Diffraction Theory Research Articles

Revisiting the structures and phase transitions of Ba2NaNb5O15.

The room-temperature and low-temperature structure(s) of Ba2NaNb5O15 (BNN) have been debated since the structure was proposed in the 1960s. This work revisits the structures and phase transitions of BNN, combining high-resolution X-ray and neutron powder diffraction with density functional theory calculations. Temperature-dependent high-resolution X-ray powder diffraction patterns are collected from 4 to 918 K, and sequential batch Rietveld refinement using a symmetry mode approach to describe the structure is used to extract the main structural changes as a function of temperature. The data show that the average structure of BNN is best described by the Ama2 space group, and no other structural phase transitions were observed below the ferroelastic transition. The symmetry mode analysis, combining results from diffraction and density functional theory, shows significant octahedral tilting and corrugations of both the A1 and A2 sites along the c direction. A strong correlation between the spontaneous strain and the octahedral tilting was observed, and a potential connection with emerging microstructure at low temperatures is proposed, all enabled by the symmetry mode approach used in this work.

Aeroacoustic investigation of airfoil at near-stall conditions

This paper presents a detailed aeroacoustic investigation of a controlled-diffusion airfoil at near-stall condition. The study aims at answering two research questions: identify the flow mechanism responsible for separation noise for an airfoil near-stall conditions and whether the noise is generated by a dipole for airfoil close to stall and can be quantified by Amiet's diffraction theory. The study uses synchronized particle image velocimetry, remote microphone probes, and far-field microphone measurements to perform experiments at two chord-based Reynolds numbers of about 150 000 and 250 000. The results show that when the airfoil is placed at a higher angle of attack, such as 15°, strong amplification of flow disturbance is seen, resulting in the rolling up of the shear layer in the aft region of the airfoil, forming large coherent structures. While these rollers play a central role in the increase in noise due to flow separation, the flapping of shear layer does not contribute to the separation noise. The present study conclusively shows that separation noise is dipolar in nature and that the quadrupolar contribution for low-speed airfoils at near-stall conditions can be neglected. However, the increase in flow disturbances measured close to the trailing edge of the airfoil implies that the assumption of small-amplitude disturbance is no longer valid, which is the central premise of the thin linearized airfoil theory. Outside the frequency range at which flow separation operates, Amiet's theory is able to predict the far-field noise even at high angles of attack.

Dynamic Electromagnetic Scattering Simulation of Tilt-Rotor Aircraft in Multiple Modes.

To study the electromagnetic scattering of tilt-rotor aircraft during multi-mode continuous flight, a dynamic simulation approach is presented. A time-varying mesh method is established to characterize the dynamic rotation and tilting of tilt-rotor aircraft. Shooting and bouncing rays and the uniform theory of diffraction are used to calculate the multi-mode radar cross-section (RCS). And the scattering mechanisms of tilt-rotor aircraft are investigated by extracting the micro-Doppler and inverse synthetic aperture radar images. The results show that the dynamic RCS of tilt-rotor aircraft in helicopter and airplane mode exhibits obvious periodicity, and the transition mode leads to a strong specular reflection on the rotor's upper surface, which increases the RCS with a maximum increase of about 36 dB. The maximum micro-Doppler shift has functional relationships with flight time, tilt speed, and wave incident direction. By analyzing the change patterns of maximum shift, the real-time flight state and mode can be identified. There are some significant scattering sources on the body of tilt-rotor aircraft that are distributed in a planar or point-like manner, and the importance of different scattering sources varies in different flight modes. The pre-studies on the key scattering areas can provide effective help for the stealth design of the target.

Terahertz meta-polarizers for simultaneous control of the amplitude, phase, and polarization

