Diffraction Theory Research Articles

Molecular insights into histidine adsorption on Na-montmorillonite, anatase, and goethite

The adsorption of amino acids (AAs) on minerals plays a role in the geochemical processes that determine the availability of nutrients in the environment. Histidine can be used as typical basic AA because it is frequently detected in natural waters, soils, and sediments. Herein, the pH effects and time factor were analyzed to reveal the molecular-level mechanisms of histidine adsorption on Na-montmorillonite, anatase, and goethite. Attenuated total reflectance Fourier transform infrared (ATR–FTIR) flow-cell measurements, X-ray diffraction (XRD), and density functional theory (DFT) calculations were used to determine the adsorbed species structures and the time-dependent adsorption/desorption processes. The structures of adsorbed histidine were governed by pH conditions, but were not affected by time variations. The histidine adsorbed on the minerals was in the cationic (pH 4), neutral zwitterionic (pH 7.5), and anionic (pH 10.5) forms, which was consistent with those dissolved in solution at the same pH. Adsorption on the clay mineral montmorillonite was favorable due to the dominant interlayer adsorption mechanism at pH 4 and hydrophobic attraction (external basal surface) at pH 4–10.5. Histidine adsorption on the two metal (hydr)oxides was dominated by inner-sphere surface complexation, which involved one or two O atoms of the COO− group. The adsorbed histidine was in the monodentate form on anatase and in the bidentate form on goethite.

EBSD patterns simulating multilayer twins based on dynamical theory of electron diffraction.

Electron backscatter diffraction (EBSD) can be employed to determine crystal structures but has not been used alone to identify defects at the atom scale due to the lack of understanding of the EBSD patterns generated by various structure defects. In the present work, the EBSD patterns of FCC-Fe with 9-layer, 6-layer and 3-layer twin structures are simulated, respectively, using the revised real space (RRS) method and compared with the counterpart of perfect crystals. Our results show that when the electron beam is incident along a direction parallel to the twin plane, the pattern appears symmetrical with respect to the corresponding Kikuchi band of the twin plane, and the diffraction details within the Kikuchi band also exhibit symmetry with respect to the middle line of the Kikuchi band. Moreover, the overall clarity of the patterns decreases, and the pattern becomes more blurred with increasing the distance from the Kikuchi band corresponding to the twin plane. By contrast, the incident electron beam along the direction perpendicular to the twin plane results in diffraction superposition of the matrix region and the shear region, which shows twofold rotational symmetry with respect to the Kikuchi pole corresponding to the normal to the twin plane. In addition, some extra Kikuchi bands appear in the EBSD patterns due to the long-period structures of the multilayer twins. As the number of multilayer twins decreases, the number of extra Kikuchi bands decreases and the area of the blurring pattern increases. The correlation between twin structures and EBSD patterns provides theoretical insights for identifying twin structures by the EBSD technique.

Stokes and Anti-Stokes Luminescent Rare-Earth-Doped Tantalum Oxide Nanoparticles.

Doping of nano- and microparticles of oxides with rare earth elements (REEs) is used to fine-tune their structural, optical, and electrochemical properties. On the way to establish the structure-property relationship, we dope tantalum oxide (Ta2O5) particles with REEs to study their effect on the oxide structure and luminescence. Ta2O5 is highly perspective in medicine, catalysis, and optics, but its crystal structure is insufficiently studied. Two synthesis approaches (sol-gel and solvothermal) were used to obtain powders with different textures. Experimental and theoretical studies of amorphous and crystallized tantalum oxide NPs by means of X-ray powder diffraction, Rietveld analysis, EXAFS/XANES spectroscopy, and density functional theory calculations were performed. All samples (doped and undoped) crystallized in orthorhombic phase with no admixtures. It was demonstrated that Ta2O5 is a promising wide-spectrum luminescent material: by combining REEs, both Stokes and anti-Stokes luminescence in the visible region were obtained. By means of optical absorption spectroscopy, it was shown that the prepared samples could be classified as wide band gap semiconductors.

Wavefront measurements using the Ronchi test for high-NA lithography projection lenses.

