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The far field characteristics are examined for a circular cylinder with two axial slots covered by an eccentric dielectric material. Solutionsare found by applying the boundary-value method to the wave functionsof the fields. The addition theorem and the orthogonality of Bessel and trigonometric functions are respectively used to find an infinite series expressions. Numerical results are obtained by shortening the produced series to a finite number of terms due to the convergence of the summation and compared to previous works.

An analytic solution to the problem of a plane electromagnetic wave scattering by two infinitely long lossy dielectric elliptic cylinders is presented using an iterative procedure to account for the multiple scattered field between the cylinders. To compute the higher order terms of the scattered fields, the translation addition theorem for Mathieu functions is implemented to express the field scattered by one lossy dielectric cylinder in terms of the elliptic coordinate system of the other cylinder in order to impose the boundary conditions. Scattered field coefficients of various orders are obtained and written in matrix form. Numerical results are obtained for the scattered field in the far zone for different axial ratios, electrical separations, relative dielectric constants, and angles of incidence.

Analytical solution of the problem of a plane electromagnetic wave scattering by two infinitely long dielectric coated confocal conducting elliptic cylinders is derived. The incident, scattered and transmitted fields in every region are expressed in terms of Mathieu functions. To impose the boundary conditions, the translation addition theorem for Mathieu functions is implemented to express the scattered field by one cylinder in terms of the elliptic coordinate system of the other cylinder. The resulting system of equations is written in matrix form while the scattered and transmitted field coefficients are obtained by using matrix inversion. Numerical results are obtained for the scattered field in the far zone for different axial ratios, electrical separations, relative dielectric constants, and angles of incidence.

Analytical solution to the problem of scattering of a plane electromagnetic wave by an array of conducting spheres each coated with a dielectric layer is derived. The incident, scattered and transmitted electric and magnetic fields are expressed in terms of the vector spherical wave functions. The vector spherical translation addition theorem is applied to impose the boundary conditions on the surface of each dielectric‐coated sphere. Numerical results are computed and presented graphically for the radar cross of several configurations of dielectric‐coated spheres.

An analytic solution to the problem of a plane electromagnetic wave scattering by two parallel elliptic conducting cylinders is presented using an iterative procedure to account for the multiple scattered field between the cylinders. To compute the higher order terms of the scattered fields, the translation addition theorem for Mathieu functions is implemented to express the field scattered by one cylinder in terms of the elliptic coordinate system of the other cylinder in order to impose the boundary conditions. Scattered field coefficients of various orders are obtained and written in matrix form. Numerical results are obtained for the scattered field in the far zone for different axial ratios, electrical separations and angles of incidence.

The resonant scattering characteristics of a slit coupled cylindrically eccentric impedance cavity are examined using direct integration equation technique, and the incident wave is assumed to be a H-polarized plane wave. Such a slit coupled eccentric impedance cavity is assumed to be infinite in length and of infinitely thin wall surrounded by several impedance screens. By using the Galerkin's method combined with translational addition theorem for cylindrical wave functions, a system of linear equations of infinite order for determining the induced current distributions are derived in an analytical form. Therefore, numerical results are presented to show the effects of cavity geometrical and impedance parameters on the resonant scattering characteristics of some typical structures in the far zone.

The scattering of electromagnetic plane waves from a multi-eccentric cylinder at oblique incidence is analyzed analytically and numerically. The solution is determined by solving the scalar wave equation in the cylindrical coordinates for the various geometric regions, utilizing the translational addition theorem of Bessel functions, and applying the boundary conditions at the material interfaces. Both polarizations of the incident plane wave (TM and TE with respect to the z-axis ) are considered. The resulting solution consists of a system of coupled equations for the unknown expansion or scattering coefficients. Expressions for the extinction, scattering, and back scattering cross sections are the same as those for a single homogeneous cylinder. A numerical algorithm for the solution is developed and tested for several limiting and special cases. Comparisons of the results of this algorithm with those reported in the literature show excellent agreements. Numerical calculations indicate that the scatteri...

The analytical solution for the scattering of electromagnetic plane waves from an infinitely long homogeneous cylinder of arbitrary material, in an eccentric coating at oblique incidence, is presented. The solution is determined by solving the scalar wave equation in the cylindrical coordinates, for the various geometric regions and by applying the boundary conditions at the material interfaces. Furthermore, the translational addition theorem of Bessel functions is utilized for transferring the fields component between two cylindrical coordinate systems. Both polarizations of the incident plane wave (TM and TE with respect to the z -axis) are considered. The resulting solution consists of a system of eight coupled equations for the unknown expansion or scattering coefficients. Expressions for the extinction, scattering, and back scattering cross sections are presented. A numerical algorithm for the solution is developed, implemented, and tested for several limiting and special cases. Comparisons of the re...

