Time-domain electromagnetic plane waves in static and dynamicconducting media. I

Solutions are derived for the time-domain Maxwell equations for static (J=σE) and dynamic (τ∂/∂t+J= σ₀ E) conducting media where the field is assumed to vary with respect to only one spatial direction, i.e., plane-wave propagation. The plane wave is introduced into the media via the imposition of an electric field boundary condition at the plane boundary of a half-space and it is assumed that the fields inside the half-space are initially zero. Solutions are derived directly from the first-order system of partial differential equations and it is shown that once the electric field at the plane boundary is imposed, the magnetic field is automatically determined for causal solutions. It is shown that the form of the Maxwell equations, without a magnetic conductivity term added, is sufficient to allow well and uniquely defined solutions of this problem     

Time-Domain Analysis of Millimeter Wave Circulation Around a Magnetised Ferrite Sphere

An efficient numerical method has been devised for the study of wave circulated by a magnetised ferrite sphere. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. The electromagnetic fields inside the ferrite body are calculated using special updating equations derived from the equation of motion of the magnetization vector and Maxwell's curl equations in consistency. The electromagnetic fields inside ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained in a wide frequency band with a single time domain run. It is observed that an incident plane wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide / microstrip junction circulators.     

Electromagnetic coupling between two half-space regions separatedby multiple slot-perforated parallel conducting screens

Considers the problem of electromagnetic coupling between two half-space regions separated by multiple slot-perforated parallel conducting screens. The fields are considered to be excited by either a transverse electric (TE) or a transverse magnetic (TM) plane wave. A characteristic mode solution is used for the computation of the fields in each half-space. Special attention is given to the power transmitted from one half-space to the other through the slots and to its functional dependence on various parameters. Numerical examples are presented for illustration and comparison     

Analysis of Electromagnetic Scattering from an Eccentric Multilayered Sphere

An exact analytic solution of a plane electromagnetic (EM) wave scattered by an eccentric multilayered sphere (EMS) is obtained. It is assumed that the layers are perfect dielectrics and that the innermost core is a perfectly conducting sphere. Each center of a layer is translated along the incident axis. All fields are expanded in terms of the spherical vector wave functions with unknown expansion coefficients. The addition theorem for spherical wave functions is used prior to applying the boundary conditions. The unknown coefficients are determined by solving a system of linear equations derived from the boundary conditions. Numerical results of the scattering cross sections are presented on the plane of φ=0 degrees and φ=90 degrees. The convergence of modal solutions and the characteristics of patterns are examined with various geometries and permittivity distributions     

Model of a nonlinear electromagnetic crystal

2D electromagnetic crystal with lumped nonlinear elements is considered. An electrodynamic model with a rectangular grid is developed for a crystal that is infinite in one coordinate and finite in the other. In the case when the structure is excited by a plane wave, linear boundary value problems are formulated for electromagnetic fields at multiples of the fundamental frequency. The nonlinear problem is solved by means of the harmonic balance method. A system of nonlinear equations for the amplitudes of voltage harmonics at nonlinear elements is derived. Results of numerical solution of the system are presented for resistive and capacitive nonlinear elements.     

Analysis of the power coupling from a waveguide hyperthermiaapplicator into a three-layered tissue model

The power deposition from a rectangular-aperture flanged waveguide into a three-layered stratified tissue medium is analyzed theoretically. The fields inside the tissue layers are expressed in terms of Fourier integrals satisfying the corresponding wave equations, while the fields inside the waveguide are expanded in terms of the guided and evanescent normal modes. An integral equation is derived on the aperture plane of the flanged waveguide by applying the continuity of the tangential electric and magnetic fields. This integral equation is solved by expressing the unknown electric field in terms of the waveguide mode fields and by applying a Galerkin procedure. The electromagnetic fields inside the tissue medium are then determined and patterns of the deposited power at frequencies of 432 MHz and 144 MHz for apertures of 5.6×2.8 cm² and 16.5×8.3 cm², respectively, are computed and presented     

Transmission of electromagnetic waves into time-varying media

Expressions are obtained for the electromagnetic fields transmitted into the time-varying medium when a plane wave is incident upon either a dielectric or dispersive half-space. Solutions are obtained for the case when the medium is changed in a stepwise fashion, and also for the case when the medium varies slowly and continuously.     