The Ronchi test is widely used for wavefront measurements in advanced lithography tools, and a physical optics explanation of the Ronchi test based on scalar diffraction theory can be found in numerous publications. However, for high-numerical aperture (high-NA) lithography projection lenses, the vector nature of light should be considered when performing wavefront measurements, especially the effect of polarization aberrations on the wavefront test results. In this paper, a vector model for describing shearing interferometry for high-NA lithography projection lenses is established. In addition to considering the vector nature of light, the vector model also calculates the Ronchigram on the screen of a detector at any distance from a diffraction grating, as opposed to the distance restriction for the Fraunhofer diffraction approximation used by the existing methods. Using the developed mathematical model of the Ronchi test, the Ronchigrams of high-NA lithography projection lenses under non-polarized illumination are simulated, and the effect of the distance between the diffraction grating and the detection screen on the wavefront measurement accuracy are discussed.

Near-to-Far Field RCS Calculation Using Correction Optimization Technique

Radar cross section (RCS) is a scattering measure of an object that scatters to the radar. However, existing methods for near-field (NF) measurement and data processing rarely extract amplitude characteristics, and there is a lack of effective verification of far-field (FF) data in the process of NF to FF transformation, which leads to inaccuracies in FF prediction accuracy. In this paper, we propose a method to establish the relationship between the NF and FF RCS using the state space method (SSM), which is based on accurate estimation of the NF amplitude in NF measurement, and then deriving the FF RCS from the NF scattering signal convolved with a near-to-far kernel. The proposed solution to address the uncertainty issue in reference FF data involves using the geometric theory of diffraction (GTD) scattering center model as the reference FF data and establishing a linear equation with the derived FF model. The negative gradient search (NGS) system identification concept is used to optimize the FF model in order to reduce the discrepancy between the reference and derived values. Finally, the corrected RCS error is provided as additional proof of the effectiveness of these techniques in enhancing near-to-far transformation accuracy by examining the outcomes of three experiments.

Performance analysis of single-focus phase singularity based on elliptical reflective annulus quadrangle-element coded spiral zone plates

Optical vortices generated by the conventional vortex lens are usually disturbed by the undesired higher-order foci, which may lead to additional artifacts and thus degrade the contrast sensitivity. In this work, we propose an efficient methodology to combine the merit of elliptical reflective zone plates (ERZPs) and the advantage of spiral zone plates (SZPs) in establishing a specific single optical element, termed elliptical reflective annulus quadrangle-element coded spiral zone plates (ERAQSZPs) to generate single-focus phase singularity. Differing from the abrupt reflectance of the ERZPs, a series of randomly distributed nanometer apertures are adopted to realize the sinusoidal reflectance. Typically, according to our physical design, the ERAQSZPs are fabricated on a bulk substrate; therefore, the new idea can significantly reduce the difficulty in the fabrication process. Based on the Kirchhoff diffraction theory and convolution theorem, the focusing performance of ERAQSZPs is calculated. The results reveal that apart from the capability of generating optical vortices, ERAQSZPs can also integrate the function of focusing, energy selection, higher-order foci elimination, as well as high spectral resolution together. In addition, the focusing properties can be further improved by appropriately adjusting the parameters, such as zone number and the size of the consisted primitives. These findings are expected to direct a new direction toward improving the performance of optical capture, x-ray fluorescence spectra, and forbidden transition.

Diffractive Theory Study of Twisted Light’s Evolution during Phase-Only OAM Manipulations

Twisted light, or orbital angular momentum (OAM) carrying beams or photons, is a pillar of structured photonics, a booming subfield of modern optics. The generation and transformation of twisted light, which lie with coupling topological charges into target light’s wavefunctions, are usually performed by phase-only OAM manipulations. The practical twisted lights, however, obtained by this method are actually noneigen modes of free space, leading to an evolution through the diffractive propagation. Here, we present a general theoretical frame for accurately describing this evolution. Based on the theory, the whole diffractive propagation history in a typical OAM-manipulation loop, converting Gaussian light into a twisted one and then reconverting back, is demonstrated via a set of exact analytical solutions. These results provide a powerful tool for analyzing the transverse profiles of twisted light through the diffractive evolution, as a guideline for studying the science of structured light, which would provide guidelines for research studies in nonlinear optics and high-dimensional quantum information technology based on OAM-degree of freedom.

