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The identification of unknown antennas and analysis of electromagnetic wave vulnerability are important for effective attacks and/or protection in high-power electromagnetics (HPEM). Using electromagnetic clues, antenna modeling becomes possible, and its electromagnetic properties can be analyzed by predicting area-wide radiation patterns. To model an antenna, an infinitesimal dipole modeling (IDM) technique, utilizing clues from sparse far-field patterns, was used in the present study. The IDM approach obtained the equivalent infinitesimal dipole (ID) for the antenna configuration current using Green’s function. The sparse far-field pattern was determined for a movement trajectory, using air reconnaissance. Random far-field data acquisition paths were considered cumulatively in the 1–10 range in this case. The approach also used external exposure information about the antenna, such as the operating frequency and size. For simulations and measurements, a ridged-horn antenna operating at 2.4 GHz was used. The overall radiation pattern reconstructed using the IDM approach was correlated at 0.78 when one path was considered in the simulations. As the considered paths were accumulated, the correlation tended to increase, with the correlation for ten paths exceeding 0.98. The estimated radiation pattern characteristics of antennas can be utilized for communication reception characteristics and/or electromagnetic wave vulnerability analysis. [ABSTRACT FROM AUTHOR]

Recently, many successes have been witnessed in the field of inverse scattering problems (ISPs) with deep learning schemes (DLSs). However, most of the studies focus on the spatial characteristics of interested targets, and little attentions are paid to the information from multiple incidences that can be treated as temporal information measured in a time series. In this work, a multiple-incidence framework (MIF) is introduced by incorporating the information from multiple incidences into an extra dimension of data space, helping to enrich physical knowledge in DLSs. A 3-D convolutional neural network (CNN) structure is further introduced to explore cross-frame information of the data space, which enables simultaneous utilizations of multiple-incidence information. The proposed MIF can be easily adapted into previous DLSs in the literatures, where two widely used DLSs including back-propagation scheme (BPS) and dominant current scheme (DCS) are used to demonstrate the advantages of the proposed framework. It is shown by extensive numerical and experimental examples that MIF enables consistent improvements for BPS and DCS. It is expected that the proposed MIF will also find its applications in real-time dynamic microwave imaging and multiple-frequency imaging by effectively using physical knowledge from temporal and frequency measurements, respectively. [ABSTRACT FROM AUTHOR]

Dynamic manipulation of the surface plasmon polariton (SPP) and wave steering is important in plasmonic applications. In this work, we excite a curved SPP in topological continua by applying a radial magnetic bias. We believe that it is a new technique to create a unidirectional SPP traveling along a curved trajectory. We also derive a Green’s function (GF) model for radially biased plasma, applicable to curved SPPs. We compare the properties of unidirectional curved SPPs with the usual case when an axial bias is applied. [ABSTRACT FROM AUTHOR]

A symmetry relation of the integral operators in a layered medium proved by the reciprocal theory can be applied to improve the accuracy of the magnetic-field integral equation (MFIE). Based on the symmetric layered medium Green’s function, the normal vector can be transferred into the inner integral to keep the field integral as the inner integral of the elements in the impedance matrix. When discretized by the divergence-conforming function, this field-extracted scheme shows better performance than the classic expression in accuracy. Meanwhile, this form of expression can be applied in the combined-field integral equation (CFIE). Several numerical results are provided to validate the formulation of the symmetry relations from the layered medium Green’s function to the impedance matrices and to reveal its advantages in enhancing the accuracy of the field-extracted form of MFIE. [ABSTRACT FROM AUTHOR]

In this work, we present a novel analytical model for the magnetic field in through-the-Earth (TTE) communications. The modeling approach is based on dyadic Green’s functions to compute impressed and scattered fields in a multilayered structure. Its performance is assessed through comparisons with previous models, measurements, and simulations of magnetic field. The great advantages of the proposed approach in relation to the previous ones are its flexibility in the positioning and direction of antennas and the unlimited number of layers of soil. Moreover, this approach can be more accurate than classical ones in scenarios where the soil has a high conductivity below the antenna in an uplink scenario. [ABSTRACT FROM AUTHOR]

We present a new approach to the study of the telegraph equation, which is based on analyzing the equation in phase space. We consider the phase space of time and frequency, as well as of position and spatial frequency (or wavenumber). We show that considerable simplification, both conceptual and mathematical, results from this approach. The basic reason why a phase space approach is fruitful is that when there is dispersion, the group velocity is not constant but changes with frequency, and therefore the wave changes as it propagates over space and time. Simple but effective and insightful phase space approximations to the solution of the telegraph equation are presented, with examples. [ABSTRACT FROM AUTHOR]

A surface field analytical solution of the impedance boundary condition circular cylinder canonical problem is contributed in the work at hand. The accurate representation of the primary ray contribution of the tangential surface magnetic field, of a tangential magnetic current excited relative electromagnetic structure, is given via series expansion in powers of the normalized surface impedance. Furthermore, each term in the series is represented as series of the inverse of the cylinder radius. This is achieved by approximating the Hankel functions by a uniform asymptotic expansion within the spectral integral representation of the relevant Green’s function. All the resulted integrals are evaluated analytically in an exact fashion, and thus, the final process entails only summations and differentiations. The attained formulas are valid both within and outside the paraxial region. Validity of the contributed analytical solution is provided by successful comparison with published results. [ABSTRACT FROM AUTHOR]

