Scattering by thin wire loaded with a ferrite ring

A coupled integral equation formulation and a method of moments (MoM) solution are presented for the problem of scattering by a thin conducting wire of circular cross section with ferrite loading. It is proved that ferrite loading can be used to reduce the radar cross section of long thin objects at their resonant frequency     

The RCS of a cylindrical array antenna coated with a dielectric layer

The scattering properties of dielectric coated waveguide aperture antennas mounted on circular cylinders are investigated. Both the single element antenna and the array case are treated. The array antenna consists of 4 /spl times/ 32 rectangular apertures placed in a rectangular grid on the surface of an infinitely long circular cylinder. The problem is formulated in terms of an integral equation for the aperture fields which is solved with the method of moments using rectangular waveguide modes as basis and test functions. An efficient uniform asymptotic technique is used to calculate the excitation vector and the backscattered far-field. The asymptotic solution is valid for large cylinders coated with thin dielectric layers away from the paraxial (i.e. near axial) region. A similar asymptotic solution is used to calculate the mutual coupling in the nonparaxial region. For the self coupling terms and for the mutual coupling in the paraxial region a planar approximation is used with a corresponding spectral domain technique. Numerical results are presented as a function of frequency, angle of incidence, cylinder radius, and electrical thickness of the coating.     

Backscatter RCS for TE and TM excitations of dielectric-filledcavity-backed apertures in two-dimensional bodies

Transverse electric (TE) and transverse magnetic (TM) scattering from dielectric-filled, cavity-backed apertures in two-dimensional bodies are treated using the method of moments technique to solve a set of combined-field integral equations for the equivalent induced electric and magnetic currents on the exterior of the scattering body and on the associated aperture. Results are presented for the backscatter radar cross section (RCS) versus the electrical size of the scatterer for two different dielectric-filled cavity-backed geometries. The first geometry is a circular cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the cylinder is dielectric filled and is also of circular cross section. The two cylinders (external and internal) are of different radii and their respective longitudinal axes are parallel but not collocated. The second is a square cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the square cylinder is dielectric-filled and is also of square cross section     

Scattering by a dielectric cylinder of arbitrary cross section shape

The theory and equations are developed for the scattering pattern of a dielectric cylinder of arbitrary cross section shape. The harmonic incident wave is assumed to have its electric vector parallel with the axis of the cylinder, and the field intensities are assumed to be independent of distance along the axis. Solutions are readily obtained for inhomogeneous cylinders when the permittivity is independent of distance along the cylinder axis. Although other investigators have approximated the field within the dielectric body by the incident field, we treat the total field as an unknown function which is determined by solving a system of linear equations. In the case of the dielectric cylindrical shell of circular cross section, this technique yields results which agree accurately with the exact classical solution. Scattering patterns are also presented in graphical form for a dielectric shell of semicircular cross section, a thin homogeneous plane dielectric sheet of finite width, and an inhomogeneous plane sheet. The effects of surface-wave excitation and mutual interaction among the various portions of the dielectric shell are included automatically in this solutiom     

Electromagnetic waves scattering by cylindrical dielectric structures: Application to microwave devices design

A method which allows us to analyze the electromagnetic scattering characteristics of multiple discontinuities in shielded dielectric waveguides is presented. There are not restrictions both geometry of the cross section and electrical parameters of the dielectrics which are assumed to be linear, inhomogeneous, isotropic and free from losses. Each discontinuity is analyzed combining a modal matching technique with a generalized telegraphist's equations formulation; in this way, we obtain its scattering matrix. By using the concept of the generalized scattering matrix of two discontinuities, the equivalent generalized scattering matrix (EGSM) of the cascaded set is calculated. Theoretical and experimental results were obtained for different dielectric structures such as dielectric posts, isolated and coupled, as well as dielectric waveguides with circular cross section connected by means of abrupt and gradual transitions. The experimental values for the scattering properties show a good agrement with the theoretical ones. This study has shown the possibility of using cylindrical dielectric structures to design microwave devices such as: resonators, power-dividers and filters.     

Combined field solution for TM scattering from multiple conducting and dielectric cylinders of arbitrary cross section

A simple moment solution is given for the problem of electromagnetic scattering from multiple conducting and dielectric cylinders of arbitrary cross section. The system of conducting and dielectric cylinders is excited by a plane-wave polarized transverse magnetic to the axis of the cylinders. The equivalence principle is used to obtain three coupled integral equations for the induced electric current on the conducting cylinders and the equivalent electric and magnetic currents on the surface of dielectric cylinders. The combined field integral equation (CFIE) formulation is used. Sample numerical results are presented. The agreement with available published data is excellent.     

