Resonant properties of conducting polyhedral spheres with polygon mesh surfaces

Abstract

A spherical polyhedron constructed from open surface polygons is an electromagnetic wave resonator that can be excited by an external plane wave. After an initial transient, a plane wave pulse achieves a balance of EM wave energy entering the sphere though the surface polygons and the internal EM wave leaking out of the sphere through the same polygons. The resonant frequencies of the porous sphere are primarily determined by the radius of the sphere and, to a lesser degree, by the size of the openings in the surface of the sphere. The strength of the internal electric fields is influenced by the width of the conducting edges that comprise the polyhedron frame. With thin edges, the internal resonance is too weak to produce large electric fields. With thick edges that nearly close the openings in the sphere, not much of the external electric field is available to excite the internal fields and again they are weak. The optimum edge width is found where the external EM wave field excites the strongest internal field amplitudes. The WIPL-D EM simulation model is used to determine the optimum porous resonator for a polyhedron with 180 vertices, 92 open polygon faces, and 270 conducting edges [1]. With a sphere radius of 5 meters, the resonance for the TM 101 like mode occurs at a frequency of 25.228 MHz with edges having a radius of 225 mm. Excited with a right-hand-circular EM wave at 1 V/m, the internal resonant electric field is calculated to be 91.5 V/m. The Q of this resonator is 885 assuming infinitely conducting edges. With this high Q, an EM pulse takes about 100 micro seconds to build up a large electric field inside the sphere. Other spherical cavity modes were simulated to provide different distributions of electric fields on the interior of the porous spherical cavity resonator (PSCR). The PSCR may be used to greatly increase the electric fields in a high power radio beam for the purpose of plasma generation. For certain wavelengths, the porous sphere becomes a resonator with large internal electric fields. At resonance, the radar cross section increases by over 40 dB. The radar wavelength is small relative to the size of the surface holes. The resonator theory is being tested at 2.45 GHz using an open-face, sphere with 960 vertices and tuned conducting edges. The large variations in RCS with frequency are studied with inside a compact range, anechoic chamber at the Naval Research Laboratory.