Phase holograms for the three-dimensional patterning of unconstrained microparticles

Acoustic radiation forces can remotely manipulate particles. Forces from a standing wave field align microscale particles along the nodal or anti-nodal locations of the field to form three-dimensional (3D) patterns. These patterns can be used to form 3D microstructures for tissue engineering applications. However, standing wave generation requires more than one transducer or a reflector, which is challenging to implement in vivo. Here, a method is developed and validated to manipulate microspheres using a travelling wave from a single transducer. Diffraction theory and an iterative angular spectrum approach are employed to design phase holograms to shape the acoustic field. The field replicates a standing wave and aligns polyethylene microspheres in water, which are analogous to cells in vivo, at pressure nodes. Using Gor’kov potential to calculate the radiation forces on the microspheres, axial forces are minimized, and transverse forces are maximized to create stable particle patterns. Pressure fields from the phase holograms and resulting particle aggregation patterns match predictions with a feature similarity index > 0.92, where 1 is a perfect match. The resulting radiation forces are comparable to those produced from a standing wave, which suggests opportunities for in vivo implementation of cell patterning toward tissue engineering applications.

Focusing pattern of the Laguerre-Gaussian beam with polarization mixing helical-conical phase modulation.

This paper focuses on the focusing pattern of the Laguerre-Gaussian (LG) beam with polarization mixing helical-conical phase modulation, which is based on the vector diffraction theory. The results show that the topological charge number l can sensitively control the intensity of the intensity peaks. The focal spot will split along the optical axis under different polarization parameters P. When l=1, the spot position and the peak intensity can be modulated by changing the polarization parameter P. The truncation parameter β makes the focusing spot form an optical trap. By adjusting the eccentricity parameter K, the opening direction of the optical trap can be well controlled. These results may be helpful in optical applications such as optical manipulation, optical focusing, and optical information transmission.

Reflectarrays and Metasurface Reflectors as Diffraction Gratings: A tutorial

Reconfigurable reflectors have significant potential in future telecommunication systems, and approaches to the design and realization of full and tunable reflection control are now actively studied. Reflectarrays, being the classical approach to realize scanning reflectors, are based on the phased-array theory (the so-called generalized reflection law) and physical optics approximation of the reflection response. To overcome the limitations of the reflectarray technology, researchers actively study inhomogeneous metasurfaces, using the theory of diffraction gratings. To make these devices tunable and fully realize their potential, it is necessary to unify the two approaches and study reconfigurable reflectors from a unified point of view. Here, we offer a tutorial on reflectarrays and metasurface reflectors, explaining their common fundamental properties that stem from the diffraction theory. This tutorial is suitable for graduate and postgraduate students and hopefully will help to develop deeper understanding of both phased arrays and diffraction gratings.

Fast and rigorous optical simulation of periodically corrugated light-emitting diodes based on a diffraction matrix method.

Increasing the light extraction efficiency has been widely studied for highly efficient organic light-emitting diodes (OLEDs). Among many light-extraction approaches proposed so far, adding a corrugation layer has been considered a promising solution for its simplicity and high effectiveness. While the working principle of periodically corrugated OLEDs can be qualitatively explained by the diffraction theory, dipolar emission inside the OLED structure makes its quantitative analysis challenging, making one rely on finite-element electromagnetic simulations that could require huge computing resources. Here, we demonstrate a new simulation method, named the diffraction matrix method (DMM), that can accurately predict the optical characteristics of periodically corrugated OLEDs while achieving calculation speed that is a few orders of magnitude faster. Our method decomposes the light emitted by a dipolar emitter into plane waves with different wavevectors and tracks the diffraction behavior of waves using diffraction matrices. Calculated optical parameters show a quantitative agreement with those predicted by finite-difference time-domain (FDTD) method. Furthermore, the developed method possesses a unique advantage over the conventional approaches that it naturally evaluates the wavevector-dependent power dissipation of a dipole and is thus capable of identifying the loss channels inside OLEDs in a quantitative manner.

