Spherical Wave Research Articles

Phase‐reconstruction from magnitude‐only data of electrically small antennas for body‐centric wireless communication

AbstractA method for phase retrieval from magnitude‐only data for electrically small antennas intended for use in relation to body‐centric wireless communication, is presented. The method utilizes the spherical wave expansion (SWE) description of the electromagnetic field radiated by the antenna under test (AUT). The expansion coefficients of the SWE are optimized such that errors between the reconstructed and provided data magnitudes are as small as possible. The required additional phase information is acquired from additional magnitude‐only data sets of the AUT in different orientations. These orientations are defined by rotations of the AUT along the Eulerian angles. The performance of the method is evaluated for a realistic configuration, which consists of an inverted‐A antenna in the vicinity of an ear. The sensitivity of the method to the angular resolution of the field data, as well as to the Eulerian rotation accuracy, is investigated. Finally, the reconstruction method is tested on a set of practical antenna measurements conducted in an RF‐anechoic chamber.

Application of Python-Based Abaqus Secondary Development in Laser Shock Forming of Aluminum Alloy 6082-T6.

Aluminum alloy 6082-T6 is an important material for manufacturing the outer skin of high-speed trains, and laser shock forming can realize the rapid forming of complex-shaped plates. In order to improve the efficiency of the simulation modeling of laser shock forming for aluminum alloy 6082-T6, Python scripting language was used for the secondary development of Abaqus. A plugin was utilized to simulate and analyze the laser shock forming process of aluminum alloy 6082-T6. The coordinates of the plate after laser impact molding were measured using a coordinate measuring machine to calculate the arc bow height of the plate. The accuracy of the simulation model was verified by comparing with the simulation results. The deformation characteristics of plastic strain and arc height of aluminum alloy 6082-T6 under different laser process parameters were analyzed. The simulation plugin has a concise interface, high operability, and accurate results with the other parameters unchanged. When the laser energy is 5 J, 6 J, and 7 J, the corresponding arc heights are 5.9 mm, 6.6 mm, and 7.2 mm, respectively. As the thickness of the sheet increases, the deformation changes from concave at 1 mm to convex at 2 mm, 3 mm, 4 mm, and 5 mm. As the spot size increases from 1 mm to 5 mm, the transmission mode of the shock wave gradually changes from spherical wave to planar wave, and the arc height of the sheet increases from 4.6 mm to 8.2 mm. With the increase in the spot overlap rate, the impact area accumulates residual stress, and the arc height of the sheet is 5.7 mm, 6.6 mm, 7.3 mm, and 8.5 mm, respectively. The secondary development of ABAQUS 2021 using Python 3.6 scripting language has improved the efficiency of simulation modeling and provided reference for rapidly predicting the deformation characteristics of aluminum alloy 6082-T6 under different laser process parameters.

Spectral analysis of intricate orbital angular momentum modes in multiplexing communication using a residual neural network

Vortex beams carrying orbital angular momentum (OAM) modes offer a compelling avenue for increasing optical communication capacity. Despite significant efforts in OAM mode (de)multiplexing, challenges persist in signal demodulation and noise monitoring of multiplexed channels. This challenge largely stems from the absence of efficient feature extraction methods capable of analyzing the OAM spectrum, which delineates mode components and intensity weights. Herein, we introduce a novel strategy for OAM mode spectrum analysis using a residual neural network incorporating interference techniques. By introducing interference between target vortex beams and a spherical wave, resulting in the mapping of OAM distributions onto the stripe features observed in the interferogram. To effectively extract spectrum details from these interferograms, we construct a residual neural network exhibiting high feature processing capabilities, which enables precise analysis of intricate OAM mode spectrum. We demonstrate the effectiveness of this OAM spectrum analysis by obtaining the intensity weights for 15 superimposed modes ranging from −10 to +10, achieving a mean-square-error of 2.3 × 10−4. To validate its practicality, we showcase an 80-channel three-dimensional multiplexing communication system including five OAM modes, two polarizations, and eight wavelengths. The 4 Tbit/s quadrature-phase-shift-keying signals are successfully demodulated with a bit-error rate below 3.34 × 10−6. Additionally, the measured optical signal-to-noise ratio reaches 11.5 dB, indicating the potential applications of this OAM spectrum analysis strategy in signal demodulation and noise monitoring.

Description and reconstruction of typical structured light beams with vector spherical wave functions.

