Diffraction Intensity Distribution Research Articles

Measuring the orbital angular momentum of generalized higher-order twisted partially coherent beams

Recently a new family of partially coherent fields incorporating generalized inseparable cross-coupled phases named generalized higher-order twisted partially coherent beams (GHTPCBs) have been introduced. The twist factor u is a key parameter that not only quantifies the strength of the generalized cross-coupled phase for a given order, but also determines the amount of the concomitant orbital angular momentum (OAM). In this paper, we propose a simple and reliable method to measure the factor u using a two-pinhole mask. Without need of complicated optical system, it only requires to capture the far-field diffraction intensity distribution of the GHTPCB passing through the mask. By analyzing the Fourier spectrum of the intensity distribution, the value of twist factor can be derived nearly in real time. The influence of the separation distance between two pinholes and the pinholes’ diameter and position on the measurement accuracy are thoroughly studied both in theory and experiment. The experimental results agree well with the theoretical results. Our methodology can also be extended to measure the sole factor of similar position dependent phases such as the topological charge of a vortex phase.

Investigation of diffraction grating in three-level gain medium

This research investigates the modulation of diffraction intensity distributions in both one- and two-dimensional scenarios within a three-level atomic system. The study employs a partially coherent light beam as the probe field, engaging with the atomic medium. Additionally, a control field capable of generating a standing wave is introduced. Analysis reveals that various parameters, including spatial coherence, beam width, and mode index of the partially coherent light, exert influence on the diffraction intensity distribution. The presence of a microwave field in the three-level atom is also considered, impacting the diffraction intensity distribution. Remarkably, the study observes that altering parameters such as microwave field strength and beam width of the partially coherent light results in the maximum energy of the probe field being transferred to higher orders, concurrently minimizing the central intensity. This distinctive method allows for the manipulation of diffraction intensity distribution through external control parameters. The proposed theoretical framework for creating a diffraction grating presents a novel avenue for experiment.

Dynamical and kinematical X-ray diffraction in a bent crystal

Numerical modeling of kinematical and dynamical X-ray diffraction in a bent crystal was performed on the basis of two approaches to integrating the Takagi–Taupin equations, and using two-dimensional recurrence relations. Within the framework of kinematical diffraction, a new equation is obtained that describes the distribution of diffracted intensity inside a bent crystal. The time taken for numerical calculations based on this equation is significantly reduced in comparison with the use of algorithms of the dynamical diffraction theory. The simulation shows for the first time that, for strongly bent crystals, the maximum value of the diffraction intensity is formed inside the deformed structure and not on its surface. In the case of strong bending of the crystal structure, the deviation of the X-ray beam from the Bragg angle does not change the diffraction pattern but shifts it along the lateral direction. The results of calculations of diffraction in a strongly bent crystal based on the equations of dynamical and kinematical diffraction coincide, while the computations for weakly bent crystals differ. The possibility of estimating the primary extinction length of a bent crystal as a function of the bending radius is shown. In the case of kinematical diffraction in bent crystalline microsystems, a new method has been developed to calculate X-ray reciprocal-space mapping.

A study to analyze the importance of establishing a mathematical model for teaching college physics

Abstract Numerical simulation technology to assist the teaching of university physics is a higher education to continuously adapts to the social development of its own needs. This paper classifies the common forms of university physics courses involving numerical computation, explores the current computer simulation in physics teaching, and establishes the development process of the university physics computer numerical computation simulation program. Numerical simulation technology is applied to the design of university physics teaching, and two examples of numerical simulation technology assisting university physics teaching are designed from two cases of grating diffraction intensity distribution and gas diffusion based on Matlab. In Example N = 10, the light intensity distribution of diffraction grating with different slit numbers is analyzed by numerical simulation, and it is obtained that at 1, there are 9 minima between two adjacent main maxima, 8 sub-maxima, and the maximum value is 100, which verifies the theoretical results of the physical derivation of the grating diffraction intensity distribution. In the exposition, mathematical modeling is combined with examples to show that mathematical modeling can greatly exert the role of mathematical ideas in physics teaching, simplify physics teaching, and further cultivate students’ ability to solve practical problems.

