Robert A. Shore

Correction to "Application Of Incremental Length Diffraction Coefficients To Calculate The Pattern Effects Of The Rim And Surface Cracks Of A Reflector Antenna"

Incremental length diffraction coefficients (ILDCs) for the half-plane are integrated around the rim of a paraboloid reflector antenna to obtain well-behaved far fields of the nonuniform current for all angles of observation. These far fields, when added to the physical optics far field, produce a more accurate total far field of the reflector. Excellent agreement with the far fields obtained from a method-of-moments solution to the electric field integral equation applied to a 20-wavelength-diameter reflector shows that the cross polarization, farther-out sidelobes, and fields near nulls of reflector antennas can be appreciably modified by the fields of the nonuniform currents. ILDCs are also used to investigate the effect of cracks on the surface of reflectors that can result from the imperfect fitting together of panels to form large reflectors. Three models of cracks are studied. Significant pattern effects are found, depending on the model and orientation of the cracks. >

Traveling Electromagnetic Waves on Linear Periodic Arrays of Lossless Penetrable Spheres

Traveling electromagnetic waves on infinite linear periodic arrays of lossless penetrable spheres can be conveniently analyzed using the source scattering-matrix framework and vector spherical wave functions. It is assumed that either the spheres are sufficiently small, or the frequency such, that the sphere scattering can be treated using only electric and magnetic dipole vector spherical waves, the electric and magnetic dipoles being orthogonal to each other and to the array axis. The analysis simplifies because there is no cross-coupling of the modes in the scattering matrix equations. However, the electric and magnetic dipoles in the array are coupled through the fields scattered by the spheres. The assumption that a dipolar traveling wave along the array axis can be supported by the array of spheres yields a pair of equations for determining the traveling wave propagation constant as a function of the sphere size, inter-sphere separation distance, the sphere permittivity and permeability, and the free-space wave number. These equations are obtained by equating the electric (magnetic) field incident on any sphere of the array with the sum of the electric (magnetic) fields scattered from all the other spheres in the array. Both equations include a parameter equal to the ratio of the unknown normalized coefficients of the electric and magnetic dipole fields. By eliminating this parameter between the two equations, a single transcendental equation is obtained that can be easily solved numerically for the traveling wave propagation constant. Plots of the k - β diagram for different types and sizes of spheres are shown. Interestingly, for certain spheres and separations it is possible to have multiple traveling waves supported by the array. Backward traveling waves are also shown to exist in narrow frequency bands for arrays of spheres with suitable permittivity and permeability.

Dual-surface integral equations in electromagnetic scattering

A brief review is given of the derivation and application of dual-surface integral equations, which eliminate the spurious resonances from the solution to the original electric-field and magnetic-field integral equations applied to perfectly electrically conducting scatterers. Emphasis is placed on numerical solutions of the dual-surface electric-field integral equation for three-dimensional perfectly electrically conducting scatterers.

Traveling Waves on Three-Dimensional Periodic Arrays of Two Different Alternating Magnetodielectric Spheres

An exact k-beta (dispersion) equation to within the dipole scattering approximation has been obtained for a 3D array of two different alternating magnetodielectric spheres. The dispersion equation has the form of equating to zero the determinant of a system of four homogeneous equations in the normalized scattered field coefficients. Computationally efficient expressions are obtained for the coefficients of the homogeneous equation system as functions of the sphere radii, permittivities, and permeabilities, the free-space electrical separation distance of the array elements (kd), and the electrical separation distance (betad) for the traveling wave supported by the array. For a given value of kd and an array of lossless scatterers the determinant equation can be solved for real betad by a simple search procedure. For an array of lossy scatterers betad is complex and a more difficult minimization in the complex plane is required to solve the determinant equation. The solution to the dispersion equation also yields values for the effective permittivity and permeability of the array regarded as a continuous medium. Computations were performed to investigate the performance of two-sphere arrays of lossless dielectric spheres, with the permittivities and radii of the two different dielectric spheres composing the array chosen so that the first magnetic dipole resonant frequency of one set of spheres equals the first electric dipole resonant frequency of the second set of spheres. Although it is shown that arrays composed of two different alternating purely dielectric spheres can behave as isotropic DNG media unlike arrays of identical dielectric spheres, the bandwidths are considerably narrower than those achievable with arrays of identical magnetodielectric spheres with appreciable permittivity and permeability close to each other. The practicality of using arrays of alternating two different purely dielectric spheres to fabricate DNG media depends on whether the narrow bandwidths are acceptable for the desired applications.

