Electromagnetic scattering by a multilayer elliptic cylinder undertransverse-magnetic illumination: series solution in terms of Mathieufunctions

An exact solution to the electromagnetic scattering by a dielectric multilayer infinite cylinder of elliptic cross section is proposed. The interfaces between different media, which are assumed to be lossless and nonmagnetic, are confocal elliptic cylinders. Starting from the series expansions in terms of Mathieu functions, an efficient recursive procedure for the computation of fields and radar cross sections per unit length under a transverse-magnetic illumination is developed. The mathematical formulation is detailed and some numerical results are provided     

Radiation from harmonic sources in a uniformly moving medium

In this paper the Maxwell-Minkowski equations are used to find a general integral for the electromagnetic fields in an infinite moving medium. The medium is assumed to be homogeneous, isotropic, and to move with a constant velocity much less than the speed of light. Only time-harmonic fields are considered. A wave equation for the electric field is derived and is integrated by means of a Green's Identity and an appropriately defined Dyadic Green's Function. The result gives the electric field inside a volume of space in terms of known sources in the volume and the tangential components of the electric and magnetic fields over the enclosing surface. Finally, the fields radiated by a point dipole are found.     

An Analysis of Scattering Caused by Dielectric Bodies Using Semi-Analytic Methods

A novel set of integrodifferential equations is formulated for the analysis of electromagnetic scattering and radiation by three-dimensional homogeneous dielectric bodies. The use of the Stratton-Chu integrals, the Atkinson-Wilcox and multipole representations of electromagnetic fields underlies the considered approaches. The equations are reduced to the infinite algebraic systems solved in a truncated representation. The results obtained by the numerical solution of these systems have been mutually compared and they have been shown to be in agreement. The investigation of convergence and time efficiency of the algorithms have been performed by the solution of the scattering problem for a cube and sphere excited by plane waves. Resonant regimes of dielectric cubes and spheres excited by probes have also been studied and the numerical results have been compared against the results predicted by the approximate theory of dielectric resonators. The convergence criterion for the Atkinson-Wilcox expansion has been formulated.     

Electromagnetic waves of dielectric structures in plasma

The electromagnetic waves of a dielectric layer and of a dielectric cylinder in homogeneous infinite plasma are considered. The dispersion dependences of surface and volume-surface E and H electromagnetic waves are investigated. A classification of the waves of dielectric structures in plasma is proposed.     

Suspended Slot Line Using Double Layer Dielectric

This paper presents a rigorous analysis of a) slot line on a double layer dielectric substrate, and b) slot line sandwiched between two dielectric substrates. The structure is assumed to be suspended inside a conducting enclosure of arbitrary dimensions. The dielectric substrates are assumed to be isotropic and homogeneous and are of arbitrary thickness and relative permittivity. The conducting enclosure and the zero thickness metallization on the substrate, are assumed to have infinite conductivity. The effect of shielding on the dispersion, characteristic impedance, and the effective dielectric constant are illustrated. These results should find application in the design and fabrication of MIC components and subsystems.     

General Solution for Excitation by Slotted Aperture Source in Conducting Cylinder with Concentric Layering

We present a general matrix analysis for the electromagnetic fields produced by an aperture source on the inner metallic snrface of a concentrically layered structure. Each layer is homogeneous and characterized by arbitrary permittivity, conductivity and magnetic permeability. The structure itself is assumed to be of infinite length so Maxwell's equations yield separable solutions. An explicit result is given for the electric current density on the inner metallic cylindrical surface which could model the mandrel in a borehole logging tool.     

Currents induced in an anatomically based model of a human forexposure to vertically polarized electromagnetic pulses

The finite-difference time-domain (FDTD) technique is used to calculate the internal fields and the induced current densities in anatomically based models of a human using 5628 or 45024 cubical cells of dimensions 2.62 and 1.31 cm, respectively. A layer of dielectric constant of ε_r=4.2 and having a thickness of 2.62 cm is assumed under the feet to simulate a human wearing rubber-soled shoes. The total induced currents for the various sections of the body and the specific absorptions for several organs are given for two representative electromagnetic pulses. The calculated results for the induced currents are in excellent agreement with the data measured for a human subject. The FDTD method is ideally suited for exact representation of the pulse shapes and offers numerical efficiency to allow detailed modeling of the human body and the various organs     

Electromagnetic wave propagation on a double-layer dielectric film

The nature of the eigenvalues characterising the electromagnetic wave propagation in a homogeneous isotropic double-layer dielectric structure of infinite extent on a perfectly conducting ground plane is discussed.     

Scattering from an anisotropic cylindrical dielectric shell

The electromagnetic scattering from an anisotropic cylindrical dielectric shell is formulated by using the wave functions for anisotropic media and the boundary-value method. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. Numerical results for the effects of various geometrical and electrical parameters on the bistatic radar cross section are presented.     