The late-time evaluation of electromagnetic (EM) field quantities yielded by convolution integrals that combine Green’s functions available at discrete time samples and strictly causal excitations is critically revisited. A typical situation is used for tracing the causes of the divergent late-time behavior that is often experienced. A framework combining a suitable integral partitioning with a polynomial approximation is shown to effectively guarantee the integrals’ convergence. The formulation is validated via numerical experiments evidencing its accuracy and computational efficacy. The method is amenable to be used in a wide range of problems requiring the late-time evaluation of convolution integrals of the indicated type. [ABSTRACT FROM AUTHOR]

An accelerated integral equations (IE) field solver for determining scattered fields from electrically large electromagnetic metasurfaces using fast multipole method (FMM) is proposed and demonstrated in 2-D. In the proposed method, practical general metasurfaces are expressed using an equivalent zero thickness sheet model described using surface susceptibilities, and where the total fields around it satisfy the generalized sheet transition conditions (GSTCs). While the standard IE-GSTC offers fast field computation compared with other numerical methods, it is still computationally demanding when solving electrically large problems, with a large number of unknowns. Here, we accelerate the IE-GSTC method using the FMM technique by dividing the current elements on the metasurface into near- and far-groups, where either the rigorous or approximated Green’s function is used, respectively, to reduce the computation time without losing solution accuracy. Using numerical examples, the speed improvement of the FMM IE-GSTC method { $O(N^{3/2})$ } over the standard IE-GSTC { $O(N^{3})$ } method is confirmed. Finally, the usefulness of FMM IE-GSTC is demonstrated by applying it to solve electromagnetic propagation inside an electrically large radio environment with strategically placed metasurfaces to improve signal coverage in blind areas, where a standard IE-GSTC solver would require prohibitively large computational resources and long simulation times. [ABSTRACT FROM AUTHOR]

We investigated how to construct low-order subspace basis sets to accurately represent electromagnetic (EM) fields generated within inhomogeneous arbitrary objects by radio frequency sources external to Huygen’s surface. The basis generation relies on the singular value decomposition of Green’s functions integrodifferential operators, which makes it feasible to derive a reduced-order yet stable model. We present a detailed study of the theoretical and numerical requisites for generating such basis and show how it can be used to calculate performance limits in magnetic resonance imaging applications. Finally, we propose a novel numerical framework for the computation of characteristic modes of arbitrary inhomogeneous objects. We validated accuracy and convergence properties of the numerical basis against a complete analytical basis in the case of a uniform spherical object. We showed that the discretization of Huygens’s surface has a minimal effect on the accuracy of the calculations, which mainly depends on the EM solver resolution and order of approximation. [ABSTRACT FROM AUTHOR]

We present a surface integral equation (SIE) solution for a special class of anisotropic media, whose permittivity and permeability are both symmetric full tensors with the same or multiple values. This kind of media is generated from the invisible cloaking or absorbing material of a perfectly matched layer (PML) design. A new derivation based on the potential functions is presented to obtain the closed-form Green’s function. Detailed and rigorous proofs of some vector identities are given for the first time. Special treatments are detailed to address the singularity of the anisotropic Green’s function for discretizing the SIE. Numerical experiments validate the accuracy, stability, and high efficiency of the proposed solution compared with the analytical solution or the finite element-boundary integral (FE-BI) method. [ABSTRACT FROM AUTHOR]

A plane-wave spectrum method is presented for the fast computation of radiation integrals for source and observation plates, which can be arbitrarily tilted and separated by an intermediate-to-far-field distance. The method expedites the direct and inverse transforms between spatial and spectral domains using unequally spaced fast Laplace transforms. These fast algorithms allow one to combine fast Fourier transforms (FFTs) and contour deformation in the complex plane with controllable accuracy and computation times close to that of a single 2-D FFT. Hence, scattering interactions between plates of sizes up to thousands of wavelengths can now be computed within seconds using current desktop computers. The fast method is validated here for the case of radio propagation in a canyon street modeled with electrically large facets using the physical optics approximation. [ABSTRACT FROM AUTHOR]

Modeling the electromagnetic response of carbon nanotube (CNT) reinforced composites is inherently a 3-D multiscale problem that is challenging to solve in real time for nondestructive evaluation (NDE) applications. This article presents a fast and accurate full-wave electromagnetic solver based on a multilayer dyadic Green’s function approach. In this approach, we account for the effects of the dielectric slab, where the CNTs are embedded, without explicitly discretizing its interfaces. Due to their large aspect ratios, the CNTs are modeled as arbitrary thin wires (ATWs), and the method-of-moment (MoM) formulation with distributed line impedance is used to solve for their coupled currents. The accuracy of the in-house solver is validated against the commercial MoM and the finite element method (FEM) solvers over a broad range of frequencies (from 1 GHz to 10 THz) and for a wide range of dielectric slab properties. Examples of 100 nm-long vertical and horizontal CNTs embedded in a 1 $\mu \text{m}$ -thick lossy dielectric substrate are presented. The in-house solver provides more than $50\times $ speed up while solving the vertical CNT and more than $570\times $ speed up while solving the horizontal CNT than a commercial MoM solver over the GHz-to-THz frequency range. [ABSTRACT FROM AUTHOR]

In this communication, a semianalytical solution for the computation of the 2-D Green’s function for a cylindrical perfect electric conducting (PEC) enclosure containing an arbitrary number of confocal elliptic dielectric layers is provided. The approach relies on an expansion of the Green’s function into Mathieu functions, whose coefficients are found in an efficient way through a recursive procedure. The effectiveness of the technique is evaluated by comparisons with analytical formulas and against the results provided by independent numerical solvers. Moreover, the applicability of the solution to forward scattering problems using integral formulations is also assessed. In all the considered cases, the developed approach has been found to provide accurate results. [ABSTRACT FROM AUTHOR]

