Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers. I. Plane layer

High-frequency propagation of electromagnetic wavefields from an extended planar aperture distribution through a complicated environment is addressed. Geometric optical ray tracing provides a versatile approximate approach to the class of problems, but it fails in transition regions surrounding shadow boundaries and caustics. The uniformity required there can be established by field tracking with Gaussian beams. The basic theory is summarized and applied to the two-dimensional test problem of transmission of radiation from a finite one-dimensional plane aperture through a planar dielectric layer. For a truncated uniform or focused aperture illumination, tracking the edge or caustic transition regions through the layer when it is located within the Fresnel zone of the aperture poses a problem of substantial complexity. It is shown that narrow-waisted beams, which can be propagated in their far zone as complex ray fields, reconstruct the correct transmitted field in these cases, as established independently by numerical evaluation of an exact spectral integral