Dyadic Green Research Articles

An efficient method of moments for analysis of electromagnetic scattering from a multilayered arbitrary‐shape anisotropic dielectric object

AbstractThis paper introduces an efficient method of moments (MoM) designed to explore electromagnetic scattering in multilayered anisotropic structures. Each layer is made up of a dielectric anisotropic material characterised by a generalised tensor for permittivity, which is unrestricted in its geometrical configuration. The authors’ approach analyses each layer independently, employing the surface equivalence theorem to substitute the interfaces between layers with suitable equivalent electric and magnetic surface current densities. The authors derive the necessary surface integral equations (SIEs) for each interface by implementing the proper boundary conditions. The analysis utilises rotated dyadic Green's functions that populate the infinite space with the material properties specific to each anisotropic layer. The rotation angle corresponds to the deviation between the local principal coordinate system of the material and the global coordinate system, which is determined by diagonalising the full dielectric tensor of the respective anisotropic material given in the global coordinate system. To address the SIEs for determining the unknown equivalent electric and magnetic surface current densities, Galerkin's MoM is applied. This involves expanding the unknown surface currents using suitable basis functions, simplifying the issue to a matrix equation solved through the inversion of a block‐tridiagonal impedance matrix. The diagonal nature and sparse structure of the impedance matrix, along with an effective block‐inversion method, significantly boost computational efficiency and reduce memory demands. To demonstrate the feasibility of the proposed method, the authors present a detailed derivation of the impedance matrix for the case of non‐magnetic uniaxial anisotropic media for which the Green's functions are available in closed form. The validity and efficiency of the proposed SIE‐MoM scheme are demonstrated by comparing the results of several case studies against those found in literature and results obtained via commercial numerical codes.

Strong dipole-dipole interactions via enhanced light-matter coupling in composite nanofiber waveguides

We study the interaction of emitters with a composite waveguide formed from two parallel optical nanofibers in regimes of experimental importance for atomic gases or solid-state emitters. Using the exact dyadic Green's function we comprehensively investigate the coupling efficiency and the fiber-induced Lamb shift accounting for variations in emitter positions and fiber configurations. This reveals coupling efficiencies and Purcell factors that are enhanced considerably beyond those using a single fiber waveguide, and robustness in the figures of merit. We finally investigate resonant dipole-dipole interactions and the generation of entanglement between two emitters mediated through the composite waveguide under excitation. We show that the concurrence can be enhanced for two fiber systems, such that entanglement may be present even in cases where it is zero for a single fiber. All-fiber systems are simple in construction and benefit from a wealth of existing telecommunications technologies, while enjoying strong couplings to emitters and offering interesting light-matter functionalities specific to slot waveguides. Published by the American Physical Society 2024

Breast tumor detection with TR‐DORT based on multilayered Green's function theory

AbstractUltrawideband (UWB) time‐reversal techniques are widely used in microwave imaging systems to detect and localize breast tumors. Measuring the scattering electromagnetic fields from a breast phantom can be time‐reversed and back‐propagated to refocus on a tumor. In this study, a Debye model was applied to the breast phantom. Using the decomposition of the time‐reversal operator (TR‐DORT), images were obtained in the UWB frequency range of 3.1–10.6 GHz. The conventional TR imaging method employs the free‐space Green's function to refocus on the tumor, which degrades refocusing in a lossy and dispersive breast phantom. We propose the use of the cylindrical dyadic Green's function in a three‐layer medium for TR imaging. The excitation system consists of a circular array of spiral antennas. The imaging results of the proposed Green's function in TR‐DORT were subsequently calculated, indicating successful tumor detection in different application scenarios of the lossy and dispersive breast phantom.

A rigorous theory on electromagnetic diffraction by a planar aperture in a perfectly conducting screen

In this paper, we revisit the classic problem of diffraction of electromagnetic waves by an aperture in a perfectly conducting plane. We formulate the diffraction problem using a boundary integral equation that is defined on the aperture using Dyadic Green’s function. This integral equation turns out to align with the one derived by Bethe using fictitious magnetic charges and currents. We then investigate the boundary integral equation using a saddle point formulation and establish the well-posedness of the boundary integral equation, including the existence and uniqueness of the solution in an appropriately defined Sobolev space.

Investigation of super-resolution in microsphere-assisted microscopy with the Poynting vector of the dipole model.

