Electromagnetic Propagation Problems Research Articles

A Boundary Integral Method for 3-D Nonuniform Dielectric Waveguide Problems via the Windowed Green Function

This communication proposes an efficient boundary-integral-based “windowed Green function” (WGF) methodology for the numerical solution of 3-D general electromagnetic problems containing dielectric waveguides. The approach, which generalizes a recently introduced 2-D version of the method, provides a highly effective solver for such problems. In particular, using an auxiliary integral representation, the proposed method is able to accurately model incident mode excitation. On the basis of a smooth window function, the integral operators along the infinite waveguide boundaries are smoothly truncated, resulting in errors that decay faster than any negative power of the window size.

Numerical Treatment for Electromagnetic Wave in Time-Variant Medium Using Generalized PITD Method

In this letter, the propagation of an electromagnetic (EM) wave in a time-variant medium is treated with a novel methodology stemming from the precise integration time domain (PITD) method. This methodology is a generalized version of the conventional PITD method (thus GPITD, for short). In the GPITD method, the electric displacement and the magnetic induction serve as the iteratively calculated components. In order to overcome the difficulty in implementing the precise integration (PI) routine caused by the time variation of the original coefficient matrix, an effective piecewise constant coefficient matrix is constructed. Both the numerical dispersion relation and the numerical stability condition of the GPITD method are described. Successful application of the GPITD method to solve the EM propagation problem associated with a layer whose permittivity suffers: 1) an abrupt change to a new value and 2) a sinusoidal modulation, confirms its effectiveness.

Automated netlist generation for 3D electrothermal and electromagnetic field problems

We present a method for the automatic generation of netlists describing general three-dimensional electrothermal and electromagnetic field problems. Using a pair of structured orthogonal grids as spatial discretisation, a one-to-one correspondence between grid objects and circuit elements is obtained by employing the finite integration technique. The resulting circuit can then be solved with any standard available circuit simulator, circumventing the need for the implementation of a custom time integrator and dealing with non-linearities. Additionally, the approach straightforwardly allows for field-circuit coupling simulations by appropriately stamping the circuit description of lumped devices. As the computational domain in wave propagation problems must be finite, stamps representing absorbing boundary conditions are developed as well. Representative numerical examples are used to verify the approach. The results obtained by circuit simulation on the generated netlists are compared with appropriate reference solutions.

Improved Cylindrical HIE-FDTD Method and Its Application to a Metal Disk-Type Surface Wave Splitter

The cylindrical hybrid implicit–explicit finite-difference time-domain method, in which the implicit scheme is adopted only in the circumferential direction, is improved in order to treat general electromagnetic problems. The connection of the field in a specific plane gives the problem with a cyclic matrix, the solution of which is performed with the Sherman–Morrison formula. The convolutional perfectly matched layer is also introduced in cylindrical coordinates. The present method is used to analyze a metal disk-type surface wave splitter. The computational time is reduced to less than 20% of the explicit method, yielding almost the same numerical results. Calculated radiation patterns are compared with experimental results.

On atmospheric humidity and acoustic ducts

The development of various propagation ducting phenomena (elevated or surface) has been studied extensively for electromagnetic and electro-optical wave propagation. The influence of changes in temperature, pressure, and humidity gradients on the strength and geometry of the duct in the electromagnetic propagation problem is well-documented, and there is substantial literature regarding the influence of temperature gradient on atmospheric acoustic propagation. Analytical results indicate that moisture gradients in warm air above a sea surface contribute meaningfully to the refraction of sound. This work uses numerical simulation to explore the atmospheric conditions that would support development of acoustic ducts or wave guide conditions during moderate range (<1 km) acoustic propagation. The aim of this overall effort is an improved numerical model of acoustic refraction and attenuation over moderate to long distances above a sea surface that accounts for sea state as well as boundary layer wind, temperature, and humidity profiles.