It is well known that the generalized Lorenz-Mie theory (GLMT) is a rigorous analytical method for dealing with the interaction between light beams and spherical particles, which involves the description and reconstruction of the light beams with vector spherical wave functions (VSWFs). In this paper, a detailed study on the description and reconstruction of the typical structured light beams with VSWFs is reported. We first systematically derive the so-called beam shape coefficients (BSCs) of typical structured light beams, including the fundamental Gaussian beam, Hermite-Gaussian beam, Laguerre-Gaussian beam, Bessel beam, and Airy beam, with the aid of the angular spectrum decomposition method. Then based on the derived BSCs, we reconstruct these structured light beams using VSWFs and compare the results of the reconstructed beams with those of the original beams. Our results will be useful in the study of the interaction of typical structured light beams with spherical particles in the framework of GLMT.

In situ calibration of shear ratio for quadriwave lateral shearing interferometry using double-slit interference.

A new method, to the best of our knowledge, based on double-slit (DS) interference is proposed to accurately estimate the shear ratio of the system, with plane wave or spherical wave incidence. Existing shear ratio calibration methods, designed primarily for lateral shearing interferometry (LSI) with plane wave incidence, are not applicable to LSIs directly testing divergent or convergent spherical waves. Equations for calculating the shear ratio using the fringe spacing of the DS interferogram and the NA of the incident spherical wave are derived in this paper. The simulation result shows that the relative error of the shear ratio value is about 0.3%, when the shear ratio is 0.1. In the experiment, the quadriwave LSI is designed with a plug-in feature. The shear ratio at integer multiples of 1/6 Talbot distance from the modified Hartmann mask was calibrated using a DS, and the results were in good agreement with theoretical values, confirming the accuracy of the method. Subsequently, with the assistance of an inductance micrometer, the shear ratio was calibrated at intervals of 0.5mm, and the results closely matched the theoretical variation of the shear ratio caused by displacement, confirming the high precision of the method.

Mine seismic source location via forward modeling of spherical waves in a multilayered horizontal or inclined medium

Seismic source location is a classic inverse problem in seismology. In mathematical physics, inverse problems have multiple natural solutions. The objective of this study was to develop a generic theory and method of seeking the true solution from multiple solutions for the location of a coal mine seismic source in an idealized velocity structure model of a coal mine with a small scale and complex geological environment. Starting from the simplest velocity structure model, the complexity of the model gradually increased, until it approached the real velocity structure model, i.e., the multilayered horizontal and inclined velocity structure model, in order to find a generic method for solving the multi-solution inverse problem of coal mine seismic source location. Specifically, the wavefront distribution equation in a two-layer horizontal medium was derived and then expanded to any multi-layer horizontal medium. Based on this equation, a positive definite nonlinear equation system was established from the perspective of any observation system. The equation system contained four unknown variables of the spatiotemporal position of the seismic source. To determine the spatiotemporal parameters of the seismic source, nonlinear equations for four stations were required. To solve the nonlinear equation system, an initial iteration value was determined. In order to reduce the difficulty of determining the initial iteration value, the variable substitution method was used to reduce the number of location parameters. By rotating the original geodetic coordinate system of the station to be parallel and orthogonal to the medium interface, the wavefront method was extended to inclined medium. In conclusion, in this study, the problem of coal mine seismic source location in a multi-layer horizontal or inclined medium was effectively solved. The method proposed in this study provides a reference for solving the true solution from multiple solutions for the location of a coal mine seismic source in small-scale coal mines with complex geological environments.

An advanced light scattering imaging model for total internal reflection microscopy considering a stratified medium

An advanced light scattering model for Total Internal Reflection Microscopy (TIRM) is presented. The model considers the specific TIRM geometry and deals with the scattering by an axisymmetric particle of arbitrary orientation placed in a stratified medium and the imaging of the scattered field. The scattered field is computed by truncating the scattered and internal field expansions and by using spherical and plane wave expansions for the free-space dyadic Green’s function. While the first expansion is valid outside a sphere enclosing the particle, the second one is valid outside the tangent planes bounding the particle from above and below. We demonstrate that in both cases, the results are the same, and thus, that the restrictive condition according to which the interface should not intersect the particle’s circumscribed sphere is not relevant. The image of the scattered field is computed by using the Debye diffraction integral and fast Fourier transform, while for a better reconstruction of the particle orientation, an image processing step consisting in a contour extraction and ellipse fitting is considered. The numerical simulations dealing with scattering by a prolate spheroid provide evidence of the remarkably sensitivity of the geometric parameters of the image ellipse to the particle orientation angles, as well as, of the integral response of the detector to the distance between the particle and the interface.

