Scattering by thin dielectric strips

A plane wave incident on a thin dielectric strip with infinite length is considered, letting the incident electric field vector be parallel with the edges of the strip. The field is expanded in the dielectric region as the sum of three plane waves (the forced wave and two surface waves). Thex-axis andy-axis propagation constants are known for each wave, and Galerkin's method is employed to determine the amplitudes of these waves. Finally, the far-zone scattered field is determined by considering the polarization currents radiating in free space. Numerical data are presented to illustrate the scattering properties of lossless and lossy dielectric strips as a function of the angle of incidence and the width of the strip. The calculations show excellent agreement with an earlier moment method using pulse bases and point matching.     

Electromagnetic scattering interaction between a dielectriccylinder and a slightly rough surface

An electromagnetic scattering solution for the interaction between a dielectric cylinder and a slightly rough surface is presented in this paper. Taking the advantage of a newly developed technique that utilizes the reciprocity theorem, the difficulty in formulating the secondary scattered fields from the composite target reduces to the evaluation of integrals involving the scattered fields from the cylinder and polarization currents of the rough surface induced by a plane wave. Basically, only the current distribution of isolated scatterers are needed to evaluate the interaction in the far-field region. The scattered field from the cylinder is evaluated in the near-field region using a stationary phase approximation along the cylinder axis. Also, the expressions for the polarization current induced within the top rough layer of the rough surface derived from the iterative solution of an integral equation are employed in this paper. A sensitivity analysis is performed for determining the dependency of the scattering interaction on the target parameters such as surface root mean square (RMS) height, dielectric constant, cylinder diameter, and length. It is shown that for nearly vertical cylinders, which is of interest for modeling of vegetation, the cross-polarized backscatter is mainly dominated by the scattering interaction between the cylinder and the rough surface. The accuracy of the theoretical formulation is verified by conducting polarimetric backscatter measurements from a lossy dielectric cylinder above a slightly rough surface. Excellent agreement between the theoretical prediction and experimental results is obtained     

Pulsed EM Field Response of a Thin, High-Contrast, Finely Layered Structure With Dielectric and Conductive Properties

The response of a thin, high-contrast, finely layered structure with dielectric and conductive properties to an incident, pulsed, electromagnetic field is investigated theoretically. The fine layering causes the standard spatial discretization techniques to solve Maxwell's equations numerically to be practically inapplicable. To overcome this difficulty, an approximate method is proposed that models the interaction of the layer with an incident electromagnetic field via a boundary condition that expresses the in-plane conduction and contrast electric polarization currents in terms of the exciting incident field by relating the jump in the tangential component of the magnetic field strength across the layer in terms of the (continuous) tangential component of the electric field strength in the layer. In the pertaining layer admittance coefficient, the integrated values of the conductance and the contrast permittivity profiles across the layer occur. The model is applied to the scattering of an incident plane wave with pulsed time signature by a layer of infinite extent. Expressions for pulse shapes of the scattered field are obtained. In them, the layer properties and the direction of incidence and polarization of the incident wave occur as parameters. Numerical results are presented for reflected and transmitted wave pulse shapes for some parameter values.      

A three-wave FDTD approach to surface scattering with applicationsto remote sensing of geophysical surfaces

A major difficulty in physical interpretation of radio wave scattering from geophysical surfaces is the lack of detailed information on the signatures of geologically plausible discrete objects. Although the aggregate response will never be dominated by any single object, differences in the population of discrete objects on or near the surface (their sizes and shapes, for example) can change the character of a radio echo markedly. When the average surface is modelled as a flat, homogeneous half-space, the field that “drives” the scattering process is a composite consisting of the incident plane wave and the reflected and transmitted plane waves, all of which are known quantities; the total field can then be defined as the sum of the driving field and the scattered field. When a discrete object is near the surface, the total field can be calculated using finite-difference time-domain (FDTD) techniques, and the scattered near field can be calculated accordingly. The Green's functions for electric and magnetic currents above and below the surface, obtained by Sommerfeld theory and employed in conjunction with Huygens' principle, transform the local scattered fields to the far field. The FDTD implementation accommodates discrete lossy dielectric and magnetic scatterers in the vicinity of a dielectric surface; extension to a lossy half-space is straightforward. Two-dimensional results for scattering from perfectly conducting circular cylinders above and below a dielectric surface agree with moment method solutions within a few percent. Results for scattering from a dielectric wedge exhibit expected forward diffraction and internal reflection phenomena     

