Time-Domain Radiation From Large Two-Dimensional Apertures via Narrow-Waisted Gaussian Beams

This paper deals with the short-pulse radiation of three-dimensional (3-D) vector electromagnetic fields from arbitrarily polarized large two-dimensional (2-D) truncated aperture distributions, which are parameterized in terms of narrow-waisted ray-like pulsed Gaussian basis beams centered on a discretized Gabor lattice in a four-dimensional (4-D) configuration-spectrum phase space. The study extends our previous Gabor-based investigation of time-domain (TD) short-pulse radiation of 2-D fields from 1-D large truncated apertures with nonphased, linearly phased (delayed) and nonlinearly phased focusing aperture field profiles [1]. We begin with, and summarize, a Gabor-based frequency domain (FD) formulation of the 2-D aperture problem which has been presented and tested elsewhere [2], [3], but we include additional numerical examples for validation and quality assessment. As in [1], we access the time domain by Fourier inversion from the FD, starting from the initial 3-D space-time Kirchhoff formulation (whose numerical integration furnishes reference solutions), and then passing on to Gabor-parameterized field representations in terms of pulsed beam (PB) wavepackets which are launched by linearly and nonlinearly phase-delayed focusing aperture distributions. Example calculations and comparisons with numerically generated reference data serve to calibrate the Gabor-PB algorithms and assess their domains of validity.