In this paper, the Fourier spectrum of an image in microsphere-assisted microscopy (MAM) and the wavenumber decomposition of the Poynting vector of the dipole model are compared for the first time to study the super-resolution performance within several wavelengths in MAM. Firstly, an experiment using microsphere-assisted microscopy is performed, and the fast Fourier transformation (FFT) spectra of the images along the distance are studied. Then the Poynting vector in the point dipole field is theoretically investigated based on the spectral decomposition of dyadic Green's function. Our study finds that the result of decomposition of the Poynting vector corresponds with the propagation results of components with different transverse wavenumbers kρ in an experiment. Even when kρ reaches 1.7k0, the waves can still arrive outside one wavelength. Our work is the first effort (to our knowledge) to associate the Fourier spectrum and the decomposition of the Poynting vector together, and it may contribute to the quantitative exploration of super-resolution performance in MAM in the future.

A Complete Nonuniform Asymptotic Expansion of the Dyadic Green’s Function for Dielectric Half-Space

A Complete Nonuniform Asymptotic Expansion of the Dyadic Green’s Function for Dielectric Half-Space

Dipole-dipole interactions in the presence of a topological insulator stratified sphere: dyadic Green’s function method

Dyadic Green’s functions (DGFs) are developed for calculating electric fields induced by multiple sources in the presence of a topological insulator (TI) stratified sphere within the framework of axion electrodynamics. Generalizing our previous work, these sources can be placed at arbitrary locations rather than be limited outside the TI stratified sphere. Utilizing these DGFs, we explore the topological magneto-electric (TME) effect of the dipole–dipole interaction in the presence of composite structures of an alternating metal-TI stratified sphere, causing some modifications of the energy transfer (ET) enhancement spectrum. Furthermore, for the multipolar resonances of the metal shells, we find the TME-induced red-shifts of each bonding and antibonding mode in the ET enhancement spectrum are independent on the locations and orientations of the two dipoles but only depend on the configuration of these composite structures. These phenomenological findings provide some useful guidance with experimenters to design realistic experiments for exploring possible unique TME signatures via the energy transfer between molecules near/in TI multicoated nanoparticles in the near-infrared region.

Complete Uniform Asymptotic Expansion of Finite-Range Integral Representation of Dyadic Green’s Function for Ordinary Dielectric Half-Space

Complete Uniform Asymptotic Expansion of Finite-Range Integral Representation of Dyadic Green’s Function for Ordinary Dielectric Half-Space

Electron-assisted probing of polaritonic light-matter states.

Thanks to their exceptional spatial, spectral and temporal resolution, highly-coherent free-electron beams have emerged as powerful probes for material excitations, enabling their characterization even in the quantum regime. Here, we investigate strong light-matter coupling through monochromatic and modulated electron wavepackets. In particular, we consider an archetypal target, comprising a nanophotonic cavity next to a single two-level emitter. We propose a model Hamiltonian describing the coherent interaction between the passing electron beam and the hybrid photonic-excitonic target, which is constructed using macroscopic quantum electrodynamics and fully parameterized in terms of the electromagnetic dyadic Green's function. Using this framework, we first describe electron-energy-loss and cathodoluminescence spectroscopies, and photon-induced near-field electron emission microscopy. Finally, we show the power of modulated electrons beams as quantum tools for the manipulation of polaritonic targets presenting a complex energy landscape of excitations.

Closed-Form Dyadic Green’s Functions for Dipole Excitation of Planar Periodic Structures

Closed-Form Dyadic Green’s Functions for Dipole Excitation of Planar Periodic Structures

Dual-band higher-order topological states and four-wave mixing in plasmonic valley-Hall metasurfaces

Higher-order topological states in plasmonic metasurfaces are of great importance in practice for their tight confinements and high field enhancements, providing many promising nonlinear applications such as robust quantum light source through four-wave mixing (FWM). However, previous works are limited to single-band modes and FWM processes based on second-order topological corner states have still not been revealed. In this work, we propose a plasmonic valley-Hall topological metasurface, which is modelled based on coupled dipole approximation with dyadic Green's functions containing retarded long-range interaction terms. Simultaneous lifting of Dirac degeneracies in two bandgaps due to inversion-symmetry breaking results in dual-band second-order topological states, which are robust against structural disorder. We present a theoretical approach for considering the nonlinear interaction in dipole arrays and numerically show nonlinear generation of corner mode at signal frequency via the FWM process by pumping with edge modes. The results presented in this work will pave a broad way towards the wide applications of topological plasmonic metasurfaces.