A Convolutional Neural Network for Parameter Estimation of the Bi-GTD Model

In this paper, a novel parameter estimation method based on a convolutional neural network (CNN) is proposed to extract geometrical features of radar objects. The CNN’s design is inspired by the inversion process of a physically relevant model, called the geometrical theory of diffraction (GTD) model, whose bistatic form can be used to describe the bistatic scattering response from the target in the netted radar system. This model-inspired inversion method can automatically compensate for phase errors between multiple signal channels and obtain better parameter estimation performance than traditional methods, such as the orthogonal matching pursuit (OMP), the estimation of signal parameters via rotational invariance techniques (ESPRIT) and the multiple signal classification (MUSIC). The experimental results not only verify the validity of the proposed intelligent inversion method but also demonstrate the interpretability and generalization ability of the CNN, whose architecture is designed based on mathematical derivation.

UTD-Based Ray-Tracing MIMO Channel Modeling for the Next-Generation Communications Within Underground Tunnels

Limited work has previously been conducted into deterministic modeling of the 5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> Generation (5G) millimeter (mm)-wave wireless communications within geometrically non-uniform tunnels. This study predicts and analyzes broadband Multiple–Input Multiple–Output (MIMO) propagation in underground mine tunnels for 5G communications and beyond. At extremely short wavelength, each rugged and uneven surface of the tunnel is modelled as a group of diffracting rectangular prism wedges. A deterministic Ray-Tracing (RT) MIMO model is developed based on the Uniform Theory of Diffraction (UTD). All predicted MIMO sub-channels have been successfully fitted with the experimental measurements. MIMO multipath fading of underground tunnels are found to be lognormally distributed and strongly depends on the tunnel’s size and shape.

Diffraction Theory of Propagation of High-Frequency Radio Waves in a Spherically Layered Ionospheric Radio Channel

Diffraction Theory of Propagation of High-Frequency Radio Waves in a Spherically Layered Ionospheric Radio Channel

Propagation and focusing dependency of a laser beam with its aberration distribution: understanding of the halo induced disturbance

In various applications, it is necessary to understand laser field dynamics during its propagation, especially at the focal position including the dispersed energy surrounding the main pulse, called the halo effect. For instance, the properties of electron beams produced by laser wakefield acceleration (LWFA) strongly depend on the laser energy distribution and its halo in the vicinity of the focus. Indeed, under certain conditions, this halo, or even its internal structures, can propagate and be self-focused independently of the main pulse in the plasma. This paper aims to provide sufficient tools to properly describe the behavior of a focused laser beam, including the halo. Subsequently, an optical description regarding the source of this halo is provided. A more accurate estimation of the input laser beam that should be used in simulations of high-power laser applications may now be obtained. Finally, one may also find ways to positively manipulate the laser beam. Using Fresnel diffraction theory, the propagation and focusing of an experimental high-power (sub-petawatt) aberrated beam is numerically calculated. The shape of the focused beam pattern within a few Rayleigh lengths is analysed as a function of main aberrations (up to the 14 th term of Zernike polynomials). Furthermore, at the focus position, the spreading of the energy is compared to both the case of a perfect diffraction-limited Gaussian and a super-Gaussian beam.

Design of an off-axis axiparabola with inclined wavefront correction to obtain a straight focal line.

The axiparabola is a novel reflective element proposed in recent years, which can generate a long focal line with high peak intensity, and has important applications in laser plasma accelerators. The off-axis design of an axiparabola has the advantage of separating the focus from incident rays. However, an off-axis axiparabola designed by the current method always produces a curved focal line. In this paper, we propose a new method to design its surface by combining geometric optics design and diffraction optics correction, which can effectively convert a curved focal line into a straight foal line. We reveal that the geometric optics design inevitably introduces an inclined wavefront, which leads to the bending of the focal line. To compensate for the tilt wavefront, we use an annealing algorithm to further correct the surface through diffraction integral operation. We also carry out numerical simulation verification based on scalar diffraction theory, which proves that the surface of this off-axis mirror designed by this method can always obtain a straight focal line. This new method has wide applicability in an axiparabola with any off-axis angle.

