Computational Electromagnetic Methods Research Articles

Numerical framework for modeling quantum electromagnetic systems involving finite-sized lossy dielectric objects in free space

The modified Langevin noise formalism [A. Drezet, Phys. Rev. A 95, 023831 (2017); O. D. Stefano, S. Savasta, and R. Girlanda, J. Mod. Opt. 48, 67 (2001)] has been proposed for the correct characterization of quantum electromagnetic fields in the presence of finite-size lossy dielectric objects in free space. The main modification to the original one [T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996); H. T. Dung, L. Kn\"oll, and D.-G. Welsch, Phys. Rev. A 57, 3931 (1998)] (also known as the Green's function approach for a bulk inhomogeneous lossy dielectric medium) was to introduce another fluctuating source in reaction to the radiation loss. Consequently, the resulting electric field operator is now determined by (i) boundary-assisted and (ii) medium-assisted fields on an equal footing, which originate from radiation and medium losses, respectively. However, due to the lengthy mathematical manipulation and complicated concepts, the validity of the modified Langevin noise formalism has not been clearly confirmed yet. In this work, we propose and develop a numerical framework for the modified Langevin noise formalism by exploiting computational electromagnetic methods. Specifically, we present utilization of the finite-element method to numerically solve plane-wave-scattering and point-source-radiation problems whose solutions are boundary-assisted and medium-assisted fields, respectively. We numerically validated the modified Langevin noise model calculating the Purcell factor of a two-level atom inside or outside a lossy dielectric slab. The proposed numerical framework is particularly useful for analyzing the dynamics of multilevel atoms near plasmonic structures or metasurfaces in the open space.

A Numerical Mode Matching (NMM) Method for Optical Fibers With Kerr Nonlinearity

Recently, the reshaping of the transverse light field profile in nonlinear multimode fibers (MMFs) has attracted great attentions. However, the electromagnetic (EM) fields in such nonlinear media cannot be easily and accurately calculated by using the traditional computational electromagnetics methods due to the nonlinearity of Kerr optical materials in graded-index (GRIN) MMFs. The iterative division method based on the 2.5-D spectral element numerical mode matching (SNMM) method is developed to address this problem. The SNMM method is a semi-analytical method, which can effectively reduce the computational costs to obtain highly accurate solutions. Starting from the numerical results of SNMM, the iterative division method solves electromagnetic fields of the linear-to-nonlinear transition process together iteratively. In this work, several improvements are proposed to extend the SNMM for Kerr optical nonlinear MMFs. The governing equations with anisotropic permittivity with Kerr optical nonlinear media are established in the cylindrical coordinate system. The absorbing boundary condition (ABC) is introduced to replace the perfectly matched layer (PML) so that the eigenmodes of a waveguide can be obtained accurately. Numerical results show the validity, accuracy and advantages of the proposed method in simulated MMFs.

Light attenuation analysis based on integral equations

The shadowing and masking of a rough surface is an important problem for reflection models in computer graphics. The widely used Smith’s geometry attenuation factor (GAF) takes a few factors such as root-mean-square (rms) into account and makes too many assumptions. In our research, we construct a brand-new calculation technique for issues involving light attenuation on a rough surface. The GAF algorithm is derived from a scattering field based on integral equations and the computational electromagnetic method. Specifically, our use of the method of moments has enabled us to tackle the problem of analytically computing the shadowing and masking on a rough surface by taking practical factors such as wavelength, surface contour, polarization, material, rms, and so on into consideration. It is more precise than Smith’s GAF theory.

Diffractive optical element design based on vector diffraction theory and improved PSO-SA algorithm

The existence of the beam vector effect requires rigorous electromagnetic computational methods for the optimization of subwavelength diffractive optical elements (DOEs). To design DOEs with high performance, we proposed an optimization strategy combining a global optimization algorithm with the finite difference time domain (FDTD) method. First, scalar initial solutions are obtained by the Gerchberg–Saxton algorithm. Then, regarding the diffraction efficiency, the uniformity error and figure of merit are calculated by FDTD as evaluation functions, and the optimization of the initial solutions is implemented by improved particle swarm optimization and continues with the simulated annealing algorithm. After several numerical simulations, the analysis results confirm the robustness of the algorithm and the reduction of the computational cost. The experimental data demonstrate that the correlation of diffraction energy orders between the simulated design and fabricated sample are above 85%. This method efficiently improves the DOEs design.

Research on the computational method of creeping waves diffraction of arbitrary complex target based on the planar mesh model.