Terahertz (THz) waves hold immense potential for advancements in areas such as in 6G wireless communications, non-destructive testing, and biomedicine. However, the underdeveloped control level of THz devices has been a severe obstacle. Here, a THz meta-polarizer, comprising rectangular metallic holes, is proposed to achieve the simultaneous control of the amplitude, phase, and polarization. Each unit of this meta-polarizer can function as a miniature linear polarizer. The component polarized along the short side can pass through the unit, while the component polarized orthogonally is unable to do so. Leveraging the principles of the Malus' law, we can adjust the desired amplitude distribution of the transmitted x-polarized wave by modifying its polarization distribution. This adjustment is made possible by tuning the azimuth angle of each hole. The phase delay of the transmitted wave can be further manipulated by adjusting the hole dimensions perpendicular to the polarization direction. For given near-field amplitude distributions, the required phase distributions for generating far-field target holograms can be calculated using the Gerchberg–Saxton algorithm based on Fresnel diffraction theory. The meta-polarizer then realizes calculated phase distributions, enabling the creation of the required holograms. As a proof of concept, we designed THz meta-polarizers that can achieve two- and four-level amplitude holograms in the near field, respectively. Moreover, we also manipulated the phase distributions, allowing us to decouple the near- and far-field holograms. The experimental results agree well with the simulations. Owing to its ability to simultaneously control the phase, amplitude and polarization, the proposed THz meta-polarizer holds great application potential in 6G wireless communications, radar detection systems, and holography.

Facile scalable multilevel structure engineering makes Ti0.667Nb1.333O4 a new promising lithium-ion battery anode

Titanium/Niobium oxide-based lithium-ion battery anodes are characterized by their excellent safety features, superior rate capability and high theoretical capacity. However, the intrinsic poor electron conductivity of the metal oxides significantly limits anode performance. In this work, Ti0.667Nb1.333O4 (TNO4) has been synthesized and utilized as the lithium-ion battery anode for the first time. A facile scalable multilevel structure engineering in terms of electronic, morphology, and surface structures is applied to TNO4, leading to an effective performance improvement. The electronic structure, in regard to the band gap and lithium-ion diffusion energy barrier, is well tuned by a stoichiometric atomic substitution of titanium by niobium. The reduced band gap (0.38 eV vs. 3.10 eV) and increased energy barrier along the c-axis (0.13 eV vs. 0.04 eV) accelerate electrochemical kinetics and increase actual capacities. In combination with particle size reduction and surface carbon composition, the electrochemical performance is further improved. The lithiation/delithiation mechanism of the TNO4 anode is investigated by in situ X-ray diffraction (XRD) and density functional theory (DFT) computations. In situ transmission electron microscopy (TEM) is applied to reveal the structure change upon lithiation and delithiation, where a limited volume change is observed. Differential electrochemical mass spectrometry (DEMS) shows a slight gassing process of TNO4/carbon.

Research on Propagation Characteristics Based on Channel Measurements and Simulations in a Typical Open Indoor Environment

At present, it is difficult to obtain the indoor propagation loss quickly and accurately by directly using measurements in the millimeter wave band. To solve this problem, in this paper, a ray tracing method suitable for indoor scenes based on geometric optics theory, the uniform theory of diffraction and image theory is presented; the space-alternation generalized expectation-maximization (SAGE) algorithm is used to analyze the measured data and the multipath information of the wireless channel is analyzed; three deep learning models are used to predict the path loss at different receiving distances based on 1600 sets of path loss data. The results show that the comparison between the ray tracing and experimental results shows a good agreement. Moreover, the root-mean-square error (RMSE) and mean absolute error (MAE) of the long short-term memory (LSTM) network are the smallest, and the LSTM has a better fitting effect on the propagation loss sequences predicted at more distant locations when compared with the recurrent neural network (RNN) and gate recurrent unit (GRU) methods, which can better reflect the propagation trend. This provides theoretical support for the layout of base stations and network optimization in typical open indoor environments.

Intensity correlation properties of x-ray beams split with Laue diffraction

Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundred-micrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated. Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.

Sub-micron weak phase particle characterization using the reconstructed volume intensities from in-line digital holography microscopy

Digital holography microscopy is a powerful technique for retrieving particle properties that are often challenging to obtain with other methods. However, analyzing holographic data using non-linear fitting algorithms and machine learning is difficult without prior information. In this paper, we present a novel technique for sizing and determining the refractive index of sub-micron, weak phase, spherical particles using the Rayleigh-Sommerfeld diffraction theory. Our method involves reconstructing the volume of synthetic holograms using the HoloPy software for particles of different sizes and material properties. We then fit a Gaussian function at the point of numerical re-focus, as given by the first local minima after the Gouy-phase shift, for size and sub-pixel position estimates. By retrieving the magnitude and location of the maximum scattered intensity, we build a scattered interpolant that relates all the parameters of interest. We demonstrate that our technique had a mean error in particle refractive index of 1.24 ± 1.74% with synthetic data and accurately estimates the size and refractive index of similar-sized nanoparticles in experiments. Compared to least-squares fitting, our method performs similarly with synthetic data but outperformed it with experimental data, showcasing its superior accuracy and reliability. Furthermore, we use our technique combined with function-fitting approaches. This hybrid method uses our proposed technique to approximate the initial conditions of non-linear fitting algorithms, leading to improved accuracy. Finally, we explore the potential of using the intensity cubes as well-defined thresholds to differentiate particles from interference caustics in a reconstructed volume. Overall, our results demonstrate the efficacy and accuracy of our technique for retrieving particle properties from holographic data, even when prior information was not available. This technique could have broad applications in the field of nanoparticle characterization.