A new Laguerre‐based discontinuous Galerkin time‐domain method

AbstractIn this article, a Laguerre‐based discontinuous Galerkin time‐domain (DGTD) method using a new temporal basis function has been developed to solve transient electromagnetic problems. The new temporal basis function is a linear combination of weighted Laguerre polynomials, and can be easily implemented by adding some extra terms in the conventional Laguerre‐based DGTD method. With the proposed temporal basis function, initial condition of a general electromagnetic problem can be implicitly satisfied, and thus the resultant computational accuracy can be improved. Numerical results including a parallel‐plate waveguide, a dual‐mode circular waveguide filter, and a conducting ship demonstrate good performance of the proposed method.

Time-filtered leapfrog integration of Maxwell equations using unstaggered temporal grids

A finite-difference time-domain method for integration of Maxwell equations is presented. The computational algorithm is based on the leapfrog time stepping scheme with unstaggered temporal grids. It uses a fourth-order implicit time filter that reduces computational modes and fourth-order finite difference approximations for spatial derivatives. The method can be applied within both staggered and collocated spatial grids. It has the advantage of allowing explicit treatment of terms involving electric current density and application of selective numerical smoothing which can be used to smooth out errors generated by finite differencing. In addition, the method does not require iteration of the electric constitutive relation in nonlinear electromagnetic propagation problems. The numerical method is shown to be effective and stable when employed within Perfectly Matched Layers (PML). Stability analysis demonstrates that the proposed method is effective in stabilizing and controlling numerical instabilities of computational modes arising in wave propagation problems with physical damping and artificial smoothing terms while maintaining higher accuracy for the physical modes. Comparison of simulation results obtained from the proposed method and those computed by the classical time filtered leapfrog, where Maxwell equations are integrated for a lossy medium, within PML regions and for Kerr-nonlinear media show that the proposed method is robust and accurate. The performance of the computational algorithm is also verified by analyzing parametric four wave mixing in an optical nonlinear Kerr medium. The algorithm is found to accurately predict frequencies and amplitudes of nonlinearly converted waves under realistic conditions proposed in the literature.

Fractional-Calculus-Based FDTD Algorithm for Ultrawideband Electromagnetic Characterization of Arbitrary Dispersive Dielectric Materials

A novel finite-difference time-domain algorithm for modeling ultrawideband electromagnetic pulse propagation in arbitrary multirelaxed dispersive media is presented. The proposed scheme is based on a general, yet computationally efficient, series representation of the fractional derivative operators associated with the permittivity functions describing the frequency dispersion properties of a given dielectric material. Dedicated uniaxial perfectly matched layer boundary conditions are derived and implemented in combination with the basic time-marching scheme. Moreover, a total field/scattered field formulation is adopted in order to analyze the material response under plane-wave excitation. Compared with alternative numerical methodologies available in the scientific literature, the proposed technique features a significantly enhanced accuracy in the solution of complex electromagnetic propagation problems involving higher order dispersive dielectrics, such as the ones typically encountered in geoscience and bioengineering applications.

Fast and accurate finite element analysis of large-scale three-dimensional photonic devices with a robust domain decomposition method

A fast and accurate full-wave technique based on the dual-primal finite element tearing and interconnecting method and the second-order transmission condition is presented for large-scale three-dimensional photonic device simulations. The technique decomposes a general three-dimensional electromagnetic problem into smaller subdomain problems so that parallel computing can be performed on distributed-memory computer clusters to reduce the simulation time significantly. With the electric fields computed everywhere, photonic device parameters such as transmission and reflection coefficients are extracted. Several photonic devices, with simulation volumes up to 1.9×10(4) (λ/n(avg))3 and modeled with over one hundred million unknowns, are simulated to demonstrate the application, efficiency, and capability of this technique. The simulations show good agreement with experimental results and in a special case with a simplified two-dimensional simulation.

