Rotationally symmetric arrays of apertures on conducting spherical surfaces

Performance of rotationally symmetric arrays of apertures on conducting spherical surfaces has been investigated. Circular waveguide fed apertures are arranged in equispaced rings around the conducting spherical surface. The electromagnetic fields in the exterior spherical region as well as in the interior spherical cavity region are expanded in terms of spherical transmission lines modes whereas the aperture fields are expressed in terms of circular waveguide modes. The array problem is formulated assuming dominant TE sub 11 mode fields, in general dually polarized, at the apertures. M rings of N aperture elements each are considered. Consecutive rings are in general staggered. For each phase sequence excitation of the array, the array problem reduces to that of an unit cell spherical waveguide containing M apertures (angular frequency domain formulation). Alternatively, the same problem is formulated via unitary transformation in eigen basis of the original array admittance matrix (azimuthal angular domain formulation).