Convolutional symmetric compressed look-up-table method for 360° dynamic color 3D holographic display.

In this paper, we propose a convolutional symmetric compressed look-up-table (CSC-LUT) method to accelerate computer-generated hologram (CGH) computation based on the Fresnel diffraction theory and LUT. The proposed method can achieve one-time high-quality fast generation of color holograms by utilizing dynamic convolution operation, which is divided three processes. Firstly, the pre-calculated data of maximum horizontal modulation factor is compressed in 1D array by coordinate symmetry. Then, the test object is resampled to satisfy convolutional translation invariance. Finally, the dynamic convolution operation is used to simplify CGH computation process rather than the point-by-point computation. Numerical simulation and optical experimental results show that our proposed method can achieve faster computation speed, higher reconstruction quality and wider application compared to conventional SC-LUT method. The further optimization method for parallel acceleration on the GPU framework can achieve real-time (>24fps) color holographic display corresponding to three perspectives of a 3D scene.

Generation and characteristics of hollow structured optical fields based on multiple off-axis vortices.

In this paper, various hollow structured optical fields are generated by skillfully adjusting the number and positions of multiple off-axis vortices loaded in a Gaussian beam. The focal-field characteristics of the generated hollow structured optical fields after passing through an ordinary lens are studied based on the scalar diffraction theory. Firstly, a variety of hollow structured optical fields are theoretically simulated by adjusting the number and positions of multiple off-axis vortices loaded in the Gaussian beam. The focal-field characteristics of the hollow structured optical fields after passing through a lens are theoretically analyzed. On this basis, the experiments are implemented in the built optical system for multi-off-axis vortex beam focusing through an ordinary lens. In the experiments, various hollow structured optical fields are detected in CCD which are consistent with the theoretical results. The manipulations of size and rotation direction of the hollow structured optical fields are realized. We believe that this study will contribute to extending the potential applications of off-axis vortex beams in fields such as optical field shaping, optical manipulation and laser processing.

On UV Photon Distribution of Discharge in GIS Busbar Based on Ray Tracing

In order to clarify the distribution law of the ultraviolet photon field in gas insulated switchgear busbar, meanwhile to correct the detection range of the ultraviolet sensor, the optical model of the gas insulated switchgear busbar based on the uniform theory of diffraction is proposed based on ray tracing. the distributions of the radiation ultraviolet fields are calculated when partial discharge occurs at the key positions such as basin insulator and conductor. Based on the average irradiance, maximum irradiance, and attenuation characteristics, the distribution law in the busbar is further analyzed, which provides a new method to confirm the location of ultraviolet sensors.

High-voltage stability of O3-type sodium layered cathode enabled by preferred occupation of Na in the OP2 phase

Cobalt-free O3-type layered sodium nickel manganese oxide, Na[Ni0.5Mn0.5]O2, is one of the most attractive candidates as a cathode material for low-cost and practical sodium-ion batteries (SIBs). However, stable cycling with high reversible capacity in SIBs using Na[Ni0.5Mn0.5]O2 as a cathode is still hampered by an irreversible phase transition at voltages above 4.0 V (vs. Na/Na+). In this study, to suppress the detrimental phase transition, Mg substitution into Ni sites is proposed, and a series of Na[Ni0.5-xMgxMn0.5]O2 (x = 0, 0.05, 0.1 and 0.15) materials are synthesized and characterized. The substitution of Mg over 10 mol% into Ni site regulates sodium occupancy into P-type stacking, resulting in the OP2 phase upon high-voltage operation. This enables the material to tolerate strains in the crystal structure by alleviating the irreversible O3′−O3″ phase transition, which was evidenced by the results of operando X-ray diffraction and density functional theory calculation. Compared to its corresponding members, the optimized Na[Ni0.4Mg0.1Mn0.5]O2 cathode delivers a high reversible capacity of 177 mAh g−1 as well as improved cycling stability and rate capability in the wide voltage range of 2.0 − 4.3 V. Moreover, the Mg substitution strategy enhances the thermal and chemical stability against moisture, indicating its excellent practical applicability.

