Efficient Sampling and Interpolation-Based Representation of the Fields Produced by Gaussian Window Source Distributions

Gaussian beam summation methods rely on the phase-space representation of aperture fields and induced sources using Gaussian window-based frames and the analytical propagation of their radiated fields. The radiation can be conveniently approximated by Gaussian beam propagators or by their full-wave extensions, namely, the complex source beams, at O(1) operation per observation point. These approximations, however, are only accurate along the beam axis. Off the beam axis, they become increasingly inaccurate. The error may not be of importance, in most cases, for the analysis of fields in slowly varying inhomogeneous media. However, in multiple-scattering or intricate propagation scenarios, which typically involve diffraction phenomena, the field may be of particular interest in shadow regions. In these areas, the fields can be governed by diffraction contributions. When these are excited by off-axis parts of the beam, the results can exhibit a significant relative error and render the model inadequate. For such cases, computation of the radiation by Gaussian windows to a prescribed accuracy, without needing to compute aperture field integrals, is desirable.