in this energy range is larger for nickel than for copper. For the (111) surface of nickel, the (11) resonance is missing, but the (10) resonance and all $\text{1}\text{3}$ order secondary Bragg peaks between the second and fifth orders are observed. For Cu(111) both the (10) and (11) resonances are observed, but the $\text{1}\text{3}$, $\text{2}\text{3}$, 1$\text{2}\text{3}$, and 3$\text{1}\text{3}$ order secondary Bragg peaks are missing in this energy range. These data indicate that multiple scattering with evanescent intermediate waves, or “shadowing”, is predominate on the (111) surfaces on nickel and copper for energies above 30 eV, and that below 30 eV multiple scattering with propagating intermediate waves is predominate on Cu(111). Correlation of the (00) beam intensity profiles from clean Ni(111) at 0°, 2°, and 6° with the intensity profiles of the (10). (1̄0), and (11) non-specular beams is nearly one-to-one from 30 eV to 100 eV, thus supporting the dynamical theories of LEED in which peaks in the (00) beam are expected to occur at nearly the same energies as peaks in the non-specular beams.     

Magnetooptical diffraction from a strip domain structure in the case of oblique incidence of light

The distribution of the magnetization component longitudinal with respect to the beam propagation is shown to be trapezoidal in shape in the case of oblique incidence of light on a strip domain structure with vertical domain walls. Features of intensity and polarization characteristics of the diffracted light field are studied with reflections of incident and diffracted beams from the entrance and the exit surfaces of the film taken into account.     

Talbot effect in metallic gratings under Gaussian illumination

Metallic gratings can be found in applications such as optical metrology. Due to their fabrication process, the surface presents a certain roughness. In this work, the effect of roughness on Talbot effect has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used in order to determine the intensity distribution in the near field. Contrast of the self-images is obtained and it is found that it decreases in terms of the distance between the grating and the observation plane. When the autocorrelation function of roughness presents a Gaussian behaviour, the diffracted beams are still Gaussian although some of their properties change. For example, the width of the diffracted beams increases with respect to the case of the standard chrome on glass gratings. On the other hand, the power of each diffracted beam is independent on the roughness properties of the surface.     

Polarization characteristics and magneto-optic diffraction efficiency at oblique light incidence

In a great number of papers that deal with the study of the magneto-optic diffraction (MOD), theoretical analysis and interpretation of experimental data are performed without regard for reflection effects of the incident and diffracted light beams on the entrance and exit surfaces of the transparent film. In consequence the MOD parameters are not connected with the angle of light incidence and the orientation of the incident light polarization plane. In the present work the reflection effects are taken into account. For the Raman-Nat diffraction region the general expressions involving the relationships of diffracted light polarization and intensity with the symmetry of the grating, angle of incidence and polarization of the incident light are obtained. In particular it is shown that even for a symmetrical grating the polarization of the zeroth-order diffracted beam differs from that of the incident light, and the polarization of higher-order beams differs from the orthogonal one providing that the incident light is not s- or p-polarized. A maximum in the angular dependence of diffraction efficiency is predicted being observed experimentally.     

超衍射极限相干反斯托克斯拉曼散射显微成像技术中空心光束的形成

空心光束的质量是超衍射极限相干反斯托克斯拉曼散射显微成像技术中决定成像质量的一个至关重要的因素. 本文基于菲涅耳衍射理论,分析了螺旋相位片法产生空心光束的物理机理,并且模拟了不同的入射条件对产生的空心光束的影响. 模拟结果表明:波长与相位片中心波长匹配且光强呈圆对称分布的高斯光垂直入射到相位片上,当高斯光束中心与相位片中心完全对准时,可获得较理想的空心光束;入射光光强分布的圆对称性以及入射光中心与相位片中心的对准程度都会影响产生的空心光束的强度分布;同时,高斯光束小角度倾斜入射时,空心光的强度分布仍呈圆对称,却在观察面发生一定的位移;此外,入射光中心波长偏离相位片中心波长不大时,对产生的空心光束的强度分布几乎没有影响. 上述分析结果对用于超衍射相干反斯托克斯拉曼散射显微成像技术中理想空心光束的获取具有重要的指导意义. 关键词： 空心光束 超衍射极限 相干反斯托克斯拉曼散射 螺旋相位片     

Manipulation of Particles with Counter-Propagating Evanescent Waves

Two counter-propagating evanescent beams are used to align and manipulate polystyrene particles on a prism surface. Since the radiation pressure transferred laterally from the evanescent wave is negated on both sides, particles can be stably aligned. By projecting a circular and a linear beam spot onto the interface, both multiple and single arrays of particles are achieved. Arrays of particles trapped on the interface can be easily moved adjusting the intensity of incident beams on either side. We also simulate electromagnetic distribution of scattering light that is converted from the evanescent wave using the FDTD method. The results show that scattering light converts from an evanescent wave propagating through a particle array and has a distance longer than that propagating from a normal evanescent wave.     

