A phase-space Gaussian beam summation representation of rough surface scattering

Abstract

A Gaussian beam (GB) summation representation for rough surface scattering is introduced. In this scheme, the coherent and incoherent scattered fields are described by a phase-space summation of GBs that emanate from the rough surface at discrete set of points and directions. It thus involves stochastic GB2GB scattering matrices for the coherent and incoherent fields, and deterministic GB propagators. It benefits from the simplicity and accuracy of the latter, and can be used in applications involving propagation in complex scenarios comprising inhomogeneous media with rough surface boundaries. The GB2GB matrices are calculated from the statistical moments of the scattering amplitude, which are given either analytically or empirically. An analytical and numerical example for weakly rough surface is presented and discussed. Applications to the more complicated propagation scenario of doubly rough surface waveguide with multiple reflection phenomena will be presented in a follow-up publication.

Gaussian Beam Summation Representation of Beam Diffraction by an Impedance Wedge: A 3D Electromagnetic Formulation Within the Physical Optics Approximation

“…The first condition in (29) implies that the beam is well collimated, while the second one implies that the discretization is sufficiently fine on the beamwidth scale. Finally, the azimuthal beam angles in (22) are given by (30) …”

“…where is defined in (29). Equation (32) also defines the waist-width and the diffraction-angle in that plane.…”

Time-Dependent Tilted Pulsed-Beams and Their Properties

“…Furthermore, beam-type expansions are usually tuned such that the scattering of a single spectral PB occurs in the well-collimated zone were the tiled PBs exhibit an enhanced accuracy. It should be noted though that in some practical applications the choice of is a tradeoff between collimation and spatial localization in relation to the size of the details in the medium [47], [48].…”

TE and TM beam decomposition of time-harmonic electromagnetic waves

“…(28) is applied here for the special case of Gaussian frames, which have been used extensively for modeling beam propagation because they maximize the localization as implied by the uncertainty principle and yield analytically trackable beam-type propagators [1,2,[4][5][6][7]9,10,15,16]. The Gaussian synthesis windows are defined as…”

“…The directional and spatial localization of beam-type (phasespace) spectral representations make these schemes highly suitable for propagation in complex environments [1][2][3][4][5][6]. In these expansion schemes, the propagating elements are Gaussian beams, which have been termed phase-space (spectral) Green's functions [7,8].…”