TY - JOUR

T1 - Gaussian beams summation representation of half plane diffraction

T2 - A full 3-D formulation

AU - Katsav, Michael

AU - Heyman, Ehud

N1 - Funding Information:
Manuscript received June 09, 2008; revised November 17, 2008. Current version published April 08, 2009. This work is supported in part by the Israeli Science Foundation under Grant 674/07, and by NATO’s Public Diplomacy Division in the framework of the Science for Peace program, under Grant SfP982376.

PY - 2009

Y1 - 2009

N2 - The diffracted field due to a general 3-D Gaussian beam (GB) impinging close to an edge of a half-plane is expressed as a sum of diffracted GB's emerging from a discrete set of points and directions along the edge axis. The expansion utilizes an edge-fixed lattice of expansion beams, involving a phase-space beam expansion along the edge and an angular spectrum of beam around the edge. The excitation amplitudes of the diffracted beams, defined as the beam to beam (B2B) scattering matrix, are derived, interpreted, and validated via a comparison with an exact numerical solution. The representation is valid uniformly as a function of the incident beam direction and its distance from the edge. The asymptotic limits when the beam impinges far from the edge are interpreted via the geometrical theory of diffraction (GTD). The general procedure for calculating the B2B scattering coefficients may be applied for other wedge-type configurations. The new formulation enables the construction of self-consistent Gaussian beams summation (GBS) representations in complex configurations, in which the field is described as a sum of beam propagators, and the diffracted fields due to the propagators that hit near edges are also expanded in terms of beams. Applications to GBS modeling of urban propagation are discussed.

AB - The diffracted field due to a general 3-D Gaussian beam (GB) impinging close to an edge of a half-plane is expressed as a sum of diffracted GB's emerging from a discrete set of points and directions along the edge axis. The expansion utilizes an edge-fixed lattice of expansion beams, involving a phase-space beam expansion along the edge and an angular spectrum of beam around the edge. The excitation amplitudes of the diffracted beams, defined as the beam to beam (B2B) scattering matrix, are derived, interpreted, and validated via a comparison with an exact numerical solution. The representation is valid uniformly as a function of the incident beam direction and its distance from the edge. The asymptotic limits when the beam impinges far from the edge are interpreted via the geometrical theory of diffraction (GTD). The general procedure for calculating the B2B scattering coefficients may be applied for other wedge-type configurations. The new formulation enables the construction of self-consistent Gaussian beams summation (GBS) representations in complex configurations, in which the field is described as a sum of beam propagators, and the diffracted fields due to the propagators that hit near edges are also expanded in terms of beams. Applications to GBS modeling of urban propagation are discussed.

KW - Astigmatic Gaussian beams

KW - Beam diffraction

KW - Beam-to-beam (B2B) scattering matrix

KW - Edge-diffraction

KW - Gaussian beams summation method

KW - Uniform asymptotics

UR - http://www.scopus.com/inward/record.url?scp=65549084861&partnerID=8YFLogxK

U2 - 10.1109/TAP.2009.2013436

DO - 10.1109/TAP.2009.2013436

M3 - מאמר

AN - SCOPUS:65549084861

VL - 57

SP - 1081

EP - 1094

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 4 PART 2

ER -