Dislocation arrangements in 4H-SiC and their influence on the local crystal lattice properties.

Two wafers of one 4H-silicon carbide (4H-SiC) bulk crystal, one cut from a longitudinal position close to the crystal's seed and the other close to the cap, were characterized with synchrotron white-beam X-ray topography (SWXRT) in back-reflection and transmission geometry to investigate the dislocation formation and propagation during growth. For the first time, full wafer mappings were recorded in 00012 back-reflection geometry with a CCD camera system, providing an overview of the dislocation arrangement in terms of dislocation type, density and homogeneous distribution. Furthermore, by having similar resolution to conventional SWXRT photographic film, the method enables identification of individual dislocations, even single threading screw dislocations, which appear as white spots with a diameter in the range of 10 to 30 µm. Both investigated wafers showed a similar dislocation arrangement, suggesting a constant propagation of dislocations during crystal growth. A systematic investigation of crystal lattice strain and tilt at selected wafer areas with different dislocation arrangements was achieved with high-resolution X-ray diffractometry reciprocal-space map (RSM) measurements in the symmetric 0004 reflection. It was shown that the diffracted intensity distribution of the RSM for different dislocation arrangements depends on the locally predominant dislocation type and density. Moreover, the orientation of specific dislocation types along the RSM scanning direction has a strong influence on the local crystal lattice properties.

Measurement of Residual Stress Distribution in the Depth Direction of Annealed Materials of Lapped Bearing Steel Using Weighted Averaging Analysis Method

This paper reports the results of an experimental examination using X-rays to test annealing materials for lapped bearing steel (STB2), to confirm the validity of the weighted averaging analysis method. The distribution behavior for the αψ-sin2ψ diagram and the presence or absence of differences in the peak method, half-value breadth method, and centroid method were investigated. When lapping the annealed bearing steel (STB2) material, a residual stress state with a non-directional steep gradient appeared in the surface layer, and it was found that the weighted averaging analysis method was effective. If there is a steep stress gradient, the sin2ψ diagram is curved and the diffraction intensity distribution curve becomes asymmetric, resulting in a difference between the peak method, half-value breadth method, and centroid method. This phenomenon was evident when the stress gradient was more than 2~3 kg/mm2/µm. In this case, if the position of the diffraction line is determined using the centroid method and the weighted averaging analysis method is applied, the stress value on the surface and the stress gradient under the surface can be obtained more accurately. When the stress gradient becomes a problem, since the curvature of the sin2ψ diagram appears clearly in the region of sin2ψ > 0.5, it is necessary to increase the inclination angle ψ as much as possible. In the case of a lapping layer, a more accurate value can be obtained by considering σ3 in the weighted averaging analysis method. In an isotropic biaxial residual stress state, the presence or absence of σ3 can be determined as the presence or absence of strain for sin2ψ≈0.4.

Generation of multiple-vortex beams in the process of diffraction of cosine-Laguerre–Gaussian laser beam by the fork-shaped grating

We present the theoretical study about Fraunhofer diffraction of cosine-Laguerre–Gaussian laser beam of mode l,n=0 by the fork-shaped grating with a phase singularity of integer order p. The analytical expressions for the diffracted wave field amplitude and intensity distributions are derived. The transverse intensity and phase profiles of the diffracted beam, in a given diffraction order and for different values of l and p, are calculated. They show that the higher diffraction orders are multiple-vortex beams. In addition, the interference patterns of the diffracted wave field with a slightly inclined plane wave are presented, for confirming the presence of the optical vortices and determining the values and signs of their topological charges. We have shown how an azimuthally shaped, non-vortex beam, consisting of 2l bright lattices, can be transformed into a fan of multiple-vortex beams in the higher diffraction orders.

Phase retrieval and reconstruction of coherent synthesis by genetic algorithm

In the context of diffractive optics, phase retrieval is a heavily investigated process of recreating an entire complex electric field from partial amplitude-only information through iterative algorithms. However, existing methods can fall into local minima during reconstructions or struggle to recover unusual and novel electric field distributions. We present a numerical method based on a global-optimization genetic algorithm that reconstructs non-trivial electric field distributions from single diffracted intensity distributions. Diffraction and propagation of the optical fields over arbitrary distances is modeled through implementation of the angular spectrum technique. Additionally, a coherently-locked laser array system is used as an experimental case-study demonstrating 0.09π phase reconstruction accuracy of initial laser parameters from single intensity images.

