Directivity and Image Principle From Reflective Surfaces

The theory of one or more radiating sources above a reflective surface with an arbitrary reflection coefficient is presented in this letter. Using this generalized approach, it is demonstrated that optimal configurations exist between the sources and the reflective surface. Examples are given for one or two infinitely small electric dipoles above a reflective surface. A maximum directivity of approximately 10.2 dBi and 14.1 dBi is obtained, respectively. Furthermore, using a more hypothetical approach that considers the reflective behavior of a given surface, a directivity limit for vanishingly small Huygens sources over a generalized reflective surface is derived to be $ 12$ dBi.