Optimal tuning of open 2D resonators by thin metallic rods located near the aperture

Thin metallic rods or wires are often used for tuning slotted resonators and waveguides. A vast number of publications have appeared in the literature and some of the approaches are exemplified in references [1] - [5] In this paper we consider a perfectly electrically conducting two-dimensional slotted cylindrical cavity of arbitrary cross-section, and a thin metallic rod or wire aligned with the axis of the cavity, also of arbitrary cross-section. The electromagnetic interaction between the rod and cavity may be posed as a classical boundary value problem for the 2D Helmholtz equation, where the structure is illuminated by an E-polarised time-harmonic electromagnetic plane wave.