Gaussian ray basis functions for EM fields and their applications in rapid analysis of parabolic reflector antennas

A modified geometrical optics (GO) field with a Gaussian exponential amplitude taper resembling the far zone behavior of a conventional Gaussian beam (GB) is presented. Unlike a well-focused GB which is narrow in its angular spread but is spatially wide, the modified GB field presented remains small in both the angular and spatial domains in much the same manner as does a discrete GO ray tube. Such a modified GO field is referred to as a Gaussian ray basis function (GRBF) because a scalar (acoustic) wave field can be expanded in a set of GRBFs In much the same fashion as one can expand a wave field in terms of Gaussian beams (GBs); also, within its region of validity, the GRBF can be shown to satisfy the wave equation within the asymptotic high frequency approximation. Furthermore, the scalar GRBF can be extended in a simple manner to obtain a GRBF for the vector electromagnetic (EM) case. A direct application of the GRBFs is for rapidly analyzing the high frequency EM radiation from an electrically large reflector antenna.