Exact Plane-Wave Expansion With Directional Spectrum: Application to Transmitting and Receiving Antennas

A new exact plane-wave expansion is presented for general time-harmonic electromagnetic fields radiated by an arbitrary finite source region in three dimensions. The plane-wave expansion employs a directional spectrum that is proportional to the far-field pattern of the source. The directionality is achieved through an exact representation that involves a beam parameter, which determines the sharpness of the spectrum. When the beam parameter is set to zero, the new expansion becomes identical to the plane-wave expansion employed in the fast multipole method. The expansion is exact for observations points all the way up to the source region and includes evanescent waves. An antenna- antenna transmission formula follows straightforwardly. Numerical examples demonstrate that the new plane-wave expansion requires fewer plane waves than previously derived plane-wave expansions.