The volume integral equation (VIE) that describes the forward scattering problem is generally solved by iterative methods, such as the conjugate gradient (CG) method. In this work, we unfold the CG method into an iterative deep neural network to accelerate solving the VIE. After the dielectric scatterer’s relative permittivity and the incident field are input into the network, the total field is trained to converge to the ground truth iteratively. In the neural network, Green’s function is taken as an explicit operator to describe wave physics, and the fast Fourier transform (FFT) is applied to accelerate the computation of volume integrations. The global influence of all points in the space is compressed into a layer by the volume integration. In numerical tests, we validate the accuracy, efficiency, and generalization ability of the proposed neural network, and investigate the feasibility of changing the input size and the frequency in the prediction. Results show that the network is scale-independent and adaptable to predict fields in a narrow frequency band. This work provides us a new perspective of incorporating both learned parameters and physics into numerical algorithms for fast computation, and has the potential of being applied in deep-learning-based inverse scattering problems. [ABSTRACT FROM AUTHOR]

A method of moments (MoM)-based procedure is developed to calculate the scattering from homogeneous dielectric bodies. The technique uses quadrilaterals for the approximation of geometry and piecewise sinusoidal (PS) basis functions for the approximation of surface currents. The notable advantage of the PS basis is its radiated fields can be expressed in closed-form. The proposed approach therefore circumvents the need to use Green’s function in formulating the integral equations. Combined with a simple testing procedure, the matrix filling time is reduced and the concern of singularity is removed. To further reduce the computational complexity and enhance the performance, a characteristic basis function method (CBFM) is implemented and embellished with a new characteristic basis function (CBF) generation strategy. Specifically, a cubical surface bounding the entire target is first specified and discretized. A set of auxiliary sources are then defined in a manner similar to that done for a scattering body. These auxiliary sources are defined once and shared by different blocks. In comparison to the traditional plane wave spectrum (PWS) method, the CBFs generated by the new approach are valid not only for plane wave excitations but also for localized excitations. Numerical results are provided to validate the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This work presents a full-wave Green’s function approach for the rigorous investigation of a probe-coupled dielectric resonator antenna (DRA) configuration with an imperfect inner conductor. The impedance boundary condition is applied over the imperfect conductor in the formulation to derive the fields inside and outside the dielectric region, considering all higher-order modes. The technique enhances the applicability of the full-wave Green’s function in the evaluation of input impedance and radiation characteristics for an antenna structure with imperfectly conducting spherical surface, which to the best of our knowledge has not been reported before in the DRA literature. The role of the surface impedance on the antenna resonance and quality factor is thoroughly characterized. A suitable choice of the surface reactance depending on the radius of the imperfect conductor and dielectric-coating thickness enables the simultaneous reduction in the resonant frequency and quality factor for the antenna configuration. The effect of the surface reactance with varying coating permittivities is also investigated. The parametric variations in the input impedance, reflection coefficient, and antenna bandwidth with change in the surface impedance and coating permittivity for the antenna configuration are analyzed. The radiation characteristics for the antenna configuration are also examined. [ABSTRACT FROM AUTHOR]

This article addresses the problem of efficiently and accurately evaluating the singular or near-singular double volume (6-D) reaction integrals fundamental to the solution of volume integral equations (VIEs) using the method of moments (MoM). VIE techniques based on the MoM are used to obtain accurate solutions for electromagnetic (EM) problems of all types, and the accurate computation of the singular and near-singular reaction integrals that occur in the resulting system matrices is crucial for accurate EM modeling. Here we propose a scheme to treat, as a whole, the 6-D reaction integrals appearing in the MoM. The divergence theorem is directly applied twice in the physical space domain, not a transformed domain, thus eliminating restrictions to well-shaped elements. With appropriate integration reordering, the 6-D volume integrals are expressed as two radial integrals followed by two surface integrals over source and observation domain boundaries. We further smooth the integral by removing the static form of the kernel and evaluating it separately using a semi-analytical approach. The method is numerically validated for static and dynamic kernels arising in the electric field VIEs (i.e., for kernels having $1/R$ singularities) and for linear basis functions. [ABSTRACT FROM AUTHOR]

Nearfield (NF) 3-D imaging provides an effective solution of objects’ radar cross section (RCS) within a compact range. This article proposes a precise RCS extrapolation via NF 3-D imaging with adaptive parameter optimization Bayesian learning (APOBL), i.e., first, in the process of NF 3-D imaging, objects’ scattering centers may vary with the observation angle, while it is hard for the existing Bayesian learning via presetting parameters to reach an optimal estimation. For this issue, we present a parameter self-adaption solution, improving precision, and stability. Second, we also apply a block-based optimization idea in Bayesian-learning-based 3-D imaging, ensuring NF 3-D imaging quality. Third, in the process of RCS extrapolation, we apply a weighted Green’s function operator into the 3-D imaging-based NF-to-far-field (NF–FF) compensation, further ensuring high precision. The simulation and experiment results verify that the proposed method has an advantage in precision over the existing 3-D imaging-based RCS extrapolation methods. [ABSTRACT FROM AUTHOR]

An efficient ping-pong algorithm is presented to deal with electromagnetic scattering from reflecting surface antennas such as the reconfigurable intelligent surfaces (RISs) of arbitrary geometric shapes. The proposed computational electromagnetics (CEM) algorithm does not require formation, storage, and inverse of the impedance matrix used by the method of moments (MoM). Instead, a rigorous formula is obtained for the computation of the surface current from the scattered electric field. Besides, the algorithm only contains convolution operations with the scalar Green’s function and second derivatives operations to iteratively update the surface currents and scattered electric field. Also, hypersingular integration arising from the singularities of the surface current and scattered electric field is properly regularized. Furthermore, the algorithm converges fast and satisfactory results are obtained after a few iterations, and it is about ten times as fast as the MoM. Besides, the first iteration gives the solution for reflecting surface antennas on substrates of perfect absorption. Numerical solutions are obtained for some typical antennas and comparisons are made to those in the literature and from the MoM. [ABSTRACT FROM AUTHOR]