Iterative numerical computation of the electromagnetic fieldsinside weakly nonlinear infinite dielectric cylinders of arbitrary crosssections using the distorted-wave Born approximation

The electromagnetic scattering by weakly nonlinear infinite dielectric cylinders is the topic dealt with in this paper. The cylinders are assumed to be isotropic, inhomogeneous, and lossless and to have arbitrarily shaped cross sections. A time-periodic illumination of the transverse magnetic type is considered. The nonlinearity is assumed to be expressed by the dependence of the dielectric permittivity on the internal electric field, under the hypothesis that the operator responsible for the nonlinearity does not modify the scalar nature of the dielectric permittivity and produces a time-periodic output. The electromagnetic scattering is then described by an integral equation formulation, and the electromagnetic field distributions inside and outside a scatterer are approximated by an iterative numerical procedure starting with the application of the distorted-wave Born approximation. In a simplified version of the approach, the classic first-order Born approximation is used. The convergence of the approach is discussed in several examples. In the computer simulations concerning cylinders with different cross-section shapes, the effects of the nonlinearity on the field-component fundamental frequency were evaluated for different values of the nonlinear parameters in the case of a Kerr-like nonlinearity and of a uniform incident plane wave. The generation of higher-order harmonics was also considered     

Application of the Finite-Difference Time-Domain Method to Sinusoidal Steady-State Electromagnetic-Penetration Problems

A numerical method for predicting the sinusoidal steady-state electromagnetic fields penetrating an arbitrary dielectric or conducting body is described here. The method employs the finite-difference time-domain (FD-TD) solution of Maxwell's curl equations implemented on a cubic-unit-cell space lattice. Small air-dielectric loss factors are introduced to improve the lattice truncation conditions and to accelerate convergence of cavity interior fields to the sinusoidal steady state. This method is evaluated with comparison to classical theory, method-of-moment frequency-domain numerical theory, and experimental results via application to a dielectric sphere and acylindrical metal cavity with an aperture. Results are also given for a missile-like cavity with two different types of apertures illuminated by an axial-incidence plane wave.     

Formulation of probe-corrected planar near-field scanning in thetime domain

Probe-corrected planar near-field formulas in the time domain are derived for both acoustic and electromagnetic fields, so that a single set of near-field measurements in the time domain yields the fields of the test antenna directly in the time domain. The time-domain probe-corrected formulas are first derived by taking the inverse Fourier transform-of the corresponding frequency-domain formulas, and then by using a time-domain expansion for the fields of the test antenna and a time-domain receiving characteristic of the probe. Because these general formulas, which involve a double integral over the scan plane and an infinite time-convolution integral, are rather complicated, we consider a special probe whose output due to an incoming time domain plane wave is proportional to the time derivative of the field of that plane wave. For this special “D-dot probe”, the probe-corrected formulas simplify to give the time-domain far-held pattern as a double spatial integral of the time-domain output of the probe over the scan plane multiplied by the angular dependence of the inverse receiving characteristic of the probe. Time-domain reciprocity relations are derived for reciprocal probes, and their time-domain receiving characteristics are related to their far fields. Finally, a time-domain sampling theorem is derived and a numerical example illustrates the use of the time-domain probe-corrected formulas     

Electromagnetic Waves in Toroidal Vessels of Arbitrary Cross Section Filled with Radially Inhomogeneous Dielectric Medium

In this paper, analytical solutions of Maxwell's equations in cylindrical coordinates are presented for toroidal resonators filled with homogeneous or inhomogeneous unmagnetized plasma or another dielectric medium. It is shown that the electromagnetic boundary conditions valid on a conducting toroidal surface of arbitrary meridional cross section can be satisfied by the general solution since the general solution contains an infinite set of arbitrary constants. A method is given to show how these constants and the eigenfrequency of the resonator can be calculated for a given cross section of the toroidal vessel.     

Extension of on-surface radiation condition theory to scattering bytwo-dimensional homogeneous dielectric objects

A recent analytical formulation by G.A. Kriegsmann et al. (see ibid., vol.AP-35, p.153-61, Feb. 1987) of electromagnetic wave scattering by perfectly conducting two-dimensional objects using the on-surface radiation boundary condition approach is extended to the case of two-dimensional homogeneous convex dielectric objects. It is shown that a substantial simplification in the analysis can be obtained by applying the outgoing radiation boundary condition on the surface of the object. The analysis procedure decouples the fields in the two regions to yield explicitly a differential equation relationship between the external incident field excitation and the corresponding field distribution in the interior of the dielectric object. The interior fields can be obtained by solving the differential equation using either an analytical approach or a suitable numerical method. Two-dimensional scattering examples along with validations are reported, showing the near-surface field distributions for a homogeneous circular dielectric cylinder and an elliptic dielectric cylinder, with with transverse magnetic plane-wave excitation     

The geometric optics contribution to the scattering from a large dense dielectric sphere