About the approximation of a field of an extended source by a sphere wave in the far illumination region

On the base of a coherent emitting straight segment, the problem of approximate description of the field of an extended source in the far illumination region is considered. It is shown that in regions close to the directions of intensity maximums the source field can be approximated by mean of sphere waves. The sphericity condition in corresponding region is found. The problem of approximation of an extended source field by means of a plane wave is also discusses. As a result of a next approximation of a spherical wave, the condition for the approximation of a field of extended source by means of a plane wave was found.

Multi-Directional Viscous Damping Absorbing Boundary in Numerical Simulation of Elastic Wave Dynamic Response

Numerical seismic wave field simulation is essential for studying the dynamic responses in semi-infinite space, and the absorbing boundary setting is critical for simulation accuracy. This study addresses spherical waves incident from the free boundary by applying dynamic equations and Rayleigh damping. A new multi-directional viscous damping absorbing boundary (MVDB) method is proposed based on regional attenuation. An approximate formula for the damping value is established, which can achieve absorbing the boundary setting by only solving the mass damping coefficients without increasing the absorbing region grid cells or depending on the spatial and temporal walking distance. The validity and stability of the proposed method are proven through numerical calculations with seismic sources incident from different angles. Meanwhile, the key parameters affecting the absorption of the MVDB are analyzed, and the best implementation scheme is provided. In order to meet the requirements of mediums with different elastic parameters for boundary absorption and ensure the high efficiency of numerical calculations, the damping amplitude control coefficients k can be set between 1.02 and 1.12, the thickness of the absorbing region L is set to 2–3 times of the wavelength of the incident transverse wave, and the thickness of the single absorbing layer is set to the size of the discrete mesh of the model Δl.

Efficient methods for iterative ultrasound image reconstruction using L1 and L2 norm regularization

Ultrasound image reconstruction can be posed as an inverse problem, with image pixels as parameters to a model of wave propagation that are estimated from raw ultrasound channel data. Such framework allows one to make assumptions about channel signals and image properties in form of regularization that can be used to improve reconstruction accuracy in the presence of electronic and acoustic noise. A simple model assumes spherical wave propagation from point sources in a homogeneous medium, similar to delay-and-sum (DAS) beamforming; solving such problems numerically can require many iterations and can result in blurred images when traditional L2 norm regularization is used. We use Fast Iterative Shrinkage Thersholding Algorithm (FISTA) to reduce the number of iterations to less than 10, and to apply L1-norm regularization to the data, which improves edge sharpness and image contrast. We demonstrate the concept using FIELD II simulated ultrasound signals from point, speckle, and anechoic targets with controlled levels of electronic and speckle noise. The FISTA-reconstructed point targets show reduced sidelobe levels by 15 dB compared to the traditional DAS image, and the reduction in full-width at half maximum by a factor of 2. We also implement iterative reconstruction in omega-k frequency domain, which allows factoring the forward and adjoint operators at each spatial frequency and paves the way for an intuitive and more memory efficient, multi-threaded implementation of the method.

Scattering by a biisotropic obstacle and the properties of the Beltrami spherical vector waves

In this paper, we take a fresh look at the determination of the transition matrix for a homogeneous, biisotropic particle employing the Null‐field approach. The condition for passivity of the material is discussed. In particular, we focus on some previously unproved properties of the Beltrami spherical vector waves, such as completeness, orthogonality, and linear independence, which are all instrumental in the analysis of the scattering problem with the Null‐field approach. Some numerical examples illustrate the approach.

Imploding Detonation Waves in Self-gravitating Ideal Gas

In the present paper, the propagation of strong spherical imploding detonation waves in a reacting ideal gas under the effect of self-gravitation of the non-homogeneous medium has been investigated, by the help of Chester-Chisnell-Whitham (CCW) theory. It is considered that detonation wave is initially Chapman-Jouguet. Initial taking the density distribution law as power decreasing with distance, the analytical expressions for the detonation velocity just behind the front along with other flow variables are derived. Neglecting the effect of overtaking disturbances the variation of non-dimensional detonation velocity, the pressure and density with the propagation distance have been calculated numerically. The effect of change in density parameter at different Alfven Mach number on the convergence of detonation front have been discussed through graphs in details. Finally, it is found that density parameter and Alfven Mach number of gas have a significant role on propagation of strong spherical detonation front in reacting ideal gas with gravitation effect on all the post-flow variables. The software MATLAB have been used for computation of the problem. Keywords: Self-gravitating gas, Strong detonation waves, CCW theory.