For a long time, due to the difficulty of obtaining accurate propagation trajectories, the research on creeping waves is limited to canonical geometries or simple targets, which leads to the situation that it is relatively mature in theoretical research on creeping waves, while the practical application scope of creeping waves for complex targets is narrow. In this paper, a thorough electromagnetic computation method for creeping waves on complex planar mesh model is systematically proposed. This approach broadens the field of creeping waves applications due to the generality of planar mesh models in electromagnetic engineering. The contents consist of the tracing of creeping waves, the calculation of the diffraction field, and the coupling effect with other scattering mechanisms. Aiming at the trajectory of creeping waves, we propose a set of tracing algorithms that enable rapid, real-time tracing based on analytical geometry and related computer graphics algorithms. Utilizing information such as vertices, triangles, and topological relations in the mesh model, one can recover the mathematical properties of the surfaces of the model and then, the corresponding parameters can be obtained. Therefore, the uniform geometrical theory of diffraction (UTD) can be used to accurately calculate the diffraction field. Moreover, for complex targets, the multiple coupling effect caused by creeping waves is the main source of radar echoes in many cases, which is not unimportant. Hence based on the electromagnetic accurate modeling, the coupling mechanism of creeping waves and various scattering mechanisms are studied. The research content is expected to have high application values in target recognition and characteristics.

Modeling Terahertz Properties of Vanadium Dioxide by Ab Initio Computational Scheme and its Experimental Verification

A complete simulation scheme is established to model the terahertz (THz) properties of vanadium dioxide (${\mathrm{VO}}_{2}$) from ab initio to computational electromagnetic method. For the monoclinic insulating phase of ${\mathrm{VO}}_{2}$, dielectric properties are computed by Hubbard-corrected density functional perturbation theory. Meanwhile, the electron-phonon interactions are studied to model the electronic transport properties of the tetragonal metallic phase of ${\mathrm{VO}}_{2}$. In order to build a bridge from the microscopic effects of first-principles calculations to the macroscopic THz properties, the Drude model and effective medium theory are applied to model the dispersion properties of the material. To validate the proposed model, a ${\mathrm{VO}}_{2}$ film grown on a sapphire substrate is fabricated and measured by a terahertz time-domain spectroscopy system. The measurement results have excellent agreements with the proposed simulations. Further, a ${\mathrm{VO}}_{2}$-based THz metamaterial modulator is simulated by using the proposed model, in great agreement with the reported measurement result. Our ab initio computational scheme improves the simulation accuracy of design, which provides a solid THz modeling approach to the ${\mathrm{VO}}_{2}$ and other insulator-metal transition metal oxides.

Analysis of the Shielding Effectiveness of Thin Wire Cages by a Hybrid DGTD-FDTD Method

Thin wire simulation is a typical multiscale problem in time-domain computational electromagnetic methods. This article addresses the shielding effectiveness of thin wire cages, and such models can be attributed to complex thin wire structures with multiwire junctions. The discontinuous Galerkin time-domain method for Maxwell's equations is used in our study, and the one-dimensional finite-difference time-domain method is used to construct the iterative scheme for the thin wire. The thin wire is expressed by the modified telegrapher's equations proposed by Holland. In this article, the mesh size is determined by the wavelength of the electromagnetic wave to be analyzed without considering the radius of the thin wire. There is no physical presence of thin wires in our model, and thin wires are expressed by current elements. The proposed method supports the simulation of arbitrarily oriented thin wires, and the proposed method can easily handle complex wire structures. The calculation efficiency can be greatly improved after avoiding multiscale modeling.

Snow Parameters Inversion from Passive Microwave Remote Sensing Measurements by Deep Convolutional Neural Networks.

This paper proposes a novel inverse method based on the deep convolutional neural network (ConvNet) to extract snow’s layer thickness and temperature via passive microwave remote sensing (PMRS). The proposed ConvNet is trained using simulated data obtained through conventional computational electromagnetic methods. Compared with the traditional inverse method, the trained ConvNet can predict the result with higher accuracy. Besides, the proposed method has a strong tolerance for noise. The proposed ConvNet composes three pairs of convolutional and activation layers with one additional fully connected layer to realize regression, i.e., the inversion of snow parameters. The feasibility of the proposed method in learning the inversion of snow parameters is validated by numerical examples. The inversion results indicate that the correlation coefficient () ratio between the proposed ConvNet and conventional methods reaches 4.8, while the ratio for the root mean square error (RMSE) is only 0.18. Hence, the proposed method experiments with a novel path to improve the inversion of passive microwave remote sensing through deep learning approaches.

Computational Electromagnetics for Industrial Applications

Nowadays, computational electromagnetics (CEMs) methods play an important role in the rapid modeling and design of electromagnetic (EM) systems and their industrial applications [...]

