A Transmission-Line Model for Wave Excitation of a Porous Conducting Sphere

A wire mesh conformed to a spherical surface forms a spherical polyhedron that has unique resonator and scattering properties for electromagnetic (EM) waves. Excitation of the spherical polyhedron by an incident plane wave at specified resonant frequencies yields large internal electric fields. Narrowband enhancements in the backscatter radar cross section are found at these same frequencies. These effects are explained with a model where the mesh is treated as an inductive frequency-selective surface that is used to match a shorted-line resonator attached to a transmission line. With this transmission-line model, the impedance of the inductive surface is shown to be an addition to the expression for the spherical harmonic series used to describe solid conducting spheres and spherical cavities. The resonant modes for the internal and external electric fields of the porous sphere are found with this formulation. The surface mesh is used in the low-frequency limit, where the EM wavelength is much larger than the polygon's holes in the mesh. The impedance (inductance and resistance) of the mesh are adjusted by varying the radii of the edges of the polygons and the conductivity of the edge material. Applications of the spherical porous conducting resonator (SPCR) include glow plasma discharges, measurements of dielectric constants of gases, and frequency-selective radar targets.