A novel expression for the mutual admittance of planar radiating elements

The mutual admittance between two identical planar radiating apertures can be expressed as the bidimensional Fourier transform of a function (defined in the wavenumbers plane), obtained by taking the inner product of the plane wave spectrum (representing the field radiated by the element) by another plane wave spectrum obtained from it by reversing the sense of propagation of each component wave. The asymptotic evaluation of the expression shows that (under certain limitations) the mutual admittance, for large spacing among the radiators, tends to be proportional to the power radiation pattern on the plane of the aperture. By using the formalism here introduced the "grating lobes series" for the driving point admittance of an element in an infinite periodic array can be simply derived from the "mutual admittances series." As a check of the theory the mutual admittance between rectangular slots, in different relative positions, has been numerically calculated.