Optically Induced Picosecond Lattice Compression in the Dielectric Component of a Strongly Coupled Ferroelectric/Dielectric Superlattice

AbstractAbove‐bandgap femtosecond optical excitation of a ferroelectric/dielectric BaTiO3/CaTiO3 superlattice leads to structural responses that are a consequence of the screening of the strong electrostatic coupling between the component layers. Time‐resolved X‐ray free‐electron laser diffraction shows that the structural response to optical excitation includes a net lattice expansion of the superlattice consistent with depolarization‐field screening driven by the photoexcited charge carriers. The depolarization‐field‐screening‐driven expansion is separate from a photoacoustic pulse launched from the bottom electrode on which the superlattice is epitaxially grown. The distribution of diffracted intensity of superlattice X‐ray reflections indicates that the depolarization‐field‐screening‐induced strain includes a photoinduced expansion in the ferroelectric BaTiO3 and a contraction in CaTiO3. The magnitude of expansion in BaTiO3 layers is larger than the contraction in CaTiO3. The difference in the magnitude of depolarization‐field‐screening‐driven strain in the BaTiO3 and CaTiO3 components can arise from the contribution of the oxygen octahedral rotation patterns at the BaTiO3/CaTiO3 interfaces to the polarization of CaTiO3. The depolarization‐field‐screening‐driven polarization reduction in the CaTiO3 layers points to a new direction for the manipulation of polarization in the component layers of a strongly coupled ferroelectric/dielectric superlattice.

Turning Parameters Optimization for Diffraction Effect Suppression of Diamond-Turned Surface Combining Surface Micro-Topography Model and Scattering Theory

Abstract The diamond-turning process is a mean optical surface generation technique with high figure accuracy and surface finish. The diamond-turned surface has a significant diffraction effect introduced by the tool marks remaining on the surface, which heavily degrade the optical performance in the visible wavelength spectrum. The traditional approach that was used to eliminate this effect was polishing. In this paper, we present a method to find turning parameters that can generate an optical surface without diffraction effect directly by coupling a surface micro-topography model of a turned surface via the scattering theory. The surface micro-topography model of the turned surface reveals the relationship between tool marks and the diamond-turning parameters (DTPs). The scattering theory reveals the relationship between diffraction intensity distributions (DIDs) and surface micro-topography of the turned surface. Therefore, we obtained the relationship between DIDs and DTPs. The diffraction effect is considered to be eliminated when the first-order diffraction intensity is less than 0.01% of incidence intensity. The criterion of turning parameters for diffraction elimination is then obtained. Finally, turning experiments are performed to confirm the effectiveness of this method, and the diffraction-free surface finish is achieved.

Diffraction Intensity Distribution of Pinhole for Misaligned Gaussian Beam Incidence

Diffraction Intensity Distribution of Pinhole for Misaligned Gaussian Beam Incidence

Mechanisms of crack generation in high-pure tungsten exposed to high power density plasma

The mechanisms of crack formation in the tungsten divertor plates irradiated by hydrogen plasma under ITER-type steady-state and transient events are investigated. The stresses and defects of samples‘ initial structure are annealed as a result of steady-state irradiation with Falcon ion source, which generates 2 keV hydrogen ion flux of ~ 1022 m-2s−1 and power density ~ 1.7 MW × m−2. Quasi-stationary plasma accelerator QSPA Kh-50 provides pulsed hydrogen plasma loads which operating mode simulates transient events (type I ELMs) in ITER: ion impact energy is about 400 eV, maximum plasma pressure is 0.32 MPa, pulse duration is 0.25 ms. The diffraction maxima profiles, positions, intensities, half-widths, and intensity distributions are analyzed. The origin of crack formation is found to be in the plastic deformation of surface layers by the twinning mechanism. The latter is reinforced by the interaction of twins with the hydrogen-filled micro-pores. The micro-pores appear as a result of hydrogen saturation of subtraction loops formed due to the coalescence of vacancy complexes.