Diffraction by an anisotropic dielectric half-plane: a uniformasymptotic PO solution

A uniform solution is proposed to, describe the diffraction by a penetrable anisotropic dielectric halfplane illuminated at normal incidence by an electromagnetic plane wave. Resorting to second-order boundary conditions on a sheet simulating a special type of anisotropic dielectric thin layer, a physical optics (PO) approximation for the induced electric and magnetic surface currents is derived. Then, a uniform asymptotic evaluation of the corresponding radiation integral provides the diffracted field in terms of the standard transition function relevant to the uniform theory of diffraction. The effectiveness of the solution is proved by many numerical tests     

Scattering from an abruptly terminated dielectric-slab waveguide

Scattering of surface waves from an abruptly terminated dielectric-slab waveguide is investigated analytically, by means of an integral equation appropriate for the boundary-value problem of TE modes. In order to obtain a tractable solution to the equation, a Neumann Series iterative procedure is applied. Numerical results are given in several cases of abruptly ended dielectric slabs. Particular attention is directed to the behavior of electric and magnetic fields at the plane of discontinuity, since field distributions at any other region depend directly on these surface values.     

Scattering of electromagnetic waves by a system of two dielectricspheroids of arbitrary orientation

By means of modal series expansion of the incident, scattered, and transmitted electric and magnetic fields in terms of appropriate vector spheroidal eigenfunctions an exact solution is obtained to the problem of electromagnetic scattering by two dielectric spheroids of arbitrary orientation is obtained. The incident wave is considered to be a monochromatic uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions at the surface of one spheroid, the electromagnetic field scattered by the other spheroids is expressed as an incoming field to the first one, in terms of the spheroidal coordinates attached to it, using rotational-translational addition theorems for vector spheroidal wave functions. The solution of the associated set of algebraic equations gives the unknown expansion coefficients. Numerical results are presented in the form of plots for the bistatic and backscattering cross sections of two lossless prolate spheroids having various axial ratios, center-to-center separations, and orientations     

Full-Wave Analysis of Microstrip Open-End and Gap Discontinuities

A solution is presented for the characteristics of microstrip open-end and gap discontinuities on an infinite dielectric substrate. The exact Green's function of the grounded dielectric slab is used in a moment method procedure, so surface waves as well as space-wave radiation are included. The electric currents on the line are expanded in terms of longitudinal subsectional piecewise sinusoidal modes near the discontinuity, with entire domain traveling-wave modes used to represent incident, reflected, and, for the gap, transmitted waves away from the discontinuity. Results are given for the end admittance of an open-ended line, and the end conductance is compared with measurements. Results are also given for the reflection coefficient magnitude and surface-wave power generation of an open-ended line on substrates with various dielectric constants. Loss to surface and space waves is calculated for a representative gap discontinuity.     

Scattering by an inhomogeneous dielectric/ferrite cylinder ofarbitrary cross-section shape-oblique incidence case

A moment method (MM) solution is developed for the fields scattered by an inhomogeneous dielectric/ferrite cylinder of arbitrary cross-section. The incident field is assumed to be a plane wave of arbitrary polarization with oblique incidence with respect to the axis of the cylinder. The total electric and magnetic fields are the unknown quantities in two coupled equations from which a system of linear equations is obtained. Once the total electric and magnetic fields within the cylinder are computed, the scattered fields at any other point in space can be calculated. It is noted that for the case of oblique incidence, the scattered field has TE_z and TM_z polarized fields regardless of the polarization of the incident field. The echo widths of cylinders and shells of circular, semicircular, and rectangular cross section are calculated for TE_z and TM_z polarized incident fields. It is shown that the results obtained for dielectric/ferrite cylinders and shells of circular cross section with the solutions developed here agree very well with the corresponding exact eigenfunction solutions     

Diffraction by a cylinder with a dielectric shell. Surface waves and an antiradar coating

The field formed during diffraction by a circular cylinder with a dielectric shell can be represented in the form of a Watson series, i.e., as a set of azimuthal waves. The structure, velocity, and attenuation of these waves are found. It is shown that the process during which surface waves excited in the presence of diffraction by any guiding nonplanar surface carry away a portion of the incident energy and reduce the scattered wave can be used for creating a coating in the form of a dielectric layer.     

