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.     

Bidirectionality of Reciprocal, Lossy or Lossless, Uniform or Periodic Waveguides

Using the scattering-matrix equations for two antennas placed in the fields of a waveguide, it is proven that all reciprocal, lossy or lossless, uniform or periodic waveguides are bidirectional. Since Maxwell's equations imply directly that propagation constants on a lossless reciprocal waveguide come in pairs (beta,-beta*), "complex waves" on a lossless reciprocal, uniform or periodic waveguide come in quadruplets with propagation constants (beta,-beta, beta*,-beta*).     

Travelling electromagnetic waves on linear periodic arrays of lossless spheres

Source scattering-matrix analyses of travelling waves on infinite linear periodic arrays of lossless spheres and of small electric wires are applied to determine the propagation constants of dipolar travelling waves on an infinite linear periodic chain of metallic nanospheres.     

Shadow boundary incremental length diffraction coefficients appliedto 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     

Broadside radar cross section of the perfectly conducting cube

The broadside radar cross section (RCS) of the perfectly conducting cube is predicted from arbitrarily low to arbitrarily high frequencies, and compared to measured data taken for cube side lengths ranging from 0.15 to 4 wavelengths. The predicted and measured RCS curves agree to within the estimated experimental limits of accuracy ofpm 1dB. At low frequencies the magnetic-field integral equation was "augmented" to eliminate its spurious homogeneous solutions and thus to produce high accuracy beyond the resonance region up through the intermediate frequency range. At high frequencies the conventional diffraction solution was "enhanced" to produce high accuracy down through the intermediate frequency range into the resonance region. Close agreement between these two very different theoretical solutions in the intermediate frequency range confirmed the validity of each solution and permitted calculation of reliable curves for the amplitude and phase of the backscattered far field versus frequency.     

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     

Application of incremental length diffraction coefficients tocalculate the pattern effects of the rim and surface cracks of areflector 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     

Sampling in plane-polar coordinates

A number of details are clarified regarding the sampling-reconstruction theorem for near-field scanning in plane-polar coordinates. The rigorous sampling-reconstruction theorem is applied to the near-field measurement of a circular aperture test antenna offset from the plane-polar axis of rotation, so that a large number of angular modes are necessary to represent the fields of the test antenna. An algorithm is described for computing accurately and rapidly the required zeros of Bessel functions of arbitrary integer order     

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