Effects of Plant Crown Shape on Microwave Backscattering Coefficients of Vegetation Canopy.

A microwave scattering model is a powerful tool for determining relationships between vegetation parameters and backscattering characteristics. The crown shape of the vegetation canopy is an important parameter in forestry and affects the microwave scattering modeling results. However, there are few numerical models or methods to describe the relationships between crown shapes and backscattering features. Using the Modified Tor Vergata Model (MTVM), a microwave scattering model based on the Matrix Doubling Algorithm (MDA), we quantitatively characterized the effects of crown shape on the microwave backscattering coefficients of the vegetation canopy. FEKO was also used as a computational electromagnetic method to make a complement and comparison with MTVM. In a preliminary experiment, the backscattering coefficients of two ideal vegetation canopies with four representative crown shapes (cylinder, cone, inverted cone and ellipsoid) were simulated: MTVM simulations were performed for the L (1.2 GHz), C (5.3 GHz) and X (9.6 GHz) bands in fully polarimetric mode, and FEKO simulations were carried out for the C (5.3 GHz) band at VV and VH polarization. The simulation results show that, for specific input parameters, the mean relative differences in backscattering coefficients due to variations in crown shape are as high as 127%, which demonstrates that the crown shape has a non-negligible influence on microwave backscattering coefficients of the vegetation canopy. In turn, this also suggests that investigation on effects of plant crown shape on microwave backscattering coefficients may have the potential to improve the accuracy of vegetation microwave scattering models, especially in canopies where volume scattering is the predominant mechanism.

Mode analysis of plasmonic waveguides in planarly layered media

Spectral properties of the modes supported by plasmonic waveguides in planarly layered media are studied by the method of Multiple MultiPoles (MMP). It is shown that the most important entities in the mode analysis are the wavenumbers of the upper and lowermost layers and the wavenumbers of the guided waves supported by the layered medium. These wavenumbers introduce branch points and associated branch cuts on the complex plane where the out-of-plane wavenumbers of the modes are searched. These branch points and associated cuts make the mode analysis in layered media more demanding than the mode analysis in homogeneous media, where there is only one branch point and associated branch cut related to the wavenumber of the homogeneous medium. Several numerical examples are given to address the differences introduced by the layered media in the mode analysis and guidelines that can be used in any well-known computational electromagnetics method are provided.

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Diagonalization of the Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode decomposition

We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably/finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode-decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as non-local dispersion cancellation of an entangled photon pair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter.

CEM methods in R.F and microwave engineering in the context of parameters that influence the outcome of modeling

The starting point toward modeling of a given electromagnetic (EM) problem is to know the modeling constraints/features of different modeling tools, and hence figure out if they are compatible to meet the intended objectives. In the face of popularity of some modeling tools, due to either marketing strategy or researcher bias, and compounded by lack of empirical data toward bench marking different methods for comparison, an intuitive choice will compromise accuracy, speed and efficiency. In this paper, an attempt is made to present the commonly used computational electromagnetic (CEM) methods in the context of basic parameters and their limiting values that influence the modeling outcome. A prospective researcher can make a checklist of these parameters and customize them fit into the given EM problem. This facilitates the selecting of an optimal method from the many that are available. This is important to mitigate the problem of computation cost that creep in the design/synthesis emanating from wrong choice of the modeling tool, and also, in the perspective of research and development, the life cycle is reduced that add to the economic viability of the modeled prototype. For an entry-level researcher, some level of proficiency in the CEM methods and EM simulators based on these methods enhance the prospect of employment in radio-frequency and microwave industry/research.

Efficient ray-tracing procedure for radio wave propagation modeling using homogeneous geometric algebra

ABSTRACT Ray-tracing is an efficient asymptotic computational electromagnetic method for studying wave propagation. The major bottleneck of ray-tracing algorithms is the computational complexity of the geometric-processing steps. There is a clear need for designing efficient ray-tracing algorithms and implementations in computational electromagnetics applications. We use Geometric algebra for the formulation of the pre-processing of electromagnetic ray tracing. Geometric algebra provides unified mathematical representations of geometric primitives and transformations. Various kinds of geometric algebras are currently used in many practical applications. We develop a unified 2D/3D ray-tracing procedure based on the homogeneous geometric algebra. The procedure is implemented using generative programming for optimizing code compilation. Results show that combining the powerful mathematical modeling capabilities of geometric algebra with efficient automatic code generation resulted in better performance of the ray-tracing implementation compared to typical approaches.