In this work, we show that the near field of leaky-wave resonant antennas (LWAs) radiating into a dense medium can be locally represented as a spherical wave in a certain solid angle around broadside using an accurate definition of the phase center. The near field in this solid angle can be efficiently evaluated through the integration of the spectral Green’s function along the steepest descent path (SDP). Beyond this solid angle, defined as the shadow boundary angle, a residual contribution due to the leaky-wave pole must also be added to fully describe the near field. It is found that this shadow boundary angle can be used to define the phase center and geometry of a truncated lens that couples well to leaky-wave antennas, even in electrically small-to-medium sized lenses and low-contrast cases. To demonstrate the applicability of the proposed study, we combine the SDP field calculation with a Fourier optics (FO) methodology to evaluate the aperture efficiency and radiation patterns of small-to-medium sized lenses in reception. A truncated silicon lens with a diameter of only four free-space wavelengths is presented with almost 80% aperture efficiency. Excellent agreement with full-wave simulations is achieved, which demonstrates the accuracy of the proposed design and analysis methodology. [ABSTRACT FROM AUTHOR]

We present a study on beam coupling in radiating structures that support multiple simultaneous beams. The formation of multiple beams is relevant in modern wireless communication applications when diverse data streams can be sent from a single transmitter to users located in different directions. General expressions are provided that relate the coupling between radiated beams to the associated current distributions on the radiating aperture. When expanding the currents in terms of basis functions, the beam coupling can be also written in terms of coupling contributions due to each pair of basis functions. The analysis is applied to antenna arrays with different levels of mutual coupling between the array elements. More specifically, arrays of resonant elements, characterized by very low mutual coupling, are compared with arrays of connected elements, which are strongly coupled. We show that, even for a very high level of mutual coupling between individual array elements, it is possible to obtain orthogonal beams if the total current distributions associated with the beams are uncoupled. [ABSTRACT FROM AUTHOR]

Surface integral equation (SIE) methods are of great interest for the efficient electromagnetic modeling of various devices, from integrated circuits to antenna arrays. Existing acceleration algorithms for SIEs, such as the adaptive integral method (AIM), enable the fast approximation of interactions between well-separated mesh elements. Nearby interactions involve the singularity of the kernel, and must instead be computed accurately with direct integration at each frequency of interest, which can be computationally expensive. We propose a novel algorithm for reducing the cost-per-frequency of near-region computations for both homogeneous and layered background media. In the proposed extended AIM (AIMx), the SIE operators are decomposed into a frequency-independent term containing the singularity of the kernel, and a nonsingular frequency-dependent term. Direct integration is only required for the frequency-independent term and can be reused at each frequency, leading to significantly faster frequency sweeps. The frequency-dependent term is captured with good accuracy using fast Fourier transform (FFT)-based acceleration even in the near region, as confirmed with an error analysis. The accuracy and efficiency of the proposed method are demonstrated through numerical examples drawn from several applications, and CPU times are significantly reduced by factors ranging from 3 to 16. [ABSTRACT FROM AUTHOR]

In the solution of frequency- and time-domain integral equations, the singularity cancellation transformations are well-known for the treatments of the singular integrals involving Green’s functions and their gradients. The cancellation transformations for strongly near-singular integrals become inaccurate and inefficient for an extremely deformed triangular patch, and this phenomenon is referred to as shape-dependent problem in this article. As the degree of the singularity increases, the shape-dependent problem of strong near-singularity is more severe than that of the weakly near-singular integrals. Furthermore, if the source triangle is deformed, the accuracy of the cancellation methods decreases when no near singularity exists. In this work, we first investigate the reason for these problems via the theoretical analysis with numerical verification. Second, an updated framework of singularity cancellation methods for strongly near-singular integrals is proposed, which has a fast and consistent convergence rate for both regular and irregular triangles. Third, some numerical experiments are presented to illustrate the effectiveness of the theoretical framework and the proposed transformations. [ABSTRACT FROM AUTHOR]

Analog computing has emerged as a promising candidate for real-time and parallel continuous data processing. This article presents a reciprocal way for realizing asymmetric optical transfer functions (OTFs) in the reflection side of the on-axis processing channels. It is rigorously demonstrated that the presence of cross-polarization exciting normal polarizabilities (CPENPs) of a reciprocal metasurface circumvents the famous challenge of Green’s function approach in implementation of on-axis reflective optical signal processing while providing dual computing channels under orthogonal polarizations. Following a comprehensive theoretical discussion and as a proof of concept, an all-dielectric optical metasurface is elaborately designed to exhibit the desired surface polarizabilities, thereby reflecting the first derivative and extracting the edges of images impinging from the normal direction. The proposed study offers a flexible design method for on-axis metasurface-based optical signal processing and also dramatically facilitates the experimental setup required for ultrafast analog computation and image processing. [ABSTRACT FROM AUTHOR]

The current state-of-the-art error control of the multilevel fast multipole algorithm (MLFMA) is valid for any given error threshold at any frequency, but it requires a multiple-precision arithmetic framework to be implemented. In this work, we use asymptotic approximations and curve-fitting techniques to derive accurate closed-form expressions for the error control of MLFMA that can be implemented in common fixed-precision computers. Moreover, using the proposed closed-form expressions in conjunction with the state-of-the-art scheme, we report novel design curves for MLFMA that can be used to determine achievable error limits, as well as the minimum box sizes that can be solved with a given desired error threshold for a wide range of machine precision levels. [ABSTRACT FROM AUTHOR]