两层旋电磁介质球电磁散射的球矢量波函数解

在均匀旋电磁介质球矢量波函数的基础上,利用球Bessel函数的特性,给出了两层旋电磁介质球内的电磁场用波函数表示的表达式. 在平面波入射情况下,应用电磁场在球边界上切向电场和磁场连续与远区辐射条件,导出了两层各向异性旋电磁介质中电磁场用矢量波函数表示的展开函数所满足的方程组,求出了两层旋电磁介质球的散射场用均匀各向同性波函数展开的展开系数,进而得出了两层旋电磁介质球对平面波的电磁散射特性. 理论分析和数值计算的结果表明:当两层旋电磁介质球的媒质参数相同时,本文所得的结果可退化为单层各向异性旋电磁体解析解.

     

Radiation from an electromagnetic source in a half-space of compressible plasma-surface waves

The radiation characteristics of a line source of magnetic current are studied for the case in which the source is situated in a half-space of isotropic, compressible plasma which is bounded on one side by a perfectly conducting, rigid plane screen. In addition to the electromagnetic and plasma space waves, the line source excites a boundary wave. This boundary wave is a coupled wave. It has associated with it both a magnetic field component and the pressure term. This is in contrast to the space waves which can be decomposed into an electromagnetic (EM) mode with no pressure term and a plasma (P) mode with no magnetic field associated with it. The characteristics of this boundary wave are evaluated. The boundary wave propagates for all frequencies and the power carried by the boundary wave becomes smaller as the frequency is increased.     

Scattering by a conducting spheroidal object with dielectriccoating at axial incidence

An analytic solution of a plane electromagnetic wave scattering by coated prolate spheroidal bodies is obtained, for axial incidence, by expanding the incident and scattered fields in terms of prolate spheroidal vector wave functions. The unknown expansion coefficients are determined by an infinite system of equations derived using appropriate boundary conditions. To solve for the unknown coefficients, the system of equations is truncated by retaining only the first N equations in N unknowns, where N depends on the size of the body and the desired accuracy. Numerical results for the scattering cross section are presented to show the effect of different coatings on the magnitude of the scattered field     

The E-parallel polarization response of a two-dimensionalheterogeneous layer modeled by two thin sheets

The flexibility of the thin-sheet technique for modeling two-dimensional structures is extended by analyzing the response to E-parallel to the strike of the anomaly polarization, also known as the transverse electric (TE) mode, when a heterogeneous Earth is modeled by two thin sheets over a horizontally stratified half-space. The electromagnetic fields induced by the heterogeneous layer when a uniform plane wave is normally incident on the Earth are expressed as integral equations, which are then evaluated using the method of moments. The resulting matrix equations are solved by the Gauss-Seidel method, and the magnetotelluric impedance is calculated     

Dyadic Green's functions inside/outside a dielectric elliptical cylinder: theory and application

Dyadic Green's functions in two regions separated by an infinitely long elliptical dielectric cylinder are formulated in this paper. As an application, the plane electromagnetic wave scattering by an isotropic elliptical dielectric cylinder is revisited by applying these dyadic Green's functions and the scattering-to-radiation transform. First, the dyadic Green's functions are formulated and expanded in terms of elliptical vector wave functions. The general equations are derived from the boundary conditions and expressed in matrix form. Then the scattering and transmission coefficients coupled to each other are solved from the matrix equations. To verify the theory developed and its applicability, we revisit the plane electromagnetic wave scattering (of TE- and TM-polarizations) by an infinitely long elliptical cylinder, and consider it as a special case of electromagnetic radiation using the dyadic Green's function technique. The derived equations and computed numerical results are then compared with published results and a good agreement in each case is found. Special cases where the elliptical cylinder degenerates to a circular cylinder and where the material of the cylinder is isorefractive are also considered, and the same analytical solutions in both cases are obtained.     

常阻抗地平面上方垂直电偶极源电磁场的精确和有效解

地平面上方偶极源的电磁场可以分解成直达波场、镜像波场和Somm erfeld型积分三部分之和。应用圆柱波函数的球面波展开式和超几何函数理论,常阻抗地平面上方垂直电偶极源电磁场中的Somm erfeld型积分被表达成圆柱波函数(表面波模)与快速、绝对收敛的球面波函数集展开式之和;其级数展开式的系数是以表面阻抗为宗量的勒让德函数。该展开式数学物理意义明显,并且便于计算,它是此类Somm erfeld半空间问题的精确、有效解答。     

Resonant electromagnetic field coupled into a lossy cavity through a slot aperture

A new approach is proposed for determining the electromagnetic fields coupled from an incident plane wave into a lossy conducting cavity through a slot aperture under resonant conditions. Use is made of the duality between a slot and a conducting strip and of the equivalence between a strip and a wire. Simplified formulas are derived that are explicit and flexible. Determination of resonant fields inside a cavity is reduced to simple calculations. Numerical examples are given.     