An analysis is presented for calculating the backscattered fields of an electromagnetic plane wave by lossless dielectric spheres of arbitrary density. This method involves the Watson transformation which serves to split the exact Mie solution, given as an infinite series, into the geometrical optics fields and the diffracted fields. The former comes from the illuminated region of the sphere and may be obtained from the geometrical optics method. The latter comes from the shadow region and consists of two different types of surface waves. One is a "creeping wave" analogous to that of perfectly conducting spheres. The other is a wave which enters the sphere and emerges as a surface wave in the shadow region. This wave is unique to dielectric spheres and is the stronger of the two surface waves. In the widely used geometric optics methods it is assumed that the optics fields are the dominant contributors even though stationary rays which are not in the direction of backscatter must be added in to give a degree of agreement with the exact Mie series results. In this paper we derive the optics fields and show that they differ in some respects from those obtained by the geometric optics method. They are smaller than heretofore assumed and contribute negligibly to the backscatter in this particular range ofka(4-20). Using our rigorous approach we can show the diffracted fields to be the major contributors to the total backscatter. Numerical results for the backscattering cross sections using diffracted and optics fields, and optics fields alone will be presented for relative index of refraction of 1.6. The agreement between our results (diffracted and optics) and exact results from the Mie series is excellent. A subsequent paper will be concerned with the diffracted fields.     

On Radial Transmission Line Representations of Electromagnetic Fields in an Anisotropic Moving Medium

The problems of electromagnetic waves in moving isotropic or uniaxial mediums have been dealt with by numerous authors. Chawla and Unz considered the fields in a moving anisotropic plasma, and Chen and Cheng analyzed waves in an isotropic plasma in a moving dielectric medium. In this note we consider electromagnetic fields in a moving anisotropic medium and propose the network formulation of electromagnetic fields in the moving medium in the radial cylindrical coordinate. The method is an extension of the transmission line representation of electron beams on infinite magnetic fields. We can apply these results to the cases of any magnetic field intensity and, further, solve the complex problems for a stationary anisotropic plasma by a similar method.     

Planar near-field scanning in the time domain .1. Formulation

Time-domain planar near-field measurement techniques are formulated for acoustic and electromagnetic fields. Probe correction is ignored in that it is assumed that the probe measures the exact values of the field on the scan plane. Two fundamentally different approaches are used in deriving three sets of formulas that give the fields in the source-free half space z>z₀ in terms of their values on the scan plane z=z₀. In the first approach the time-domain formulas are obtained by inverse Fourier transforming the corresponding frequency-domain formulas. In the second approach the time-domain formulas are derived directly in the time domain by working with time-domain Green's functions     

Radiation from a Vertical Magnetic Dipole in Inhomogeneous Stratified Media above a Horizontal Conducting Plane†

The study of the radiation from a vertical magnetic dipole in mi inhomogeneous half space and also in inhomogeneous stratified media above a horizontal conducting infinite plane is considered. The formal expression for the Hertz potential, from which all the field components can be derived. is presented in the form of a contour integral. These formal results are employed for special cases using suitable profiles for relative dielectric constants so that the electromagnetic fields can be expressed in terms of known functions. The contour integral is evaluated asymptotically by saddle point method of integration in each of the examples using special profiles for ε(z). Possibilities of the existence of surface waves in appropriate configurations are also discussed. The results for homogeneous media are also extracted from those of the corresponding inhomogeneous media by taking appropriate limits.     

Analysis of infinite arrays of microstrip-fed dipoles printed onprotruding dielectric substrates and covered with a dielectric radome

A method for analyzing infinite arrays of antennas printed on both sides of substrates protruding from a ground plane and covered with a dielectric radome is described. Using the equivalence principle, the array unit cell is decomposed into homogeneous regions where the fields are expressed as Floquet summations, and an inhomogeneous cavity region where the fields can be found by a combination of the method of moments and modal analysis. The approach is rigorous in the sense that the combined effects of the radiating element and feed geometry printed on opposite sides of a protruding substrate are taken into account. The method is quite general, capable of modeling any antenna elements with substrate currents that are perpendicular and/or parallel to the ground plane. In addition, both the radiating and scattering/receiving modes of operation are treated in the analysis. The method is used to calculate the active element impedance of an infinite array of dipoles transmission line-coupled to microstrip feeds. Examples of numerical results are presented for various scan conditions and the effects of a near-field dielectric radome are demonstrated     

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere of multilayers

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere is formulated and obtained, where the inhomogeneous plasma anisotropic sphere is divided into (s-1) homogeneous anisotropic spherical layers. The electromagnetic fields in the inner spherical multilayers and outer free space of the inhomogeneous plasma anisotropic spherical structure can be expanded in terms of the spherical vector wave functions in plasma anisotropic medium and in isotropic medium, respectively. By applying the continuous boundary conditions of electromagnetic fields on the spherical interfaces of the (s-1)-layered homogeneous anisotropic plasma medium, the unknown expansion coefficients of fields in the multilayered plasma spherical structure are obtained, and then the electromagnetic field distributions are calculated. Numerical results for the very general inhomogeneous plasma dielectric material sphere are given and the data in a special case are obtained using the present method and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach and compared to each other to verify the correctness and applicability of the present analysis.