Harmonic generation by an electromagnetic wave in an inhomogeneous isotropic plasma

The generation of harmonic waves by a plane electromagnetic wave normally incident on a collision-free plasma with a linear density profile is considered. The solution for the primary wave in the plasma region is first obtained, and nonlinear polarization currents for the higher harmonics are expressed in terms of the lower harmonic fields by a perturbation method. The analysis shows that the plasma excites a longitudinally oscillating second harmonic electric field which is totally confined inside the plasma and has a singularity. The third harmonic wave excited in the plasma, however, radiates back into free space, although the effect is negligibly small in a quasi-homogeneous limit. The amplitude of this radiated field oscillates as a function ofomega^{3}, and the electron density gradient has little effect on it.     

Fully polarimetric bistatic radar scattering behavior of forestedhills

The bistatic radar scattering measurements of forested hills were performed at grazing incidence and at azimuth scattering angles from 28° to 66° from the forward scatter plane. Using pulse-to-pulse switching between orthogonal transmitted polarizations, the radar simultaneously measures two orthogonally polarized components of the scattered wave to obtain full polarimetric information about the scattering process. These are the first fully polarimetric terrain clutter measurements to be conducted at large bistatic angles. The complete Stokes matrix, computed by averaging successive realizations of the polarization scattering matrix, is used to examine the polarization sensitivity of the bistatic clutter. It is found that the polarization state of the EM wave scattered out of the plane of incidence strongly depends on the polarization orientation of the incident electric field. Unlike the monostatic case, these two incident wave polarization states are found to produce substantially different scattered wave behavior when trees are viewed at large bistatic angles. Scattered fields resulting from vertically oriented incident fields are found to be highly polarized and to produce bistatic clutter power levels that are strongly dependent on the polarization of the receiving antenna. In contrast, horizontally oriented incident fields are found to produce weakly polarized scattered waves with bistatic clutter power levels that are insensitive to the polarization of the receiving antenna     

Electromagnetic scattering from a chiral cylinder of arbitrarycross section

A simple moment solution is presented to the problem of electromagnetic scattering from a homogeneous chiral cylinder of arbitrary cross-section. The cylinder is assumed to be illuminated by either a TE or a TM wave. The surface equivalence principle is used to replace the cylinder by equivalent and magnetic-surface currents. These currents radiating in unbounded external medium produce the correct scattered field outside. When radiating in an unbounded chiral medium, they produce the correct total internal field. By enforcing the continuity of the tangential components of the total electric field on the surface of the cylinder, a set of coupled integral equations is obtained for the equivalent surface currents. Unlike a regular dielectric, the chiral scatterer produces both copolarized and cross-polarized scattered fields. Hence, both the electric and magnetic current each have a longitudinal and a circumferential component. These four components of the currents are obtained by using the method of moments (MoM) to solve the coupled set of integral equations. Pulses are used as expansion functions and point matching is used. The Green's dyads are used to develop explicit expressions for the electric field produced by two-dimensional surface currents radiating in an unbounded chiral medium. Some of the advantages and limitations of the method are discussed. The computed results include the internal field and the bistatic and monostatic echo widths. The results for a circular cylinder are in very good agreement with the exact eigenfunction solution     

Currents induced in a wire cross by a plane wave incident at an angle

The currents induced in a thin-wire cross with equal mutually perpendicular arms by an incident plane electromagnetic wave are determined when the normal to the wave front is perpendicular to the horizontal wire and is at an anglethetawith respect to the vertical wire; the direction of the electric vector in the wave front is arbitrary. The analysis is formulated in general terms but explicit formulas are obtained only for the zero-order currents which are generally adequate to determine the scattered field of very thin wires. The relatively simple formulas consist of even and odd parts for both the vertical and horizontal wires; they include components due to mutual coupling as well as those excited directly by the incident field.     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

A probabilistic model for the response of an electrically shorttwo-conductor transmission line driven by a random plane wave field