Magnetic transitions in V-Fe-Co-Ni-Cu-based high entropy alloys

FeCoNi, V0.85FeCoNi, FeCoNiCu1.15 and V0.85FeCoNiCu1.15 alloys have been synthesized by arc melting and analyzed by powder X-ray diffraction, electron microscopy, magnetic measurements, and density functional theory (DFT). The influence of each alloying element on the magnetic exchange interaction, Curie temperature (TC) and magnetocaloric effect is evaluated. The experimental results show that Cu and V “dilute” the magnetic properties and couple antiferromagnetically to Fe, Co, and Ni. Analysis of the microstructure reveals a lack of solubility between V and Cu with FeCoNi, and between themselves, thus lowering the concentration of V and Cu in the main solid solution of the 5-element alloy V0.85FeCoNiCu1.15. Tc decreases significantly from 997 K in FeCoNi to 245 K in V0.85FeCoNi and 297 K in V0.85FeCoNiCu1.15, respectively. The derivative of magnetization as a function of temperature (dM/dT) in the vicinity of Tc is drastically reduced due to the presence of V which indicates a reduced magnetocaloric effect. DFT calculations confirm antiferromagnetic coupling of V to the ferromagnetic FeCoNi-base and predict a similar behavior for other transition metal elements (e.g., Ti, Cr, Mn). This leads to a lowering of Tc, which is needed to establish the magnetocaloric effect at room temperature. However, it comes at a cost of reduced magnetic moments. Nevertheless, the use of V and Cu has shown possible routes for tuning the magnetocaloric effect in FeCoNi-based high entropy alloys.

Real-time phase measurement of optical vortex via digital holography

Real-time phase measurement is of great value to study the evolution of optical vortex. However, it cannot be recorded in real time due to the limitation of the exposure time of the recording device in the experiment. Therefore, based on the temporal and spatial evolution correlation of the optical phase, a real-time phase measurement method of optical vortex generated by an acoustically induced fiber grating is proposed based on digital holographic reconstruction algorithm. First, a series of holograms are continuously recorded using a low frame rate CCD. Then, the evolution of optical vortex over time is translated into changes in transmission distance. Furthermore, the unrecorded vortex phase distributions are calculated using diffraction theory. By serializing these phase maps over time, the propagation and evolution of spiral phase structure of the vortex beam can be demonstrated in real time.

Beam shaping-based design for optical imaging lens

In this paper, a beam shaping-based method for design of optical imaging lens is proposed. The optical imaging lens is designed with Fresnel diffraction theory to focus light, and the focusing parameters of the lens, such as the number of the foci, the focal length, the size and the shape of the focal spot, and so on, can be set with great freedom. Therefore, the lens has great flexibility in optical imaging, and the imaging resolution can also be varied with the design. The optical imaging lenses possess advantages such as simple structure, compact size, customized imaging effect, and high performance. The proposed method can be extensively applied to the design of flat optical elements and the customized optical imaging.

Effects and elimination of image grating defocusing on a double-Ronchi shearing interference field.

Double-Ronchi shearing interferometry is a promising wavefront aberration measurement system for advanced lithography projection lens systems. The image grating defocusing is a key systematic error of the interferometer. However, the effects and elimination of this error have not been systematically researched. In this work, the interference field effects caused by the image grating defocusing are analyzed based on the theories of scalar diffraction, and a method to eliminate the effects is proposed. The theoretical analysis has been verified by a simulation and experiments. The results show that the error of image grating defocusing is mainly expressed as the Zernike Z4 term and Z9 term in the reconstructed wavefront, and the coefficients of Z4, and Z9, respectively, are related to NA2, NA4, and the defocus distance z. When the numerical aperture (NA) of the under-test projection lens is 0.6, 99.8384% of the errors caused by the image grating defocusing can be removed. When the NA is reduced to 0.3, 99.9854% of the errors can be removed. Additionally, when the NA is less than 0.1, almost all the errors can be eliminated.