Assessment and Accurate Evaluation of Antenna Superdirectivity Limits with Spherical Wave Expansion

The spherical wave expansion characterizing the radiated field of a two-infinitesimal-dipole-end-fire array is analyzed in this work and optimized to achieve the maximum directivity. In particular, the paper shows how the maximum directivity can be analytically derived in the case where the interelement spacing tends to zero. Analytic excitation coefficients needed to reach that maximum directivity are also derived in the proposed study. A general expression of the maximum directivity achievable by P-dipole end-fire arrays is then proposed. This limit can be considered as an upper bound and generalizes the analysis proposed by Uzkov in the case of isotropic source based end-fire arrays. A numerical analysis is also proposed to validate the upper bound when infinitesimal electrical dipoles are used.