Renormalization of the Helmholtz equation for the problem of electromagnetic propagation in a layer of spherical scatterers

The main objective of the present study is to investigate the problem of coherent scattering from a half-space of discrete scatterers by importing a simple version of the renormalization formalism, which has been of great use in other fields such as solid state physics or particle physics. Thus, renormalization is applied to solve the Dyson equation for the scattering problem of a half-space of uncorrelated and isotropic, uniformly distributed scatterers of spherical shape. Renormalization has been used before for analysing wave propagation through inhomogeneous, continuous random media. However, it has not been applied to the problem of a random distribution of discrete scatterers. Here the quasiparticle view of wave propagation is introduced and renormalization in the wave vector domain for a medium containing spherical scatterers is performed. The presence of a single or even a number of well-defined scatterers, randomly repeated throughout the embedding medium, gives enough regularity to the problem so that it is possible to obtain a first-order description of the propagating field even if there is no correlation between scatterers.

Finite-Element Method Modeling of Superconductors: From 2-D to 3-D

A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is implemented in finite-element method software and is based on a recently developed 3-D formulation for general electromagnetic problems with solid conductors. It has been adapted for modeling of superconductors with nonlinear resistivity in 3-D, characterized by a power-law E-J relation. It has first been compared with an existing and verified two-dimensional (2-D) model: Compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Second, the model has been tested for computing the current distribution with typical 3-D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2-D models.

Development of a graphical user interface for the conformal finite-difference/time domain (CFDTD) software package

We present the development of the graphical user interface of a conformal FDTD software package utilizing the Visual Basic programming language. We describe a complete interface, including the drawing of three-dimensional objects, the generation of non-uniform and conformal mesh, interfacing with AutoCad and GID, and data post-processing. The engine for the software package is based on a conformal FDTD algorithm, designed to handle general electromagnetic problems, including curved PEC and dielectric surfaces, without the use of staircasing. To illustrate the versatility of the package, we present several representative simulation examples, viz., the modeling of a microwave stripline, a patch antenna, a triangular antenna, and the evaluation of the surface impedance of Earth. We also provide a comparison between the numerical results derived by using this package and other commercial software for a patch antenna.

Wavelet-Galerkin method for computations of electromagnetic fields-computation of connection coefficients

One of the key issues which makes the wavelet-Galerkin method unsuitable for solving general electromagnetic problems is a lack of exact representations of the connection coefficients. This paper presents the mathematical formulae and computer procedures for computing some common connection coefficients. The characteristic of the present formulae and procedures is that the arbitrary point values of the connection coefficients, rather than the dyadic point values, can be determined. A numerical example is also given to demonstrate the feasibility of using the wavelet-Galerkin method to solve engineering field problems.

Double diffraction at a pair of coplanar skew edges

A high-frequency solution is presented for the scattering in the near zone by a pair of coplanar skew edges when they are illuminated by a source at a finite distance. The solution is obtained by using a spherical-wave spectral representation of the first-order diffracted field from each edge. The final closed-form asymptotic solution includes terms up to the second order. It is shown that this second-order contribution is of the same order as the first one in overlapping transition regions. Moreover, the solution is cast in a convenient form, which is also directly applicable to treat the case when the two edges share a common face for both soft and hard boundary conditions. By choosing appropriate reference systems, the formulation for the scalar case is directly used to construct the solution of the more general electromagnetic problem for an arbitrarily polarized incident field. Numerical results are presented and discussed.

Hybrid spectral‐spatial method for the analysis of printed antennas

A technique is presented combining the advantages of the spatial and spectral versions of the method of moments for a general electromagnetic problem involving a printed structure. The metalizations are of arbitrary shape and are described by a shape‐conforming mesh with subdomain basis functions. The technique is based on the extraction of the leading singular terms of the Green's function, in which space and frequency dependences are separated. The part of the impedance matrix associated with these terms is efficiently evaluated in the space domain, once for all frequencies. The eigenfunctions of these singular parts (expressed in terms of the subdomain basis functions) are then used as entire‐domain basis functions for the remaining regular part, whose associated impedance matrix is evaluated in the spectral domain. This appears to be the generalization to arbitrary patch shapes of the use of entire‐domain functions (like orthogonal polynomials or cavity modes) and drastically reduces the number of unknowns, showing potential for the full‐wave analysis of printed arrays.