Study of phase objects by dynamical diffraction of a spherical X-ray wave in a crystal using a temperature gradient

The possibility of reconstructing the internal structure of a phase object by dynamical diffraction of a spherical X-ray wave in a crystal using a temperature gradient was investigated. It is shown that the use of a temperature gradient directed perpendicular to the crystal surface makes it possible to obtain a focal distribution of all point inhomogeneities in the phase object on the exit surface of the crystal. By moving the phase object along the direction of the diffraction vector and registering the entire map of obtained data, one can restore the additional phase of the wave and the internal structure of the phase object section.

Decay behavior and internal interactions of regularly reflected spherical blast waves

Blast wave reflection is a critical area in military and infrastructure defense, converging shock dynamics, and colliding blast waves. While irregular blast reflections have garnered remarkable attention, research on regularly reflected (RR) blast waves remains comparatively limited. This study presents a detailed literature on shortcomings of post-reflection quantities of RR blast waves and aims to bridge this gap by extensively analyzing RR behaviors of spherical blast waves against a planar surface in air via numerical methods. With 31 scenarios involving a 1 kg charge and scaled distances from 0.5 to 4.0 m/kg1/3, comprehensive field data on parameters including pressure, density, and velocity were gathered using a fan-like gauge array. A dedicated program for tracking the RR shock front was developed, enabling precise trajectory detection and detailed quantitative analyses of RR wave decay. First, accurate empirical trajectory equations for RR waves were formulated along its normal axis. Second, spatial decay analysis was conducted, revealing consistent decay rates for each RR field parameter under 1 m/kg1/3 and diminishing decay rates beyond this threshold. Third, parameter profiles preceding RR shock fronts at various post-reflection distances were examined, while discrepancies and complexities against generalized profiles were uncovered. Qualitatively, this study identified four internal interactions within the reflection phenomenon, categorized by scaled distance ranges, and elucidated the secondary wave's impact on RR wave propagation. The comprehensive quantitative and qualitative findings in this work offer profound insights into blast wave dynamics, addressing several gaps on RR blast wave behaviors and laying a foundation for understanding more complex blast reflection phenomena crucial in various domains.

Plane-fronted electromagnetic waves and an asymptotic limit of Liénard–Wiechert fields

Colliding or noncolliding plane-fronted electromagnetic or gravitational waves are the asymptotic limit of Robinson–Trautman spherical electromagnetic or gravitational waves. Noncolliding plane-fronted waves contain no information about their sources whereas colliding waves contain information about possibly the motion of their sources. As a first step to investigate the latter phenomenon, we construct an asymptotic limit of Liénard–Wiechert electromagnetic fields in the context of Minkowskian spacetime. This has the advantage that the source is well known and the calculations can be carried out in full detail. The final result is an algebraically general Maxwell field which consists of colliding plane-fronted waves in a subregion of Minkowskian spacetime and an interesting byproduct is a novel perspective on a Maxwell field originally discovered by Bateman.

Induced effects of a rigid boundary on a pulsating spherical source

This work develops a comprehensive analytical formalism to study the boundary-induced effects on a pulsating spherical radiating source near a rigid planar boundary in an inviscid fluid. Using the modal multipole expansion method, the image method and the translational addition theorem for spherical wave functions, exact closed-form expressions are derived for the dimensionless axial acoustic radiation force function as well as the radiation, amplification and extinction energy efficiency factors. The source-boundary distance and the dimensionless size parameter are especially addressed in the numerical simulations for spherical sources with different vibration modes. It is shown that the axial radiation force is positive or negative, depending on the choice of parameters. Moreover, cases when the extinction acoustic power completely vanishes are predicted theoretically for dipole and quadrupole vibrations, which can be used to achieve acoustic invisibility in acoustic cloaking devices and acoustic stealth technologies. Combination of more than one vibration modes is also investigated to better simulate the acoustic manipulation in practical applications. This work can help us understand the underlying mechanism in manipulating the active spherical radiating sources in a bounded field.