In this article, redefined antenna parameters regarding the additional effects occurring with on-body propagation are derived to enable a standardized characterization of on-body antennas. A model for the on-body propagation of arbitrary wearable and implantable antennas using Green’s functions based on the Norton surface wave theory and the surface equivalence principle is presented, which subsequently is used as an on-body near-field-to-far-field transformation. The defined on-body far-field enables the redefinition of the antenna parameters (gain, effective area, and efficiency) for the on-body case. Based thereon, the antennas can be deembedded from the on-body channel and the on-body link between two antennas can be calculated by an adapted Friis transmission equation similar to free-space propagation. It is demonstrated by two examples, one of a hearing aid antenna and another of an antenna of an implantable pacemaker, that the on-body antenna parameters allow for an educated design of the antennas without the necessity of electromagnetic modeling of the entire system. [ABSTRACT FROM AUTHOR]

Propagating plane-wave fast multipole translation operators (TLOPs) convert propagating plane-wave spectra radiated from a source region of finite extent into incident propagating plane-wave spectra at a distant observation region of finite extent. This translation is diagonal, and the received fields in the observation region are obtained by integration of the received plane-wave spectra. In its standard form, the TLOPs exhibit some directivity but with strong sidelobes and the integration needs to consider the entire spectra. Windowed and Gaussian-beam (GB) TLOPs with improved directivity and reduced sidelobes have been considered in order to reduce the integration effort. Both these techniques are investigated in this article, and it will be demonstrated that GB TLOPs are considerably more powerful. It is shown that GB TLOPs can be interpreted as windowed TLOPs, where a complex windowing function is multiplied with the Legendre polynomial series coefficients of the standard TLOPs. The sampling requirements of the GB TLOPs are investigated, and a numerical procedure is presented for an error-controlled determination of the imaginary shift involved in the computation of the GB TLOPs and their orders. Numerical results obtained with an inverse source solver for several antennas with aperture sizes of up to 1000 wavelengths are presented. [ABSTRACT FROM AUTHOR]

In this article, the previously introduced finite-integration technique/method-of-moments (FIT-MoM) hybrid method, which is suited for the analysis of electromagnetic scattering by inhomogeneous bodies of revolution (BoRs), is generalized to problems involving multilayered environment. Due to the fact that BoR-typical azimuthal mode decomposition is used, appropriate modal Green’s functions for multilayered media are given. They are responsible for source-field interactions within the region that is external with regard to the FIT part. Formulas for modal decomposition of incident plane wave fields as well as the approximation enabling computing fields produced by sources associated with individual modes in the far-zone are also provided. [ABSTRACT FROM AUTHOR]

A new model-based parameter estimation (MBPE) method for multilayer periodic EM surfaces is discussed in this article. By applying the proposed method to predict the generalized scattering matrix (GSM) of each unit layer section, the response of a composite structure can be determined by cascading GSMs while allowing the salient behavior of each section to be accurately captured. Based on the spectral properties of Green’s functions with high-order wavenumbers and chosen basis functions, an advanced interpolation model is developed to estimate the broadband response of periodic structures in a robust and efficient manner. It needs fewer samples in the interpolation compared to the state of the art, and no restriction for the sample selection is required. Numerical analysis has been carried out for two types of multilayer structures, and a good agreement between the conventional periodic method of moments (PMM) and the proposed method has been obtained. [ABSTRACT FROM AUTHOR]

In this article, a new inversion model for 2-D microwave imaging is introduced by means of a convenient rewriting of the usual Lippmann–Schwinger integral scattering equation. Such a model is derived by decomposing Green’s function and the corresponding internal radiation operator in two different contributions, one of them easily computed from the collected scattered data. In the case of lossless backgrounds, the resulting model turns out to be more convenient than the traditional one, as it exhibits a lower degree of nonlinearity with respect to parameters embedding the unknown dielectric characteristics. This interesting property suggests its exploitation in the solution of the inverse scattering problem. The achievable performance is tested by comparing the proposed model with the one based on the usual Lippman–Schwinger equation in both cases of linearly approximated and full nonlinear frameworks. Both numerical and experimental data are considered. [ABSTRACT FROM AUTHOR]

The repetitive computation of the forward problem in distorted Born iterative method (DBIM)-type inversion method is time-consuming and memory-costly, especially in dealing with 3-D inverse scattering problem. An improved subspace-regularized DBIM is proposed for the efficient solution of the 3-D inverse problem, which introduces the multilevel Green’s function interpolation method (MLGFIM) to accelerate the computation of the forward problem. In order to stabilize the inversion, an improved subspace-regularized DBIM is used with one new subspace-regularized induced current term in the cost function in virtue of truncated singular value decomposition (TSVD). To further reduce the computation burden, the incident field induced with updated inhomogeneous background medium is used approximately as the total field in the cost function, which saves one forward solver calculation in each iteration. Besides, the resource-intensive multiplication of inhomogeneous Green’s function can be avoided, which further improves the efficiency. Three numerical and two Fresnel experimental examples are given to demonstrate both the efficiency of the forward solver and the accuracy of the inversion algorithm. [ABSTRACT FROM AUTHOR]