A new microwave nondestructive testing method of relative permittivity and conductivity for stratified media based on dyadic Green's function I: Theory

Stratified composite materials are employed in many industrial scenes, including bridge construction, vehicle, ship, aviation, etc. However, minor imperfections in composite materials can have significant effects and even result in disasters when used. In this work, a multi-parameter inversion method that can simultaneously reconstruct the conductivity and permittivity parameters of layered media is devised and presented for microwave nondestructive testing (NDT) of the minor imperfections in stratified composite materials. Firstly, the calculations for the electric field in the layered medium model with the emission source as the point source are provided. Secondly, the spatial electric field variations (the Fréchet derivative) caused by changes in conductivity and permittivity of arbitrary layers are calculated. Then the permittivity and conductivity are reconstructed using the Distorted Born iterative method (DBIM) technique. The numerical examples at microwave frequencies show that the inversion technique has a strong capacity to reconstruct for a single parameter (relative permittivity or conductivity) and multi-parameter (relative permittivity and conductivity). Our suggested multi-parameter inversion technique in this research has excellent potential for use in the identification of multilayer composites and subsurface inclusions.

Non-local generative machine learning-based inverse design for scattering properties.

Metamaterials are created by arranging small scatterers in a regular array throughout a space to manipulate electromagnetic waves. However, current design methods view metasurfaces as independent meta-atoms, which limits the range of geometrical structures and materials used, and prevents the generation of arbitrary electric field distributions. To address this issue, we propose an inverse design method based on generative adversarial networks (GANs), which includes both a forward model and an inverse algorithm. The forward model utilizes dyadic Green's function to interpret the expression of non-local response, realizing the mapping from scattering properties to generated electric fields. The inverse algorithm innovatively transforms the scattering properties and electric fields into images and generates datasets with methods in computer vision (CV), proposing an architecture of GAN with ResBlock to achieve the design for the target electric field pattern. Our algorithm improves upon traditional methods, as it achieves greater time efficiency and generates higher quality electric fields. From a metamaterial perspective, our method can find optimal scattering properties for specific generated electric fields. Training results and extensive experiments demonstrate the algorithm's validity.

Dyadic Green’s function for a topological insulator stratified sphere

We construct the dyadic Green’s functions (DGFs) for a topological insulator (TI) stratified sphere within the framework of axion electrodynamics. For these DGFs, the additional expansion coefficients are included to account for the axion coupling effect. With the application of these DGFs, we derive the formulation of light scattering from a dipole near a TI stratified sphere. In our numerical studies, we give three types of configurations (a metal-coated TI sphere, a metal-TI-metal-coated TI sphere and an alternating metal-TI stratified sphere) to investigate how the topological magneto-electric (TME) response of the TI sphere (shells) influences on the multipolar plasmonic resonance of the metal shells. For these types, the results show that the TME effect causes some modifications of the decay rate spectrum for an emitting dipole near a TI stratified sphere. For the multipolar resonances of the metal shells, it is observed that the TME-induced red-shifts for the bonding and lower order antibonding modes are found but those for the higher order antibonding modes are insignificant. In addition, for a metal-coated TI sphere, we take into account the effects of losses in the TI core of which the dielectric function is chosen to be the form of the bulk or five quintuple layers (5QL) slab and then the some modifications of the TME-induced decay rate spectrum are obviously suppressed. These phenomenological characteristics provide useful guidance to probing the TME effect via molecular fluorescence experiments.

Predicting Statistical Wave Physics in Complex Enclosures: A Stochastic Dyadic Green's Function Approach

This article presents a physics-oriented, mathematically tractable, statistical wave model for analyzing the wave physics of high-frequency reverberation in complex cavity environments. The key ingredient is a vector dyadic stochastic Green's function (SGF) method that is derived from the Wigner's random matrix theory and Berry's random wave hypothesis. The SGF statistically replicates multipath, ray-chaotic communication between vector sources and vectorial electromagnetic fields at displaced observation points using generic, macroscopic parameters of the cavity environment. The work establishes a physics-based modeling and simulation capability that predicts the probabilistic behavior of backdoor coupling to complex electronic enclosures. Experimental results are supplied to validate the proposed work.