Treams – a T-matrix-based scattering code for nanophotonics

We report the publication of treams, a new software for electromagnetic scattering computations based on the T-matrix method. Besides conventional T-matrix calculations for individual scatterers and finite clusters of particles, a unique feature of the code is its full support for periodic boundaries in one, two, and all three spatial dimensions. We use highly efficient and quickly converging lattice summation techniques based on the Ewald method to evaluate the arising lattice sums in these cases. In addition to the common use of vector spherical waves as a basis set for the T-matrix, vector cylindrical waves are also implemented. To describe stratified media, vector plane waves are used with an S-matrix description of the electromagnetic scattering. All basis sets and the associated methods can be used together with chiral constitutive relations. Thereby, chiral embedding media are supported, as well as scatterers made from chiral materials.This contribution outlines the basic methods implemented and the program structure. Two interfaces to the implemented functionality are available: a flexible and fast low-level interface and a high-level interface for added convenience and plausibility checks. We conclude with two examples: a demonstration of the field calculation in various lattices and the explorations of quasi-bound states in the continuum. The presented code was already used in calculations for various physical systems: from the mode properties of molecular arrays in cavities to analytical models for metasurfaces and from moiré lattices to the homogenization of artificial photonic materials. With the publication of treams and the associated documentation, we hope to empower more scientists to make an efficient, fast, and precise exploration of nanophotonic systems that can be described in the broader framework of scattering theory. Program summaryProgram title: treamsCPC Library link to program files:https://doi.org/10.17632/2np8snmzfx.1Developer's repository link:https://github.com/tfp-photonics/treamsLicensing provisions: MITProgramming language: Python and CythonNature of problem: Simulating electromagnetic scattering in periodic nanophotonic structures, when different length scales are present or for large parameter sweeps, require specialized tools that can solve Maxwell's equations more efficiently than general-purpose solvers. A possible tool for these computations is the T-matrix method, which needs to be amended by suitable lattice summation schemes in the presence of periodic boundary conditions.Solution method: The properties of the individual scatterers are described by T-matrices, such that the interaction can be solved analytically. The slowly converging lattice sums that appear in the presence of periodic boundary conditions are computed by converting them to two quickly converging series using Ewald's method. Depending on the lattice dimensions and the geometry of the scatterers, vector spherical, cylindrical, or plane waves are used. Using modes of well-defined helicity enables the straightforward inclusion of chiral material parameters for scatterers and embedding media.

An acoustic investigation of the near-surface turbulence on Mars.

The Perseverance rover is carrying out an original acoustic experiment on Mars: the SuperCam microphone records the spherical acoustic waves generated by laser sparks at distances from 2 m to more than 8 m. These N-shaped acoustic waves scatter from the multiple local heterogeneities of the turbulent atmosphere. Therefore, large and random fluctuations of sound travel time and intensity develop as the waves cross the medium. The variances of the travel times and the scintillation index (normalized variance of the sound intensity) are studied within the mathematical formalism of the propagation of spherical acoustic waves through thermal turbulence to infer statistical properties of the Mars atmospheric temperature fluctuation field. The comparison with the theory is made by simplifying assumptions that do not include wind fluctuations and diffraction effects. Two Earth years (about one Martian year) of observations acquired during the maximum convective period (10:00-14:00 Mars local time) show a good agreement between the dataset and the formalism: the travel time variance diverges from the linear Chernov solution exactly where the density of occurrence of the first caustic reaches its maximum. Moreover, on average, waves travel faster than the mean speed of sound due to a fast path effect, which is also observed on Earth. To account for the distribution of turbulent eddies, several power spectra are tested and the best match to observation is obtained with a generalized von Karman spectrum with a shallower slope than the Kolmogorov cascade, ϕ(k)∝(1+k2L2)-4/3. It is associated with an outer scale of turbulence, L, of 11 cm at 2 m above the surface and a standard deviation of 6 K over 9 s for the temperature. These near-surface atmospheric properties are consistent with a weak to moderate wave scattering regime around noon with little saturation. Overall, this study presents an innovative and promising methodology to probe the near-surface atmospheric turbulence on Mars.

Room Impulse Response Reconstruction Using Pattern-Coupled Sparse Bayesian Learning With Spherical Waves

Room Impulse Response Reconstruction Using Pattern-Coupled Sparse Bayesian Learning With Spherical Waves

Fluctuations of polyspectra in spherical and Euclidean random wave models

Fluctuations of polyspectra in spherical and Euclidean random wave models