Exact Gaussian-Beam Theory for Outgoing and Standing Spherical Waves: Application to Transmitting and Receiving Antennas

Outgoing spherical vector-wave functions are expressed in terms of Gaussian beams (also called complex source-point beams) radiating in all directions. By use of a vector-wave expansion, the electromagnetic field of an arbitrary source of finite extent is thus expressed in terms of Gaussian beams with weights determined directly from the spherical expansion coefficients of the source. These outgoing-wave formulas allow the field of any transmitting antenna to be expressed in terms of Gaussian beams. Elementary Gaussian-beam receivers are introduced as the electromagnetic field at complex points in space. The outputs of elementary Gaussian-beam receivers pointing in all directions determine the spherical expansion coefficients in a standing-wave expansion. These standing-wave formulas allow the output of any receiving antenna to be expressed in terms of the outputs of elementary Gaussian-beam receivers. Combining the formulas for outgoing and standing waves produces a new antenna-antenna transmission formula based solely on Gaussian beams. The theory is exact and validated through numerical examples.