LEED crystallographic studies of the (311) surface of nickel: I. Structural analysis

An intensity analysis with low-energy electron diffraction is reported for the stepped (311) surface of nickel. Intensity versus energy curves were measured for 14 diffracted beams at normal incidence, and comparisons made with I(E) curves calculated with the layer-doubling method. The latter showed some numerical instabilities at particular energies and topmost spacings. Evidence is presented for detecting such problems by plotting, at fixed energy, emergent beam intensities as a function of topmost spacing. Calculated and experimental intensity curves were assessed with reliability indices proposed both by Zanazzi and Jona and by Pendry. Good correspondences were obtained with an unreconstructed surface model in which the topmost spacing is contracted by about 14% from the bulk value.     

Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity

Properties of vortex light beams produced by a diffraction grating with groove bifurcation (“fork” structure) are studied in the case of small diffraction angles. Analytical expressions are derived for the amplitude distribution of a diffracted beam generated from an incident Gaussian beam with arbitrary radius and wavefront curvature, transversely shifted and inclined with respect to the nominal axis (normal to the grating crossing it at the bifurcation point). In such situations, the output beam becomes asymmetric; the optical vortex core and the intensity maximum displace orthogonally to the incident beam shift direction. The nearest vicinity of the vortex core preserves its circular symmetry and the optical vortex remains locally isotropic. The effects of misalignment depend on the incident beam characteristics, the diffraction order and the propagation distance behind the grating. Experimental measurements support the results of calculations.     

Diffraction from stepped surfaces: I. Reversible surfaces

In electron or atom diffraction experiments on surfaces, the angular shapes of the diffracted beams depend upon the distribution of steps over the surface. In this paper we analyze diffracted beam profiles from stepped surfaces that are reversible. A reversible surface is one in which the pair correlation function over the surface is symmetric with respect to positive and negative directions. We show that the intensity profile across a diffracted beam can be separated into a sharp central spike due to the limit of the correlation function at large separation plus wings or shoulders due to the finite extent of the step disorder. Simple functional expressions for these angular profiles are obtained by a Markov method of treating a one-dimensional geometric distribution of steps. The result explicitly displays the deep structure found for the general case. The method reduces the calculation to a simple eigenvalue problem so that even the continuously changing step distributions that occur in epitaxial growth can be treated easily. As in the general case, the resulting intensity profile is a sharp central spike plus a step-broadened term which now is a sum of Lorentzians. The widths of the Lorentzians are the logarithms of the eigenvalues of the matrix of probabilities which describe the step distribution over the surface. This matrix method, which treats the surface as a Markov chain, also points the correct way to account for correlations between surface atoms for two-dimensional distributions of steps. For a two-dimensional surface one must consider a Markov Random Field as opposed to a simple multiplication of two one-dimensional results. We compare the results of the general calculation to the Si epitaxy experiments of Gronwald and Henzler. The coverage and momentum transfer dependencies of the shapes of the calculated profiles agree with their measurements. The calculation is also applied to the RHEED measurements of Van Hove et al. during GaAs MBE. The measured intensity oscillations can be accounted for by a cyclically changing one-dimensional geometric distribution of steps among three layers in which the third-layer scattering increases with time.     

Observation of transient adsorption or skipping motion in small angle ion-surface scattering

Transient adsorption or skipping motion of silicon ions scattered under specular conditions from a Cu(111) surface is reported. The phenomena is identified on the basis of the observation of discrete energy loss peaks in the scattered positive and negative ion kinetic energy distributions, together with their behaviour upon variation of the crystal azimuth, incidence angle of the beam to the surface, and scattering angular distributions. Up to five reflections in a binding potential were seen. We propose that the beam is trapped following an energy loss, by electron-hole pair or plasmon excitation, which exceeds the incident beam energy component normal to the surface. The results lend strong support to the thesis that ion beam techniques can probe the family of potential surfaces upon which adsorption and reaction, at thermal energies, proceed.     

Coherent X-ray radiation generated by a beam of relativistic electrons in a single crystal under conditions of multiple scattering

The dynamic theory of the coherent X-ray radiation of a divergent beam of relativistic electrons generated in a single-crystal wafer under conditions of the multiple scattering of incident particles is developed. Radiation cross sections are averaged over the divergent beam of rectilinear trajectories of electrons. Expressions describing the spectral-angular characteristics of parametric X-ray radiation and diffracted transition radiation under conditions of multiple scattering are obtained. Conditions under which the contribution of diffracted brehmsstrahlung can be disregarded are shown, and the spectral-angular characteristics of parametric X-ray radiation and diffracted transition radiation are calculated numerically for such conditions.