Focusing of Radially Polarized Electromagnetic Waves by a Parabolic Mirror

It is well-known that a strong longitudinal electric field and a small spot size are observed when radially polarized beams are tightly focused using a high numerical aperture parabolic mirror. The longitudinal electric field component can accelerate electrons along the propagation axis at high intensities in the focal region, which opens an application in particle acceleration. In this paper, we present a rigorous derivation of the electric field obtained when a radially polarized, monochromatic, flat-top beam is focused by a parabolic mirror. The formulae were deduced from the Stratton–Chu integral known from vector diffraction theory. We examined the influence of the focusing parameters on the distribution of both the longitudinal and radial electric field components. In the small numerical aperture and short wavelength regimes, excellent agreement was found with the results obtained from the Rayleigh–Sommerfeld formula. The calculation method can be adapted for various beam types and for electromagnetic pulses as well.

Generation of optical chirality by the tightly focused higher-order Poincaré sphere vector vortex beams

We derive the analytical expressions of the electric and magnetic field vectors as well as optical chirality density of tightly focused higher-order Poincaré sphere (HOPS) vector vortex beams based on the Richards-Wolf vector diffraction theory. The optical chirality density induced by the tightly focused HOPS vector vortex beams is systematically explored, and its roles with respect to ellipticity, handedness, orientation, polarization topological charge (PTC), and vortex topological charge (VTC) are deeply revealed. The research results show that apart from the orientation of the polarization ellipse, other parameters of the input vortex beams have a significant influence on the optical chirality density of the tightly focused fields. It is noteworthy that because of the introduction of vortex phase, the optical chirality density of linearly polarized light before being focused carrying no spin angular momentum (SAM) is no longer zero. The change of the sign of VTC and PTC has an important effect on the sign of optical chirality density of the tightly focused fields, whereas its spatial distribution and magnitude mainly arises from the change of the value of VTC and PTC. Furthermore, for the non-linearly polarized input beam, due to the interplay of the orbital angular momentum (OAM) and SAM, the sign and value of VTC and ellipticity have an important influence not only on the sign, but also on the spatial distribution and magnitude of the optical chirality density. These research results may provide new insights into the chiral light–matter​ interactions and find potential applications in chiral particle trapping, manipulation, and so on.

Measuring the photonic topological charge of power-exponent-phase vortex beam via cross phase

We propose a method for measuring the photonic topological charge of the power-exponent-phase vortex (PEPV) beam with the cross phase. Based on the superimposition of the power-exponent phase and the cross phase, we analyzed the axial diffraction properties of the modulated PEPV beam with different parameters by using the scalar diffraction theory. The simulations demonstrated that dark regions are embedded in the intensity profile of the modulated PEPV beam, and the number of the dark regions is just equal to the photonic topological charge carried by the PEPV beam. Moreover, the sign of the photonic topological charge can be distinguished by the alignment direction of the modulated PEPV light field. The experimental results are consistent with the theoretical ones. The method is promising in the fields of beam shaping and optical trapping.

Modulation of orbital angular momentum of vortex beam based on ordered pinhole screens

Optical vortex phase beams have unique amplitudes and phase distributions, rendering them sensitive to the position and symmetry of modulating structures. This sensitivity can facilitate their applicability to optical communications. We propose a method for modulating the topological charge of input vortex beams using a pinhole screen. By changing the pinhole arrangement to match the phase of the vortex beam and considering the Fresnel diffraction theory, the transmission light field is calculated numerically. In addition, the intensity map of the adjustable topological charges is measured near the origin, with the experimental results suitably agreeing with the theoretical simulation results. The diffraction field modulated by spiral pinholes has various orbital angular momentum modes, including the increase and decrease of orbital angular momentum, especially when the incident vortex beam is more complex. The proposed method opens new possibilities for the use of vortex beams in advanced optical applications with improved capabilities and functionalities.