Electromagnetic wave scattering from some vegetation samples

For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite length. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements     

On the correspondence of asymptotic solutions to 2D and 3D problems in antenna engineering

A method is developed for calculation of the field radiated by a system of vertically polarized dipoles in the presence of perfectly conducting cylinders whose axes are parallel to the axes of the dipoles. The asymptotic representation of a solution to the 3D vector scattering problem is analyzed. It is shown that the radiation field in the azimuthal plane corresponds to the results of the solution of the scalar problem for the coinciding geometry in the plane of the system’s cross section. The correctness of the proposed reduction is confirmed by simulation results.     

Modeling of arbitrary cross-sectional cylinder using N circular cylinders for the scattering calculations

Exact solution of the electromagnetic wave scattering by N dielectric cylinders is presented by using matrix formulation. To check this present method, two comparisons between exact solutions for a single circular conducting and dielectric cylinder and this model composed of N=25 circular cylinders are made. Numerical results of conducting and dielectric square cylinder has been also checked with well-known result (B.E.M). The scattering patterns and the near field distributions in space are presented for the concave, convex and dielectric circular cylinder with conducting reflector.     

Transient scattering by resistive cylinders

The two-dimensional scattering of an electromagnetic pulse normally incident on a collection of infinitely long cylinders of arbitrary shape is considered. ForE-polarization an electric field integral equation is derived that is applicable to solid cylinders and/or thin sheets, resistive and/or perfectly conducting. The contribution of the self-cell at later times is carefully analyzed. The expression obtained represents a generalization of previously known results. For an incident Gaussian pulse, numerical results are presented for surface currents and far-fields, for perfectly conducting and resistive circular cylinders and strips. A fast Fourier transform (FFT) algorithm is implemented to obtain the backscattering radar cross section, which is in good agreement with results obtained from either exact continuous wave (CW) solutions or the method of moments.     

A hybrid equation approach for the solution of electromagneticscattering problems involving two-dimensional inhomogeneous dielectriccylinders

A numerical procedure for the solution of electromagnetic scattering problems involving inhomogeneous dielectric cylinders of arbitrary cross section is discussed. The cases of illumination by both transverse magnetic (TM) and transverse electric (TE) plane waves are considered. The scattering problems are modeled via a hybrid integral-equation/partial-differential-equation approach. The method of moments is applied to obtain a system of simultaneous equations that can be solved for the unknown surface current densities and the interior electric field. The interior region partial differential equation and the exterior region surface integral equation are coupled in such a manner that many existing surface integral equation computer codes for treating problems involving scattering by homogeneous dielectric cylinders can be modified easily to generate the block of the matrix corresponding to the surface current interactions. The overall system matrix obtained using the method of moments is largely sparse. Numerical results are presented and compared with exact solutions for homogeneous and inhomogeneous circular cylinders     

Scattering by a chiral cylinder of arbitrary cross section

An integral equation and method-of-moments (MM) solution to the problem of scattering by an inhomogeneous chiral cylinder of arbitrary cross section is presented. The volume equivalence theorem for chiral media is developed and used to formulate a set of coupled integral equations for the electric and magnetic volume polarization currents representing the chiral cylinder. These coupled integral equations are solved using a standard pulse basis and point-matching MM solution. Numerical results, including echo width and internal fields, are presented for the scattering by chiral slabs and circular cylinders. These results are compared to exact solutions when available     

An improved pulse-basis conjugate gradient FFT method for the thinconducting plate problem

A conjugate-gradient fast Fourier transform (CG-FFT) formulation for the scattering by a thin, perfectly conducting plate is presented. Pulse basis functions and a Dirac δ function are used for expansion and testing purposes, respectively. Particular attention is paid to the generation of the terms in the impedance matrix of the resulting matrix equation. Except for the self-coupling terms, all the other terms are computed by explicit integrations. Comparison with two previously reported pulse-basis CG-FFT formulations shows that the present method is more stable when the error tolerance of the solution is reduced. When sufficient cell discretizations are used, smooth distributions can be obtained which resemble those obtained via rooftop-CG-FFT formulation. The numerical results are further validated by comparing the far-field radar cross section with an analytical technique for a circular plate     

The field feedback formulation for electromagnetic scattering computations

A new procedure is described for the solution of electromagnetic scattering problems in unbounded regions. Using this technique a spatial region enclosing the scatterer is initially decoupled from the exterior region and the fields therein are considered as the solution of an interior Dirichlet boundary value problem. The interior region solution is then recoupled to the unbounded exterior region by use of the equivalence principle. Such a process can be symbolically represented as a simple feedback system. The formulation is demonstrated for the case of plane wave scattering by finite metallic circular cylinders. A finite element solution of the interior problem is utilized in this example in conjunction with a field representation using a special case of coupled azimuthal potentials.     

