Gaussian field expansions for large aperture antennas

An approximate theory of large aperture antennas is developed where aperture, Fresnel, and far fields are expressed in the form of Ganssian field expansions. First, aperture fields, i.e., aperture distributions, are expanded in orthogonal Hermite-Ganssian and Laguerre-Gaussian functions for antennas with rectangular and circular geometries, respectively. Then solution of the Fresnel-Kirchoff diffraction integrals yields the Fresnel and far field expansions. Care is taken to assure the direct transformability of the aperture fields. Optimal scale factors contained in the aperture field expansions are derived and lead to structured field distributions where sidelobes are added sequentially as more terms in the expansions are used in the computations. Tables of optimal scale factors and series coefficients are provided for cosine, truncated Ganssian and Taylor aperture distributions. Several examples are provided that demonstrate the usefulness of the formulas.