Quantum information approach to the implementation of a neutron cavity

Using the quantum information model of dynamical diffraction we consider a neutron cavity composed of two perfect crystal silicon blades capable of containing the neutron wavefunction. We show that the internal confinement of the neutrons through Bragg diffraction can be modelled by a quantum random walk. Furthermore, we introduce a toolbox for modelling crystal imperfections such as surface roughness and defects. Good agreement is found between the simulation and the experimental implementation, where leakage beams are present, modelling of which is impractical with the conventional theory of dynamical diffraction. Analysis of the standing neutron waves is presented in regards to the crystal geometry and parameters; and the conditions required for well-defined bounces are derived. The presented results enable new approaches to studying the setups utilizing neutron confinement, such as the experiments to measure neutron magnetic and electric dipole moments.

Two New Red/Near-Infrared Ir(Ⅲ) Complexes with Reversible and Force-Induced Enhanced Mechanoluminescence.

Two novel ionic red/near-infrared Ir(III) complexes (Ir1 and Ir2) were reasonably designed and prepared using 2-(1-isoquinolinyl)-9,10-anthraquinone as the main ligand and 4,4'-dimethyl-2,2'-bipyridyl and 4,4'-dimethoxy-2,2'-bipyridyl as the auxiliary ligands, respectively. Both complexes showed bright phosphorescence in solution (peak at 618 nm with a shoulder at 670 nm). Interestingly, the phosphorescence peak of two Ir(III) complexes showed a blue-shift of about 36 nm after being ground. Simultaneously, both complexes exhibited mechanical force-induced enhanced emission, and the intensity of the luminescence for Ir1 and Ir2 increased by around two times compared to the one before being ground, respectively. Powder X-ray diffraction (PXRD) and time-dependent density functional theory (TD-DFT) calculation were utilized to understand well the mechanism of this phenomenon and suggested that the destruction of the well-ordered crystalline nature and the decline in triplet-triplet annihilation maybe responsible for the pressure-induced blue-shift and the enhancement of the phosphorescence.

Demonstration of feasibility and effectiveness of deep eutectic solvent-water system extraction of RG-I type pectin from wolfberry based on target polysaccharide, solvent and their interactions

Lycium barbarum fruit (wolfberry) is rich in rhamnogalacturonan-I (RG-I) pectin with favorable prebiotic activity. However, there is currently limited research on the targeted extraction of RG-I type pectin from Lycium barbarum fruit (LBP). DES is widely recognized as an efficient solvent for extracting bioactive compounds from plants. In this study, a mixture of choline chloride (ChCl) and propylene glycol (PG) at the molar ratio 1:2 with 20 wt% water content was optimal to extract LBP. The yield and extent of branching of LBP extracted by ChCl-PG-water system (LBP-P) were 1.74-fold and 2.87-fold higher than those of LBP extracted by water (LBP-W), respectively. Compared with LBP-W, LBP-P exhibited higher total neutral sugar and uronic acid contents, as well as lower molecular weight and viscosity. The proliferative ability of LBP-P on six Bifidobacterial strains was 1.06–1.92-fold greater than that of LBP-W. In addition, Fourier transform infrared spectroscopy (FTIR) and apparent viscosity proved that the role of water was to maintain strong hydrogen bonds of DES with reduced viscosity. Scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman spectra and density functional theory (DFT) calculations proved that the role of DES was to penetrate cell walls and interact with target substances. The effective extraction mechanism of the DES-water system was based on cell wall cellulose disassembly, side chain exposure, and high-branched LBP dissolution stages. Our results provided a theoretical basis for targeted extraction of RG-I pectin using new solvents.

Analytic plenoptic camera diffraction model and radial distortion analysis due to vignetting.

Using a mathematical approach, this paper presents a generalization of semi-analytical expressions for the point spread function (PSF) of plenoptic cameras. The model is applicable in the standard regime of the scalar diffraction theory while the extension to arbitrary main lens transmission functions generalizes a priori formalism. The accuracy and applicability of the model is well verified against the exact Rayleigh-Sommerfeld diffraction integral and a rigorous proof of convergence for the PSF series expression is made. Since vignetting can never be fully eliminated, it is critical to inspect the image degradation it poses through distortions. For what we believe is the first time, diffractive distortions in the diffraction-limited plenoptic camera are closely examined and demonstrated to exceed those that would otherwise be estimated by a geometrical optics formalism, further justifying the necessity of an approach based on wave optics. Microlenses subject to the edge diffraction effects of the main lens vignetting are shown to translate into radial distortions of increasing severity and instability with defocus. The distortions due to vignetting are found to be typically bound by the radius of the geometrical defocus in the image plane, while objects confined to the depth of field give rise to merely subpixel distortions.