Scattering by Two Parallel Thin Posts Inside a Parallel-Plate Waveguide

The scattering of a guided mode propagating inside a parallel-plate waveguide by two thin cylindrical posts is studied in the phasor domain, with a time-dependence factor exp(+j(1)t) omitted throughout. Since the wave equation is not separable in the bi-cylindrical coordinate system [1], this is a two-body problem that involves an infinite number of successive interactions between the posts. However, as originally noted by Twersky [2], an approximate solution may be obtainable in closed form when the interacting scatterers are small. In the present case, the small parameter is the ration of the wires diameter to the wavelength, i.e., ka is very small compared to one, where k = 2π/λ is the wavenumber and a is the radius of the posts. Such an approximation was implemented to obtain a closed-form solution for normal incidence of a plane wave on two parallel thin cylinders of infinite length [3], and for E-polarization that solution is also the solution for the scattering of the TEM fundamental mode inside the parallel-plate waveguide.