Cavity resonances and mutual coupling in concave waveguide arrays

A method is presented for the mutual coupling analysis of concave, circular cylindrical or spherical waveguide arrays. The array is considered as a set of waveguides that are coupled through a prefectly conducting, lossless cavity, which leads to an equivalent multiport network. The corresponding scattering matrix is obtained by matching the cavity and waveguide fields over the guide apertures and solving the resulting equation by Galerkin's method. In particular the complications are discussed, which arise from the possibly large number of degenerate, resonant cavity modes. A result obtained is the general condition that at a resonance the total aperture field (for all waveguide apertures) must be orthogonal to the set of degenerate, resonant cavity modes. This leads, with certain exceptions, to zero coupling between the guides whenever the total number of aperture modes (for all waveguides) is less than or equal to the number of resonant cavity modes.