A coupled-field volume integral equation (CFVIE) method for electromagnetic (EM) scattering on electrically large, highly inhomogeneous gyrotropic circular cylinders, under normal incidence, is developed in this work. The CFVIEs are solved by the cylindrical Dini series expansion (CDSE) method where the unknown fields are expanded by entire domain orthogonal vectorial basis functions. The main advantage of the present method is that it permits the scatterer to have continuously varying highly inhomogeneous gyrotropic characteristics, i.e., the constitutive parameters of the cylinder can be highly inhomogeneous in both gyroelectric and gyromagnetic tensors. Initially, the 2-D Green’s function (GF) is expanded in a tensorial form using the cylindrical vector wave functions (CVWFs). Then, by employing the CDSE for the unknown fields, the 2-D volumetric integrals are carried out analytically, reducing the CFVIEs to a set of algebraic equations. The method is validated by comparisons with the exact solution based on the separation of variables method (SVM) for homogeneous gyroelectric/gyromagnetic cylinders, with HFSS commercial software for three-layered gyroelectric cylinders, as well as with the recently developed hybrid projection method (HPM) for electrically large continuously varying highly inhomogeneous isotropic cylinders. Results for combined gyroelectric-continuously varying highly inhomogeneous isotropic cylinders are presented and discussed. [ABSTRACT FROM AUTHOR]

A fast back-projection (FBP) imaging algorithm is proposed to generate 3-D uniformly balanced images of an object embedded in a layered structure based on a combined near-field monostatic and bistatic synthetic aperture radar (SAR) system. The spectral layered Green’s function is used in the FBP algorithm. Like conventional real-time imaging algorithms, the complexity of the imaging function is reduced via the stationary phase method, and the fast Fourier transform is implemented to accelerate the computation. Unlike conventional real-time imaging algorithms, the singularity problem associated with Green’s function and antenna pattern is solved in this proposed algorithm by using a point spread function (PSF). For a real-time imaging system, besides fast image generation, an efficient data acquisition is needed. A combined monostatic and bistatic SAR configuration is used here to decrease the data collection time. The performance of this proposed FBP method is demonstrated by measurements of a stratified environment. [ABSTRACT FROM AUTHOR]

This article proposes a learning-based noniterative method to solve electromagnetic (EM) scattering problems utilizing pix2pix, a popular generative adversarial network (GAN). Instead of calculating induced currents directly from a matrix inversion, a forward-induced current learning method (FICLM) is introduced to calculate the induced current through a neural-network mapping. The scattered fields can be further calculated through a multiplication of the Green’s function with the predicted induced currents. Inspired by wave physics of scattering problems, we have designed three kinds of input schemes, covering different combinations of the given incident field and permittivity contrast, to evaluate the performance of the FICLM model under both single-incidence and multi-incidence cases. Numerical results prove that the proposed FICLM outperforms the method of moments (MoM) in terms of both computational speed and accuracy by use of reference data with a higher precision. The FICLM with the direct sum of permittivity contrast and a so-called Born-type induced current, achieves the best calculation accuracy and generalization capability compared to the other two inputs. The comparison with other types of neural networks, such as U-net, also demonstrates the superior performance of FICLM for dealing with complex scatterers due to the use of adversarial framework in pix2pix. The proposed method paves a new way for the fast solution of EM-scattering problems through deep learning techniques. [ABSTRACT FROM AUTHOR]

Integral equation (IE) is regarded as an efficient method for 3-D modeling of electromagnetic (EM) responses. The main contribution of this article is to develop a contraction integral equation (CIE) algorithm with a high performance for modeling of EM scattering by 3-D bodies buried in multilayered anisotropic medium. The introducing of contraction operator can ensure that the discretized IE will be iteratively convergent in large conductivity contrast between abnormal bodies and background medium. Moreover, the contraction operator can also accelerate the iteration convergence of the IE. During the discretization process of CIE, direct waves are extracted from dyadic Green’s functions (DGFs) of multilayered medium, and the singular integrals of direct waves are eliminated using equivalent sphere and ellipsoid methods. By splitting DGF into convolution terms and correlation terms, 3-D FFT can be used to accelerate the product evaluation of DGFs integral and scattering current encountered in each iteration. Validity of the proposed CIE is verified by comparing with the existing finite volume method. Modeling results show that the conventional IE will be iteratively divergent when the conductivity contrast between bodies and background is large, but the CIE is always iteratively convergent even under very large conductivity contrast. [ABSTRACT FROM AUTHOR]

To accurately simulate the electromagnetic (EM) scattering from an electrically large and complex object above a rough surface, we propose a new scattering model that can effectively capture the EM scattering phenomenon including the coupling between the object, the rough surface, and the infinite environment. Specifically, the proposed scattering model consists of the object and a representative of the underlying rough surface residing in a half-space environment. To make the model consistent with the real scenario and the simulation fast yet with reasonable accuracy, we apply the hybrid shooting and bouncing rays-physical optics (SBR-PO) method to model the interaction between the object and its representative underlying rough surface, and the far-field half-space dyadic Green’s functions to account for the effect of an infinite half-space environment. Compared with existing scattering models, this new scattering model can emulate the interaction between the object and the infinite half-space environment more accurately. In addition, graphics processing units (GPUs) are used to accelerate the intensive computations of the prediction process. The numerical results obtained validate the proposed method and its implementation in terms of accuracy, truncation stability, and runtime performance. [ABSTRACT FROM AUTHOR]

Magnetic induction tomography is a novel imaging method with promising biomedical applications. The image reconstruction problem suffers from a high computation cost because of its inherent nonlinearity. Current state-of-the-art numerical methods are based on the finite element method (FEM). To avoid artifacts at the boundaries, this method requires the discretization of a volume much larger than the actual volume of interest. A numerical model based on volume integrals only requires the discretization of the volume of interest, which greatly reduces the number of unknowns. Fewer unknowns generally imply a lower computation cost. However, a naive implementation of the volume integral equation does not yield a lower computation cost due to the bad conditioning arising from the high dielectric property values of biological tissues at low frequencies. To tackle this problem, a model based on inhomogeneous Green’s function is proposed. The forward model is validated with the Mie scattering theory. Through the resolution of the inverse problem, it is found that the reconstruction limits compare well with current state-of-the-art methods. By reducing the number of unknowns and maintaining a similar computational complexity, the proposed model offers a computation cost reduction when compared with the FEM. [ABSTRACT FROM AUTHOR]