A Posteriori Error Estimation and Adaptive Discretization Refinement Using Adjoint Methods in CEM: A Study With a 1-D Higher Order FEM Scattering Example

This study investigates and evaluates applications of the adjoint problem and its solution in frequency-domain computational electromagnetics (CEM). The study establishes and validates adjoint-based applications including higher order parameter sampling, a posteriori error estimate evaluation, and $p$ - and $h$ -refinements. These applications can improve the efficiency, automation, and robustness of CEM methods. We employ a 1-D finite-element-method scattering solver, simplifying the implementation, replicability, clarity, and intuitiveness of analysis results and conclusions, which then extend naturally to higher dimensional solvers and more complicated CEM problems. While demonstrated with a higher order solver, the derived techniques apply to low-order methodology as well. This is the first demonstration of the applicability of adjoint-based a posteriori error estimation techniques to adaptive discretization refinement in frequency-domain CEM with arbitrary-order basis functions. This work introduces the application of dual-weighted residual error estimation and selective adaptivity based on error cancellation. The proposed targeted, adaptive mesh/model $p$ - and/or $h$ -refinement heuristics informed by adjoint element-wise error contribution estimates show near-monotonic reduction of the quantity-of-interest error with increased numbers of refined elements. In general, adjoint techniques are underutilized in CEM, and another goal of this work is to promote their future use for refinement, optimization, and uncertainty quantification.

Estudio de modelos circuitales de metamateriales bidimensiones de banda prohibida electromagnética basados en la celda de Yang

Los metamateriales en las bandas de frecuencias de microondas han sido ampliamente explorados en el diseño de antenas y arreglos de antenas. En este trabajo se ha estudiado la celda de Yang, que cuando es dispuesta periódicamente sobre un plano, conforma una estructura metamaterial que presenta bandas prohibidas de frecuencia más bajas que otras estructuras, con una mayor eficiencia en el uso del espacio. Se han estudiado los campos eléctricos y magnéticos en los primeros dos modos de propagación electromagnética de esta celda unitaria. Se han construido cuatro modelos circuitales equivalentes de la celda unitaria para poder obtener la respuesta en función de la frecuencia de la estructura metamaterial de forma rápida, que se encuentran explicados en el trabajo. Los modelos fueron validados por simulación numérica electromagnética de onda completa.

Rye Canyon Radar Cross-Section Measurements of Benchmark Almond Targets [EM Programmer's Notebook

A measurement campaign was conducted at a compact radar range to provide radar cross-section (RCS) data that can serve as a reference for validation, verification, and benchmarking of computational electromagnetics methods. The facility, measurement setup, target construction, measuring instruments, data acquisition, and postprocessing steps are detailed, and sources of measurement uncertainty are identified. To quantify this uncertainty and increase confidence in the measured data, two sets of measurement results using scaled targets are compared to each other and to computational results.

Are you using the right tools in computational electromagnetics?

Have you ever wondered why we use certain computational electromagnetics methods and how we decide on the choice of tools for modeling problems in electromagnetics? Though true for any field, particularly in electrodynamics, there is a gap between current practitioners' knowledge and knowhow about different tools and the state‐of‐the‐art developments. Rapid advancements made in material science and (nano)‐fabrication techniques are demanding new tools with multiscale and multiphysics capabilities. In this article, we cover the recent developments and highlight capabilities and limitations of different electromagnetic modeling tools. One has to answer a series of questions about modeling constraints and objectives before picking the appropriate tool. We aim to clarify some of the misconceptions, discuss limits and capabilities of some of the popular electromagnetic modeling tools, and provide a few practical tips, so that applied physicists and engineers can make informed decisions while choosing appropriate tools for their applications.

A Fast Numerical Method for the Galvanic Measurement in Hydraulic Fracture Detection

Hydraulic fracturing is critical for unconventional oil and gas production. Recently, galvanic methods, including borehole-to-surface and surface-to-borehole electromagnetic methods, have been applied in hydraulic fracture evaluation. However, conventional computational electromagnetic methods require huge computational cost to simulate the common galvanic fracture model, which consists of a long cased borehole, 3-D thin fractures, and an underground stratified medium. More seriously, modeling both vertical and horizontal energized cased boreholes in layered media is exceptionally difficult. In this article, we present a hybrid numerical mode matching method with stabilized bi-conjugate gradient fast Fourier transform method (NMM-BCGS-FFT) as the forward solver to efficiently model 3-D fractures in the galvanic survey. Both vertical and horizontal energized cased boreholes are modeled in the forward solver. The numerical results show the accuracy and efficiency of the hybrid forward solver. The realistic field galvanic detection model analysis will show the practicability of the forward solver.