Analysis of superdirective Huygens source based end-fire arrays

In this paper, the directivity limit of end-fire arrays based on Huygens source elements has been numerically investigated. Firstly, the elementary infinitesimal Huygens source behavior is introduced and studied through Spherical Wave Expansion (SWE). Then, the maximum theoretical directivity of two-, three- and four-element arrays is calculated as a function of the inter-elements spacing. The optimization has been performed using a synthesis method based on SWE. For an inter-element spacing of a tenth of the wavelength, the obtained directivities are equal to 9.0 dBi, 11.7 dBi and 13.7 dBi for the two-, three- and four-element arrays, respectively.