We consider the following scattering problem: An arbitrarily polarized plane wave, propagating in an unbounded bianisotropic space, is obliquely incident on an array of parallel bianisotropic cylinders which are enclosed by another bianisotropic cylinder. The boundary value problem is formulated in terms of a set of two coupled second order differential equations. The solution technique combines the method of separation of variables with the translational addition theorem. The matrix elements of the resulting linear algebraic system are given by single-term analytical expressions. Numerical examples are presented for several cases along with comparisons with previously published results.

The effect of eccentricity on the complex resonances of a conducting sphere eccentrically coated by a dielectric one is investigated. The solution of the boundary value problem is obtained in terms of spherical eigenwaves in combination with the translational addition theorem. The resonant wavenumbers are calculated from the numerical solution of a characteristic determinantal equation. The analysis is also specialized to the case of small eccentricity and closed form expressions are derived for the resonant wavenumbers. It is found that the restriction of small eccentricity is not severe. It is also found that under the influence of eccentricity the resonant wavenumbers are considerably displaced in the complex plane. This may be used in the identification of the position and the size of inhomogeneities inside spherical bodies.

The solution to the problem of electromagnetic waves scattering by an array of spheres is used to simulate the scattering by a spheroid. The scattering by an array of spheres is formulated by expressing the incident, transmitted, and scattered fields in terms of the vector spherical wave functions, and the boundary conditions are satisfied by applying the translation addition theorem for the vector spherical wave functions. The advantage of using the proposed technique is the simplicity and efficiency in computation. The modeling of a conducting or dielectric spheroid is outlined and numerical results are presented graphically and compared with those based on other available methods to show the validity of the analysis.

The transversely bianisotropic uniaxial medium, a generalization of the well-studied chiral material, can be fabricated by mixing metal helices in an isotropic host medium in such a way as to have the axes of all helices randomly oriented but perpendicular to a fixed direction. In the present consideration, based on the concept of characteristic waves and the method of angular spectral expansion, field representations in this class of medium are developed. The analysis reveals that the solutions of source-free Maxwell's equations for transversely bianisotropic uniaxial medium can be expressed in sum-integral forms of circular cylindrical vector wave functions. The addition theorem of vector wave functions for transversely bianisotropic uniaxial medium can be straightforwardly derived from that of vector wave functions for isotropic medium. Applications of the proposed theory to electromagnetic scattering are presented.

Two efficient ways of calculating the vector addition theorem are presented. One is obtained by relating the coefficients of the vector addition theorem to that of the scalar addition theorem for which an efficient recurrence relation exists. The second way is to derive recurrence relations directly for the coefficients of the vector addition theorem. These new ways of calculating the coefficients are of reduced computational complexity. Hence, when the number of coefficients required is large, the present methods are many times faster than the traditional method using Gaunt coefficients and Wigner 3j symbols.

Recurrence relations for the elements of a translation matrix in the scalar addition theorem in three-dimensions using spherical harmonics are derived. These recurrence relations are more efficient to evaluate compared to the use of Gaunt coefficients evaluated with Wigner 3j symbols or with recurrence relations. The efficient evaluation of the addition theorem is important in a number of wave scattering calculations including fast recursive algorithms.

A review of a recursive algorithm with a more succinct derivation is first presented. This algorithm, which calculates the scattering solution from an inhomogeneous body, first divides the body into N subscatterers. The algorithm then uses an aggregate T matrix and translation formulas to solve for the solution of n+1 subscatterers from the solution for n subscatterers. This recursive algorithm has reduced computational complexity. Moreover, the memory requirement is proportional to the number of unknowns. This algorithm has been used successfully to solve for the volume scattering solution of two-dimensional scatterers for Ez -polarized waves. However, for Hz -polarized waves, a straightforward application of the recursive algorithm yields unsatisfactory solutions due to the violation of the restricted regime of the addition theorem. But by windowing the addition theorem, the restricted regime of validity is extended. Consequently, the recursive algorithm with the windowed addition theorem works well eve...

The gyromagnetic uniaxial chiral medium, which is a generalization of the well-studied reciprocal chiral material, can be created by mixing three sets of small metal helices in a host gyromagnetic medium (e.g., magnetically biased ferrite), with the axes of two sets perpendicular and parallel to a fixed direction, respectively, and the other set distributed in random orientations and locations. Based on the concept of characteristic waves and the method of angular spectral expansion, vector wave functions are rigorously developed to represent the electromagnetic fields in a source-free gyromagnetic uniaxial chiral medium. The analysis reveals that the solutions of the source-free vector wave equation for the gyromagnetic uniaxial chiral medium, which are composed of two transverse waves and a longitudinal wave, can be represented in sum-integral forms of the cylindrical vector wave functions. Addition theorem of the vector wave functions for gyromagnetic uniaxial chiral medium can be directly obtained fro...