Abstract
Using a variational method, we recently determined an electromagnetic “signature” for characterizing a straight wire in free space. The signature consists of the first five resonant frequencies and their widths, more compactly expressed as the first five complex-valued resonant frequencies. Here we apply the variational method to the much more complicated case of determining the same signature for a straight wire or wire pair on a flat interface between a homogeneous earth and air. To calculate the resonances we obtain an integral equation for the current on a wire on the interface between two dielectric media. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current in an equivalent thin strip on the interface has non-zero solutions. The variational method extracts good approximations to these complex-valued resonant frequencies, without having to solve the integral equation. A table of resonances is given for the case of a relative dielectric constant of the earth equal to 4 and for three values of the ratio of wire radius to wire half-length.
Highlights
I T has long been of interest to establish electromagnetic signatures by which to recognize objects
The problem is to find the first five resonant frequencies for electromagnetic radiation scattered by this thin strip as functions of the strip length, strip width, and the dielectric constant of earth and of air; the width of each resonance is to be determined
In order to get an idea of the size of this error, we proceed in a two-phase cycle: first we provisionally accept the value of complex-valued resonant frequency k2,n, which we rewrite as k2(1,n), determined as above and use it to obtain an improved approximation Iap(2)(x) to the current; second we use the improved approximation to the current to refine the approximation of the resonant frequency, denoted k2(2,n)
Summary
I T has long been of interest to establish electromagnetic signatures by which to recognize objects. In the early 1970’s resonant frequencies were defined as the complex values of frequency at which a homogeneous integral equation (in which the incident field is set to zero) has a non-zero solution for the current [1], [2]. 2) To obtain an integrable kernel, the trick is similar to that used in the case of a single medium: in Sec. III we determine a pair of complex-valued zeros in the Fourier transform of the electric-field kernel with respect to distance along the strip, based on an approximation valid for a thin strip. 4) In Sec. V, the complex-valued resonant frequencies are defined as the frequencies at which the homogeneous integral equation for the current in the strip has non-zero solutions.
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