FDTD simulation of TE and TM plane waves at nonzero incidence in arbitrary Layered media

Plane wave scattering is an important class of electromagnetic problems that is surprisingly difficult to model with the two-dimensional finite-difference time-domain (FDTD) method if the direction of propagation is not parallel to one of the grid axes. In particular, infinite plane wave interaction with dispersive half-spaces or layers must include careful modeling of the incident field. By using the plane wave solutions of Maxwell's equations to eliminate the transverse field dependence, a modified set of curl equations is derived which can model a "slice" of an oblique plane wave along grid axes. The resulting equations may be used as edge conditions on an FDTD grid. These edge conditions represent the only known way to accurately propagate plane wave pulses into a frequency dependent medium. An examination of grid dispersion between the plane wave and the modeled slice reveals good agreement. Application to arbitrary dispersive media is straightforward for the transverse magnetic (TM) case, but requires the use of an auxiliary equation for the transverse electric case, which increases complexity. In the latter case, a simplified approach, based on formulating the dual of the TM equations, is shown to be quite effective. The strength of the developed approach is illustrated with a comparison with the conventional simulation based on an analytic incident wave specification with half-space, single frequency reflection and transmission for the edges. Finally, an example of a possible biomedical application is given and the implementation of the method in the perfectly matched layer region is discussed.     

A macroscopic model of nonlinear constitutive relations insuperconductors

A macroscopic model is proposed for nonlinear electromagnetic phenomena in superconductors. Nonlinear constitutive relations are derived by modifying the linear London's equations. The superelectron number density as a function of applied macroscopic current density, n _s(J), is derived from a distribution of electron velocities at a certain temperature T. At temperature T≠0 K, the function n_s(J) has a smooth variation near the macroscopic critical current density J_c. Agreement has been found between this n _s(J,T) model and the temperature dependence of n_s in the two-fluid model. The nonlinear conductivities σ_s(J) and σ_n(J) are obtained from the London's equation with the modified n_s(J) function. Nonlinear resistance R(I), kinetic inductance L_k(I) and surface impedance Z_s(I) in thin wire, slab, and strip geometries are calculated     

TE/TM decomposition of electromagnetic sources

Three methods are given by which bounded electromagnetic sources can be decomposed into two parts radiating transverse electric (TE) and transverse magnetic (TM) fields with respect to a given constant direction in space. The theory applies source equivalence and nonradiating source concepts, which lead to decomposition methods based on a recursive formula or two differential equations for the determination of the TE and TM components of the original source. Decompositions for a dipole in terms of point, line, and plane sources are studied in detail. As an application of the point decomposition method, it is demonstrated that the general exact image expression for the Sommerfold half-space problem, previously derived through heuristic reasoning, can be more straightforwardly obtained through the decomposition method     

Time-domain propagating modes in a finitely conducting half-spaceand calculation of the transient reflection

Time-domain down and up going eigenmodes are identified in a finitely conducting half-space for an obliquely incident plane wave. The tangential electromagnetic fields are related to each other in each eigenmode, through a convolution kernel due to the conductivity. The propagating modes are then used to calculate the transient reflection directly in the time-domain for TE and TM modes. Numerical results are presented and compared to the ones given by others     

Extended integral equation formulation for scattering problems froma cylindrical scatterer

An extended integral equation is developed for electromagnetic scattering from a perfectly conducting cylinder and a dielectric cylinder. The conventional surface integral equations cannot yield unique solutions when the wavenumber of the electromagnetic wave is equal to an eigenwavenumber of the system. Several methods to overcome this difficulty have been presented, but each method includes some drawbacks. A numerical method is proposed in which the boundary element method is applied to the extended integral equations with the observation points lying on a closed surface inside the scatterer. It is shown that the extended integral equations have unique solutions for any given wavenumber. As examples, plane wave scattering from a perfectly conducting elliptic cylinder, a dielectric elliptic cylinder, and a dielectric rectangular cylinder is numerically analyzed     

Concerning lossy, compressible, magneto-ionic media-General formulation and equation decoupling

The governing equations for electromagnetic phenomena in lossy, compressible, magneto-ionic media are formulated in terms of a newly introduced compressivity tensor. The matrix forms of both the permittivity tensor and the compressivity tensor are given. From the new governing equations, a three-dimensional vector wave equation and a dispersion equation are derived. In a source-free region, a set of three simultaneous wave equations in the longitudinal components of the electric and magnetic fields and in the pressure distribution can be written. These equations can be decoupled in the lossless case by effecting a transformation. The required transformation matrix and the resulting uncoupled, second-order, differential equations are given. Formulas for the determination of the transverse components of the electric and magnetic fields are also derived.