Shadow boundary incremental length diffraction coefficients applied to scattering from 3-D bodies

Shadow boundary incremental length diffraction coefficients (SBILDCs) are high-frequency fields designed to correct the physical optics (PO) field of a three-dimensional (3-D) perfectly electrically conducting scatterer. The SBILDCs are integrated along the shadow boundary of the 3-D object to approximate the field radiated by the nonuniform shadow boundary current (the difference between the exact and PO currents near the shadow boundary). This integral is added to the PO field to give an approximation to the exact scattered field that takes into account both PO and nonuniform shadow boundary currents on the scatterer. Like other incremental length diffraction coefficients, any SBILDC is based on the use of a 2-D canonical scatterer to locally approximate the surface of the 3-D scatterer to which it is applied. Circular cylinder SBILDCs are, to date, the only SBILDCs that have been obtained in closed form. In this paper, these closed-form expressions are validated by applying them for the first time to a 3-D scatterer with varying radius of curvature-the prolate spheroid. The results obtained clearly demonstrate that for bistatic scattering the combined PO-SBILDC approximation is considerably more accurate than the PO field approximation alone.

Incremental length diffraction coefficients for the shadow boundary of a convex cylinder

Incremental length diffraction coefficients (ILDCs) are obtained for the shadow boundaries of perfectly electrically conducting (PEC) convex cylinders of general cross section. A two-step procedure is used. First, the nonuniform (NU) current in the vicinity of the shadow boundary is approximated using Fock (1965) functions. The product of the approximated current and the free-space Greens function is then integrated on a differential strip of the cylinder surface transverse to the shadow boundary to obtain the ILDCs. This integration is performed in closed form by employing quadratic polynomial approximations for the amplitude and unwrapped phase of the integrand. Examples are given of both the current approximations and the integration procedure. Finally, as an example, the scattered far field of a PEC sphere is obtained by adding the integral of the NU ILDCs of a circular cylinder along the shadow boundary of the sphere to the physical optics (PO) far field of the sphere. This correction to the PO field is shown to significantly improve upon the accuracy of the PO far-field approximation to the total scattered field of the sphere.

A simple derivation of the basic design equation for offset dual reflector antennas with rotational symmetry and zero cross polarization

A simple geometric derivation is given of the equation for designing an offset dual reflector antenna with perfect rotational symmetry and zero cross polarization.

A sector nulling technique revisited

Ers (1990) Lagrangian multiplier quadratic constraint technique for broad sector nulling in linear array antenna patterns is modified in several ways to increase its applicability.

Electromagnetic Waves on Partially Finite Periodic Arrays of Lossless or Lossy Penetrable Spheres

An exact computable expression is obtained for the electromagnetic field of a three-dimensional partially finite periodic array of lossless or lossy magnetodielectric spheres illuminated by a plane wave propagating parallel to the array axis. The array is finite in the direction of the array axis and is of infinite extent in the directions transverse to the array axis. Illustrative numerical examples are presented.

A LOW ORDER-SINGULARITY ELECTRIC-FIELD INTEGRAL EQUATION SOLVABLE WITH PULSE BASIS FUNCTIONS AND POINT MATCHING

Abstract : Unlike the magnetic-field integral equation, the conventional form of the electric-field integral equation (EFIE) cannot be solved accurately with the method of moments (MOM) using pulse basis functions and point matching. The highly singular kernel of the EFIE, rather than the current derivatives, precludes the use of the pulse-basis function point-matching MOM. A new form of the EFIE has been derived whose kernel has no greater singularity than that of the free-space Greens function. This new low-order singularity form of the EFIE, the LEFIE, has been solved numerically for perfectly electrically conducting bodies of revolution (BORs) using pulse basis functions and point-matching. Derivatives of the current are approximated with finite differences using a quadratic Lagrangian interpolation polynomIal. This simple solution of the LEFIE is contingent, however, on the vanishing of a linear integral that appears when the original EFIE is transformed to obtain the LEFIE. This generally restricts the applicability of the LEFIE to smooth closed scatterers. Bistatic scattering calculations performed for a prolate spheroid demonstrate that results comparable in accuracy to the conventional EFIE can be obtained with the LEFIE using pulse basis functions and point matching provided a higher density of points is used close to the ends of the BOR generating curve to compensate for the use of one-sided finite difference approximations of the first and second derivatives of the current.