Imaging properties of generalized composite aperiodic zone plates.

Generalized composite aperiodic zone plates (GCAZPs) are proposed to generate clearer images at focal planes. The images can be produced by a target object at infinity based on a collimator. The proposed zone plate consists of the proposed radial zone plate (RZP), whose original radius is not zero, and the common aperiodic zone plate, which has the coincident first-order diffraction area and the same axial first-order diffraction intensity distribution. The GCAZPs are applicable for the other aperiodic zone plates. Moreover, the modulation transfer function curve of the GCAZP is basically above that of the corresponding common aperiodic zone plate. Compared with the common aperiodic zone plates, the GCAZPs have the foci with higher intensity and the images with higher contrast at the same focal planes. In addition, a GCAZP with an arbitrary size can be designed. The construction method of the GCAZP is illustrated in details. Furthermore, it has been also proved numerically and experimentally that the GCAZPs are used to generate the clearer images than the corresponding common aperiodic zone plates. The proposed zone plates are applicable to generate clear images and trap particles stably at multiple planes simultaneously.

New method to measure domain-wall motion contribution to piezoelectricity: the case of PbZr0.65Ti0.35O3 ferroelectric

A new data analysis routine is introduced to reconstruct the change in lattice parameters in individual ferroelastic domains and the role of domain-wall motion in the piezoelectric effect. Using special electronics for the synchronization of a PILATUS X-ray area detector with a voltage signal generator, the X-ray diffraction intensity distribution was measured around seven split Bragg peaks as a function of external electric field. The new data analysis algorithm allows the calculation of `extrinsic' (related to domain-wall motion) and `intrinsic' (related to the change in lattice parameters) contributions to the electric-field-induced deformation. Compared with previously existing approaches, the new method benefits from the availability of a three-dimensional diffraction intensity distribution, which enables the separation of Bragg peaks diffracted from differently oriented domain sets. The new technique is applied to calculate the extrinsic and intrinsic contributions to the piezoelectricity in a single crystal of the ferroelectric PbZr1−x Ti x O3 (x = 0.35). The root-mean-square value of the piezoelectric coefficient was obtained as 112 pC N−1. The contribution of the domain-wall motion is estimated as 99 pC N−1. The contribution of electric-field-induced changes to the lattice parameters averaged over all the domains is 71 pC N−1. The equivalent value corresponding to the change in lattice parameters in individual domains may reach up to 189 pC N−1.

Compact radial shearing interferometer with a randomly encoded cosinusoidal zone plate for wavefront measurements.

A radial shearing interferometer (RSI) using a randomly encoded cosinusoidal zone plate (RECZP) to measure the wavefront is proposed. The RECZP has two foci, i.e., a virtual focus and a real focus, so its Fresnel diffractions contain only two beams. These two beams can be regarded as the extended beam and the contracted beam in the RSI, respectively. This RSI is composed of a RECZP and a charge-coupled device (CCD). The radial shearing rate is continuously adjustable by changing the distance between the CCD and RECZP, which is good for measurement sensitivity and dynamic range for different situation requirements. In the simulation experiment, we analyzed the influence of beam tilt error, distance error of zone plate and CCD, CCD camera nonlinearity, and noise on wavefront reconstruction results. We also analyzed the effects of different fabrication errors (randomly encoded principle error, sidewall angle error, depth error, and alignment error of amplitude zone plate and phase zone plate) on the diffraction intensity distributions, which determine the fabrication tolerance of the RECZP. Experimentally compared with a ZYGO interferometer, the RECZP-RSI optical system can get good results.

Single-shot measurements by Fresnel diffraction of divergent waves from a phase plate.

Recently, Fresnel diffraction (FD) of a plane wave from phase steps has been studied and applied for precise measurements of the light wavelength, and height and refractive index of the step, by changing the angle of incidence or step height to induce phase shifts. In this study, we formulate the FD of cylindrical and spherical wavefronts as 1D and 2D divergent waves from a phase plate. Since the phase difference of the divergent wave varies continuously along the edge of the phase plate, it can be applied for single-shot measurements. It is shown that the diffracted intensity distribution is a periodic function along the lines parallel to the plate edge. The phase distribution in this direction is a linearly varying function of the position squared, with a slope dependent on the light wavelength, plate thickness and refractive index, and the radius of wavefront curvature (RWC) on the observation plane. The diffraction patterns are simulated and experimentally verified. Also, the RWC and displacement are determined as examples of applications in the experimental part of the report.