In this contribution, a broadband $G$ -band leaky-wave (LW) fed lens antenna with an integrated dielectric grid polarizer is presented. The proposed wideband polarizer unit cell geometry enables its fabrication at frequencies higher than 100 GHz, presenting high transmission properties and low axial ratio (AR). A quasi-analytic technique based on multilayer spectral Green’s function combined with a numerical Floquet modes’ solver is used to optimize the lens aperture efficiency and AR. The proposed technique is validated via full-wave (FW) simulations. A design is proposed in low dielectric permittivity material, achieving FW simulated aperture efficiency higher than 75% over 44% relative bandwidth, and an AR lower than 3 dB over 35% relative bandwidth. The antenna is able to achieve multiple directive circularly polarized (CP) beams when fed by a focal plane array, preserving the AR bandwidth. A prototype has been fabricated and measured, exhibiting an excellent agreement with quasi-analytic and FW simulations. [ABSTRACT FROM AUTHOR]

Spectral properties of line sources carrying electric or magnetic current placed in a planarly layered medium are analyzed. It is shown that when the current along the line varies in the longitudinal direction by an exponential function with a complex exponent, classical Sommerfeld radiation condition that ensures outgoing and decaying fields simultaneously cannot always be used. Instead, depending on the exponent and the material properties of the layered medium, outgoing and exponentially increasing or incoming and exponentially decreasing waves are generated. This property is not observed when the exponent is real where the classical Sommerfeld radiation condition is fulfilled. In this article, an in-depth analysis of layered media is first performed in spectral domain as a function of the longitudinal dependence of the line sources. Then, the fields generated by the line sources are obtained by Sommerfeld integrations using two different radiation conditions separately. The effect of the radiation condition on the fields are discussed both in the spectral and spatial domains. In addition, field patterns are compared with the results obtained by finite element method (FEM) combined with perfectly matched layers (PMLs) and several guidelines for increasing the efficiency of simulations by FEM are introduced. [ABSTRACT FROM AUTHOR]

Electromagnetic metasurfaces are structured surfaces consisting of a thin array of subwavelength elements with engineered scattering properties, thus providing a promising means of holographic display by controlling the field distributions. However, the existing metasurface holography has limited capabilities in achieving 3-D fields with simultaneous features of high spatial resolution and energy efficiency due to the design methods. In this work, we present a transmissive metasurface to achieve polarization-dependent field distributions in 3-D space with both high resolution and efficiency. In the design, a new method that utilizes dyadic Green’s function (DGF) as the rigorous propagator is used. Using the method, the sources and fields are linked directly and can be located on arbitrary 3-D points with the intermediate spaces being equal or unequal. The design is successfully validated by full-wave simulations and experimental measurements. The broadband simulation results indicate that the design has a bandwidth of 0.8 GHz. This work demonstrates a feasible and simple route of field synthesis for real-world applications that require high resolution, high efficiency, and 3-D scenarios. [ABSTRACT FROM AUTHOR]

We present a multifilament current method (MFCM) incorporated with generalized sheet transition condition (GSTC) to simulate 2-D cylindrical metasurfaces with arbitrary cross sections. The GSTC casts in the form of an impedance-type boundary condition to relate the tangential fields on two sides of a cylindrical metasurface. The MFCM is subsequently introduced and formulated by employing the GSTC. The doublet-current unit, including both electric and magnetic filamentary sources, is introduced in order to capture both co- and cross-polarized scattered and transmitted fields from the GSTC characterized cylindrical metasurfaces. Three illustrative examples are presented to validate the proposed simulation technique. The behaviors of filamentary sources in terms of scattered field singularities and the ill-conditioning issue of the constructed matrix are also discussed in detail. In comparison to existing numerical methods, the proposed technique has its merits on simplicity and conciseness. [ABSTRACT FROM AUTHOR]

The classical physical optics (PO) formulation of the scattered fields suffers from the loss of accuracy when the observation angle widely deviates from the specular direction. This is even worse in the “forward region,” i.e., for the bistatic angles between 90° and 270°. The method presented in this article aims at improving the accuracy of the fields in this region by finding the currents induced on the nonilluminated part of the object, where the classical PO assumes zero currents. The proposed approach reformulates the initial problem using equivalent currents over a domain surrounding the object. The equivalent currents then act as new sources that induce electrical currents computed by the classical PO formulation. The computation of the equivalent problem is accelerated using the multipole expansion of Green’s function, including appropriate singularity extraction in the very near field. This approach provides an error that is significantly lower in the forward direction than the classical PO formulation. The principles of this new approach are presented and validated for the 2-D scenarios. [ABSTRACT FROM AUTHOR]

The increasingly popular characteristic mode analysis (CMA) techniques in the free-space have been well-established, while the half-space counterpart is less concerned. In this communication, we consider the CMA for half-space platforms such as vehicles on the ground and ships on the sea surface, which is also commonly mounted with antennas. To overcome the difficulty of CMA’s application on electrically large targets, the half-space multilevel fast multipole algorithm is integrated into the eigensolver. Numerical results of half-space CMA for realistic platforms from FM-band to ${L}$ -band are presented to validate the accuracy and the robustness of the proposed method. It has been shown that this communication can be used as a legitimate CMA tool for the antenna design and integration on half-space platforms. [ABSTRACT FROM AUTHOR]