An improved MFIE formulation for TE-wave scattering from lossy,inhomogeneous dielectric cylinders

A method-of-moments formulation involving the magnetic-field integral equation (MFIE) is presented for the analysis of nonhomogeneous electric (TE) source. The approach involves the use of triangular subdomain cells, a piecewise linear expansion for the total magnetic field, and point matching at the nodal points of the triangular-cell model. Results for internal fields and radar cross section are presented and shown to be stable and convergent, even for dielectrics characterized by a large-magnitude complex relative permittivity. It is noted that the complementary problem of TM-wave scattering from ferrite cylinders characterized by a permeability function can be treated using the dual to the approach presented     

Scattering by circular metallic disks

The eigenfunction solution for the far-field scattering by a thin, circular metallic disk is summarized. This solution yields both components of the scattered electric field for an incident plane wave of arbitrary polarization and arbitrary incidence directions. Sample amplitude, phase, and cross section results are presented.     

A finite element approach to the electromagnetic interaction withrotating penetrable cylinders of arbitrary cross section

A method for evaluating the fields excited by an obliquely incident plane wave inside and outside a rotating cylinder is presented. A differential formulation of the problem is developed with respect to the comoving reference frame of the scatterer on a closed circular domain including the scatterer cross section; the boundary conditions account for the far-field conditions through a series expansion of the total field on the domain contour. The results at oblique incidence are then particularized for normal incidence and a hybrid finite element numerical solution is presented and discussed for TM incidence. The present FEM approach and the related computer code are directly applicable to the study of rotating piecewise-homogeneous cylinders at normal incidence, as well as metallic cylinders coated by layers of penetrable materials. Through a comparison, for normal incidence, between the quasi-stationary and the Galileian relativistic approach, a method for approximately reconstructing the Doppler frequency shift in the quasi-stationary method is derived. Far-field and near-field numerical results for circular and arbitrarily shaped (metallic or dielectric) cylinders are presented     

TE-wave scattering by a dielectric cylinder of arbitrary cross-section shape

The theory and equations are developed for the scattering pattern of a dielectric cylinder of infinite length and arbitrary cross-section shape. The harmonic incident wave is assumed to have its electric vector perpendicular to the axis of the cylinder, and the fields are assumed to have no variations along this axis. Although some investigators have approximated the field within the dielectric body by the incident field, a more accurate solution is obtained here by treating the field as an unknown function which is determined by solving a system of linear equations. Scattering patterns obtained by this method are presented for dielectric shells of circular and semicircular cross section, and for a thin plane dielectric slab of finite width. The results for the circular shell agree accurately with the exact classical solution. The effects of surface-wave excitation and mutual interaction among the various portions of the shell are included automatically in this solution.     

Reduction of forward scattering from cylindrical objects using hardsurfaces

We discuss how forward scattering can he characterized in terms of an equivalent blockage width, and a relation between this and the bistatic scattering width is derived. Then, we show how cylinders such as struts and masts can be constructed to reduce their blockage widths. Thereby, when the cylinders are mounted in front of an antenna, the sidelobes and losses caused by the blockage will be reduced. For thin metal cylinders the blockage width reduction is obtained by giving its cross section an oblong shape and, in addition (for the TM case), by coating the outer metal surface with dielectric material to obtain a hard boundary condition. For thick cylinders, the reduced scattering is obtained by designing them as dielectric-filled parallel plate waveguides with the outer surfaces of the plates coated in the same way as for the thin struts. Dual-polarized performance is obtained in both cases by strip loading the outer surfaces. The performance of both the thin and the thick struts have limited frequency bandwidth. Both computed and measured results are presented; the computations being done with the moment method. The designs are based on the concept of soft and hard surfaces in electromagnetics, and the results can be regarded as a proof of the existence of hard surfaces for electromagnetic waves. The study considers reduction of forward scattering which also will give a reduction of the total integrated power of the scattered field over all directions-even backward     

Analysis of diffraction of a plane wave and of the field of a point source by a multirow grating

A multirow grating of impedance or dielectric elements is considered. The 2D problem of scattering by such a grating is solved with the help of the modified null field method and the pattern equation method. A system of integral equations is derived and the reflection and transmission coefficients are determined as functions of various parameters of the problem. The excitation of the grating by a current filament is investigated. An asymptotic solution is obtained for the case when the periods of the grating rows and interrow distances are rather large. In the low-frequency approximation, a solution to the problem for a grating of circular cylinders is presented.