Topological encoding method for data-driven photonics inverse design.

Data-driven approaches have been proposed as effective strategies for the inverse design and optimization of photonic structures in recent years. In order to assist data-driven methods for the design of topology of photonic devices, we propose a topological encoding method that transforms photonic structures represented by binary images to a continuous sparse representation. This sparse representation can be utilized for dimensionality reduction and dataset generation, enabling effective analysis and optimization of photonic topologies with data-driven approaches. As a proof of principle, we leverage our encoding method for the design of two dimensional non-paraxial diffractive optical elements with various diffraction intensity distributions. We proved that our encoding method is able to assist machine-learning-based inverse design approaches for accurate and global optimization.

Simultaneous identification of the azimuthal and radial mode indices of Laguerre-Gaussian beams using a spiral phase grating

Transfer of information using optical vortex beams as signal carriers can extremely extend the capacity and spectral efficiency in optical communication systems. One of the key problems is to accurately measure the mode indices including radial mode p and topological charge l at the receiver side of an optical vortices transmission system. In this paper, we present a new scheme to determine the mode indices of optical vortices by using spiral phase gratings. Based on the Fresnel diffraction integral theory, the far-field diffraction intensity distributions of vortex beams through the gratings are numerically calculated. Simulation results show that the annular-shaped intensity profiles of incident vortex beams evolve to bright spot array diffraction patterns, which render the information of the mode indices. Specifically, the magnitude of topological charge l and radial index p can be easily determined by counting the number of the corresponding bright stripes. And the orientation of the diffraction optical fields reveals the sign of the topological charge. Experiments are implemented to demonstrate the feasibility and validity of the proposed detecting method by uploading such phase gratings on a reflective phase-only liquid crystal spatial light modulator. The experimental observations are in good agreement with the theoretical predictions.

Thickness and defocus dependence of inter-atomic electric fields measured by scanning diffraction

Scanning diffraction uses the diffraction pattern from the sub-angstrom electron probe in scanning transmission electron microscopy (STEM) to record the probe's interaction with the sample structure. The diffraction intensity distribution carries information about the Coulomb interaction between the probe and the sample, from which the local electric field can be calculated. Although measurement of the electric field from scanning diffraction data is relatively simple under ideal conditions, theoretical and simulation studies indicate that interpretation of momentum transfer measurements is still complicated by the effects of sample thickness, dynamic scattering, and the depth of focus from the electron probe. Especially for thick samples of more than a few nanometers, simulations predicted that the measured momentum transfer in scanning diffraction is not directly correlated with the electric field. However, in our experiments, we have found that the technique is more robust than previously predicted when using specific imaging conditions. Here we systematically studied the effect of sample thickness and probe defocus on the momentum transfer of the electron probe in STEM, showing that the strong electric field close to atoms can be measured quantitatively for samples up to 5 nm and that the weak electric field in inter-atomic regions can be measured for samples up to 15 nm while maintaining qualitative accuracy in the full electric field image.

Structure Determination of Er Doped Ti-Al-Nb Alloy by Neutron Diffraction Analysis.

Neutron diffraction experiments with both conventional powder diffraction setup and under in-situ compressive loading were conducted to investigate the structural origins of large strength and toughness enhancements in Ti-16Al-27Nb alloy after Er addition. The primary phase is determined to be the ordered B2 structure form, in agreement with the previous electron microscopy study. Lattice strains of {210} and {100} planes were measured as a function of applied stress, and elastic anisotropy was found for both, and strong plastic nonlinearity was discovered for (210) reflection. The grain refinement during plastic deformation was proposed by both the 2D diffraction intensity distribution and SEM observations, while stress-induced martensitic phase transition was not observed in this study. It is believed that the activation of different slip systems and grain refinement might be the structural origin of the novel mechanical properties of this alloy.