In this two-part article, we study the ultrawideband beam-based schemes for tomographic inverse scattering. The theory utilizes discrete phase-space sets of beam waves, which constitute overcomplete frames everywhere in the propagation domain, and thus can be considered as a local alternative to the conventional plane-wave or Green’s function integrals used in conventional diffraction tomography. Specifically, we formulate two inversion schemes, a multi-frequency domain scheme, and a time domain scheme. The former utilizes isodiffracting Gaussian beams, while the latter utilizes isodiffracting pulsed beams. Both schemes consist of two phases: In the preprocessing phase, the scattering data are expanded as a sum of beams whose amplitudes, referred to as the “beam-domain data,” are extracted from the data using local beam-based transforms. In the imaging phase, the beam data are backpropagated and used for local reconstruction. In this Part I we discuss the preprocessing phase. We define the beam-based transforms, and then use the Born approximation to establish a cogent physical interpretation of the beam-domain data. Specifically, we show that these data are related to the local Radon transform of the medium, which is interpreted physically as a local Snell’s law. This relation will be used in Part II to reconstruct the medium. [ABSTRACT FROM AUTHOR]

The physics and modes of radiation in structures exhibiting extraordinary transmission (ET) can be best studied using Green’s function formalism. In this article, we find the electromagnetic response to local excitation of a canonical structure exhibiting ET, and investigate the role of complex waves. The structure is a perfectly conducting slab having a finite or infinite number of through-slits. The solution breaks up the field into even and odd modes, and solves for the fields of the structure with a finite number of slits, by setting up an integral equation. The solution is then extended to find Greens’ function of the infinitely periodic structure. The dispersion relations of the complex modes are found, and existence of proper complex modes is shown around ET frequencies. It is shown that these proper complex modes play an important role in determining the far-field and emergence of ET. [ABSTRACT FROM AUTHOR]

The $Q$ -factor for lossless 3-D structures with 2-D periodicity is here derived in terms of the electric current density. The derivation in itself is shape-independent and based on the periodic free-space Green’s function. The expression for $Q$ -factor takes into account the exact shape of a periodic element and permits beam steering. Both the stored energies and the radiated power, required to evaluate $Q$ -factor, are coordinate-independent and expressed in a similar manner to the periodic electric field integral equation and can thus be rapidly calculated. Numerical investigations, performed for several antenna arrays, indicate fine agreement, accurate enough to be predictive, between the proposed $Q$ -factor and the tuned fractional bandwidth, when the arrays are not too wideband (i.e., when $Q\geq 5$). For completeness, the input-impedance $Q$ -factor, proposed by Yaghjian and Best in 2005, is included and agrees well numerically with the derived $Q$ -factor expression. The main advantage of the proposed representation is its explicit connection to the current density, which allows the $Q$ -factor to give bandwidth estimates based on the shape and current of the array element. [ABSTRACT FROM AUTHOR]

An efficient and accurate spectral-element spectral-integral method is developed for rigorously modeling arbitrary inhomogeneous objects with doubly periodicity embedded in a layered medium background. It is an improvement over the traditional finite-element boundary-integral (BI) method. In the proposed approach, the domain decomposition between the interior spectral-element domain and the outer surface BI domain enables the BI domain to be solved by a far more efficient spectral integral method using a uniform mesh; without any loss of generality, it leaves the interior spectral-element domain with flexibility to model any inhomogeneous objects. For the BI domain, with a uniform mesh and rooftop basis functions, we can exploit the Toeplitz structure of the BI matrices with the fast Fourier transform algorithm and apply the Calderón preconditioner to achieve a high iteration convergence rate that will not slow down as the problem gets larger. With the periodic layered medium Green’s functions, the layers without objects can be treated as background and the discretization is avoided. We show that this method is very promising for large-scale problems, because the CPU time and memory required with respect to the number of unknowns grow slowly. We validate this method with a commercial finite element solver and show its ability by solving a large-scale optical lithography problem. [ABSTRACT FROM AUTHOR]

This communication describes a full-wave modal analysis of plane-wave scattering by periodic arrays of penetrable conducting bars with strip covers on both the lower and upper surfaces of each ridge to create iris-type slits across groove apertures, which altogether is sandwiched by multiple dielectric layers on both sides of the gratings. The approach entails the moment method using parallel-plate waveguide cavity Green’s functions and a numerical spectral-domain Green’s function for planar stratified media accompanied by the Floquet theorem. Computed results obtained from codes written based on this formulation are validated with those simulated by a commercial full-wave software solver as well as results from the literature. Validation is performed in terms of reflection and transmission spectra as well as modal dispersion. The new parameters arising from the special complex geometry herein studied provide the means to enhance the performances of various applications such as beam deflectors, mode converters, and grating couplers, as well as the resolution of diffraction gratings in the context of spectroscopy. Measurement results acquired from experimentations carried out on a manufactured grating that corroborate well with theoretical predictions are also presented. [ABSTRACT FROM AUTHOR]

Unidirectional surface plasmon polaritons (SPPs) at the interface between a gyrotropic medium and a simple medium are studied in a newly recognized frequency regime wherein the SPPs form narrow, beam-like patterns due to quasi-hyperbolic dispersion. The SPP beams are steerable by controlling parameters such as the cyclotron frequency (external magnetic bias) or the frequency of operation. The bulk band structure along different propagation directions is examined to ascertain a common bulk bandgap, valid for all propagation directions, which the SPPs cross. In addition, group velocity and Poynting vector for the SPPs are presented. The case of a finite-thickness gyrotropic slab is also considered, for which we present the Green function and examine the thickness and loss level required to maintain a unidirectional SPP. [ABSTRACT FROM AUTHOR]