An error based approach to the solution of full Maxwell equations

Aim of this paper is to extend the error based approach to the study of general electromagnetic problems in 3D geometries in which the displacement currents may not be neglected. The unknown variables are the three-component vector potential A and W defined as the time integrals of -E and H, respectively. These potentials are constrained to satisfy initial, boundary and interface conditions. Since in this way the Maxwell equations are automatically satisfied, the solution is obtained via minimization of a global error functional which approaches zero when the constitutive equations are satisfied. >

Nonlinear integral equations for electromagnetic inverse problems

The scaling properties of Maxwell’s equations allow the existence of simple yet general nonlinear integral equations for electrical conductivity. These equations were developed in an attempt to reduce the generality of linearization to the exclusive scope of electromagnetic problems. The reduction is achieved when the principle of similitude for quasi‐static fields is imposed on linearized forms of the field equations. The combination leads to exact integral relations which represent a unifying framework for the general electromagnetic inverse problem. The equations are of the same form in both time and frequency domains and hold for all observations that scale as electric and magnetic fields do; direct current resistivity and magnetometric resistivity methods are considered as special cases. The kernel functions of the integral equations are closely related, through a normalization factor, to the Frechét kernels of the conventional equations obtained by linearization. Accordingly, the sensitivity functions play the role of weighting functions for electrical conductivity despite the nonlinear dependence of the model and the data. In terms of the integral equations, the inverse problem consists of extracting information about a distribution of conductivity from a given set of its spatial averages. The form of the new equations leads to the consideration of their numerical solution through an approximate knowledge of their kernel functions. The integral equation for magnetotelluric soundings illustrates this approach in a simple fashion.

Complex rays for radiation from discretized aperture distributions

Many electromagnetic propagation problems require tracking of fields radiated by large actual or induced aperture distributions through complicated environments before reaching the observer. For a systematic approach to this problem area, it is desirable to represent the aperture field in terms of basis functions which are physically informative and well adapted to traversing the propagation path. At high frequencies, Ganssian beam-type basis functions meet these requirements. After referring to a rigorous aperture discretization scheme, various quasi-Gaussian basis field profiles are examined, with a special view toward expressing their radiation properties in terms of complex rays; complex ray tracing is promising for field tracking in complicated surroundings. By comparing reference solutions from numerical integration of radiation integrals with complex ray asymptotics, it is concluded that the true Gaussian has the most favorable attributes for matching aperture discretization, propagation requirements, and complex ray tracing. Thus, the analysis here may point the way toward systematic treatment of the above-noted class of propagation problems.

General method for the computation of radiation in stratified media

A general universal computational method for the general electromagnetic problem in stratified media is established. Computations are successfully performed for the field of a horizontal magnetic dipole in a microwave substrate backed by a conducting plane. The general field problem in stratified media is expressed in the form of integrals over kp. The integrands involve Bessel functions which are difficult to integrate. By using the fast Fourier transform (FFT) techniques, the integrals are computed numerically. A shortcoming of this method is that its usefulness is limited to near and intermediate fields. This method is applicable to many electromagnetic problems in microwaves, geophysical sciences, printed circuits etc

Experimental verification of network method for calculating flux and eddy-current distributions in three dimensions

A network method for the solution of general electromagnetic field problems has been introduced in a previous publication. The method was shown to give plausible results but no experimental evidence was given. The present paper describes the methods used for the solution of the circuit equations and a comprehensive set of measurements are presented which demonstrate the validity of the method. Some advantages and drawbacks of the method are also discussed.