A Low-Frequency Approximation PEEC Model for Thin-Wire Grounding Systems in Half-Space

This paper presents a PEEC model of thin-wire structures for lightning grounding analysis based on low-frequency approximation of dyadic Green's functions. To avoid the time-consuming numerical Sommerfeld integrals, the primary and quasi-dynamic terms are extracted from the spectral-domain Green's function and used as the low-frequency approximation closed-form of the full-wave solution, which is appropriate in the near-field region. The corresponding equivalent circuit is constructed with this closed-form approximated Green's function and the formulas for the partial inductance and coefficient of potential is given. Comparison in terms of the Green's function and circuit parameters between the proposed method and the conventional modified-image method is made. The validity of the proposed method is confirmed with experimental results gathered from published literature and MOM-calculated results from other researchers. A systematic parametric analysis is conducted to evaluate the accuracy and applicability of the different approximate models, which clearly shows the superiority of the proposed method over the traditional modified-image method.

Examination of the effect of cell thickness on the performance of a tandem nano-gap thermophotovoltaic system

In this paper, a study about the influence of cell thickness on the performance of a tandem thermophotovoltaic (TPV) system is performed in the near-field thermal radiation regime. This system includes an emitter made up of tungsten and two TPV cells made up of Si and GaSb, respectively. The fluctuational electrodynamics accompanied by the dyadic Green's function are applied in order to calculate the near-field thermal radiation heat flux. The generated photocurrent and the conversion efficiency are computed by solving the charge transport equations. By examination of the effect of TPV cell thicknesses on the performance of both cells, the optimum thicknesses are obtained. Furthermore, it is observed that variation of the n- or p-region thicknesses of the TPV cells also affect the performance of the system. In this regard, the best thickness for n- and p-regions of the first and second cells is also calculated.

Performance investigation of tandem nano-gap thermophotovoltaic system considering the near-field thermal radiation

In this paper, a near-field thermophotovoltaic (TPV) system with a dual TPV cell design is considered and studied numerically. The fluctuational electrodynamics accompanied by the dyadic Green's function are utilized for calculating the radiation heat flux. The generated photocurrent and the conversion efficiency are obtained by solving the photon-coupled charge transport equations. It was discovered that the addition of the second TPV cell to the system, increases the generated photocurrent of the system due to the absorption of the low-energy photons and generation of the electron-hole pairs. By increasing the gap size between the emitter and Si TPV cell from 50 nm to 1 μm, the generated photocurrent decreases because of the reduction of the near-field thermal radiation effects. Finally, the tandem nano-gap TPV system shows higher conversion efficiency compared with the single Si TPV cell for different values of the vacuum gaps, and the gap size of d1 = 200 nm is the optimum gap size due to the improvement of the conversion efficiency of the system.

Efficient Millimeter-Wave Imaging Algorithm for Layered Dielectrics Based on MIMO-SAR With Nonuniform Transmitting Array

In this letter, an efficient near-field millimeter-wave (MMW) imaging algorithm is presented for layered dielectrics based on multiple-input–multiple-output synthetic aperture radar (MIMO-SAR) with nonuniform transmitting array. First, the model of target echo under MIMO-SAR configuration is built by dyadic Green's function, and the precise spectral echo expression is obtained through fast Fourier transform (FFT) and spherical-wave decomposition. Then, the image reconstruction of sparse MIMO-SAR is divided into separate single-input–multiple-output (SIMO)-SAR imaging problems, and the target's subimage corresponding to different SIMO-SAR setup can be quickly solved by employing inverse FFT, multistep phase compensation and wavenumber integration. Finally, the fully focused MIMO-SAR reconstructed image will be obtained by coherently accumulating all the SIMO-SAR results. Simulation analysis and experimental results validate the effectiveness the proposed algorithm.

Fast and Accurate Transient Analysis of Thin-Wire Structure in Half-Space With PEEC Method

This article presents an efficient full-wave partial element equivalent circuit (PEEC) method of thin-wire structure in half-space for lightning transient analysis. In the framework of the PEEC formulation for thin-wire conductors, the partial elements are computed by double-folded line integrals. In layered media, the interaction integrals involve dyadic Green's functions, which contain a closed-form part and a Sommerfeld-integral part. The direct numerical computation of these integrals is very challenging and time-consuming, which hinders the practical application of the full-wave method. However, the efficient and accurate evaluation of partial elements has not been investigated in a comprehensive way so far. Accordingly, this article presents an efficient method for the evaluation of the partial elements between elementary segments in half space. The main novelty is that the interaction integrals are computed through a combination of the Taylor series expansion of the full-wave free space Green's function and the Sommerfeld-integral adaptive interpolation technique, which significantly reduces the computation time. The new method is systematically validated on examples from finite-difference time-domain (FDTD) method and method of moments and experimental results. The proposed method is validated with the NEC code in the frequency domain and the FDTD in the time domain.