A probabilistic approach for the characterization of wiring-harness susceptibility to external interference is presented. The problem of field-coupling onto a uniform, lossless, electrically-short two-conductor transmission line loaded by terminal resistances is considered. The external field is modeled as a plane wave with random parameters. By virtue of the low-frequency assumption, the statistical properties of the induced current magnitude in one of the line loads are derived, for different characterizations of the external wave. Investigated configurations include: waves with random amplitude, waves with random amplitude and polarization, waves with random amplitude and direction of incidence, and waves with random amplitude, polarization and direction of incidence. Analytical expressions for the probability density function of the current (voltage) induced in one of the line loads are derived. The proposed model allows the computation of statistical parameters of interest, such as expected values, variances, and confidence intervals of the currents (voltages) in the line loads     

Radiation and scattering from structures involving finite-sizedielectric regions

A full-wave approach is presented for calculating the scattered fields produced by structures that involve finite-size dielectric regions. The dielectric is first approximated by an array of interlocking thin-wall sections; the electric field boundary conditions are then applied through the use of appropriate surface impedances. Rooftop basis functions, chosen to represent the surface current, are appropriately placed on the thin-wall sections in such a way as to accurately represent the polarization current while preventing fictitious charge within the dielectric. Rooftop currents are also used to represent the current on any conductor that may be present. The matrix elements are calculated, depending upon the distance between the source and field locations, through a scheme that employs Taylor series expansions and point source approximations. The technique is applied to scattering from dielectric cubes and composite dielectric-conductor structures, and to radiation from microstrip structures. Numerical convergence and agreement with the literature are demonstrated     

Rigorous Analysis of Rectangular Dielectric Resonator Antenna With a Finite Ground Plane

A probe-fed rectangular dielectric resonator antenna (RDRA) placed on a finite ground plane is numerically investigated using method of moments (MoM). The whole structure of the antenna is exactly modeled in our simulation. The feed probe, coaxial cable and ground plane are modeled as surface electric currents, while the dielectric resonator (DR) and the internal dielectric of coaxial cable is modeled as volume polarization currents. Each of the objects is treated as a set of combined field integral equations. The associated couplings are then formulated with sets of integral equations. The coupled integral equations are solved using MoM in spatial domain. The effects of ground plane size, air gap between dielectric resonator and ground plane, probe length, and position on the radiation performance of the antenna including resonant frequency, input impedance, radiation patterns, and bandwidth are investigated. The results obtained for the antenna parameters based on the MoM investigation shows that there is a close agreement with those obtained by measurement. Moreover it is shown that the MoM results are more accurate than other simulation results using software package such as High Frequency Structure Simulator (HFSS).      

Variational Treatment of the Diffraction at the Facet of d.h. Lasers and of Dielectric Millimeter Wave Antennas

This paper presents an accurate variational treatment of the diffraction of TE and TM waves by an abrupt transverse discontinuity in a dielectric waveguide, such as the mirror of a double heterostructure (d.h.) injection laser, or the end plane of a dielectric slab antenna for millimeter waves, under the assumption of small aspect ratio. A matrix representation of the Green's function is derived analytically, in the limit of small efective frequency, for the TE case. For the TM case, the complication introduced by the discontinuity of the transverse electric field across the dielectric interface is discussed in detail. The numerical examples refer to the d.h. laser configuration. Both transverse directions (perpendicular as well as parallel) to the junction are studied. The effect of mode coupling at the mirror of a LOC laser as well as the effect of an antireflection coating are investigated.     

Analysis of a Longitudinal Gyroelectric Discontinuity Inside a Fiber Waveguide

The scattering of guided electromagnetic waves from a finite-length longitudinal gyroelectic discontinuity inside a fiber waveguide is treated analytically. An integral equation approach is employed to formulate the corresponding boundary-value problem. The induced field inside the gyroelectic discontinuity region is expanded into a Fourier-type series in terms of the well-known cylindrical waves M and N plus a purely longitudinal wave Q. Then the method of moments is applied to decouple the basic integral equation. The resulting infinite coupled system of equations is truncated and solved numerically. After determining the field inside the discontinuity, the scattered far field inside the dielectric-rod waveguide is computed by employing a steepest descent integration technique. Numerical results for the scattering coefficients of an incident HE/sub 11/ dominant mode are obtained. Finally, design principles are discussed for practical components based on the treated longitudinal gyroelectric discontinuity.