Michael Katsav

Gaussian Beams Summation Representation of Half Plane Diffraction: A Full 3-D Formulation

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 GBs 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.

Complex-source beam diffraction by an acoustically soft or hard circular cone

An analytical approach is presented to analyze the diffraction of a scalar complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone. The beam is described by a spherical-multipole expansion and impinges exactly on the tip of the cone from an arbitrary direction. The numerical results include an investigation of the total field and of the convergence properties of the method.

A Beam Summation Representation for 3-D Radiation From a Line Source Distribution

We introduce a Gaussian beams summation (GBS) scheme for radiation from a source distribution along a line in a 3-D configuration. The expansion is based on a discrete phase-space decomposition of the source distribution along the source axis, thus describing the field as a sum of Gaussian beams (GBs) emerging from a discrete set of points along the axis, at a discrete set of directions in a polar coordinate system. Applications to GBS representation of fields diffracted by edges is 3-D configurations are discussed.

Gaussian Beam Summation Representation of a Two-Dimensional Gaussian Beam Diffraction by a Half Plane

A Gaussian beam summation (GBS) representation for half plane diffraction of an incident two dimensional Gaussian beam (GB) that hits arbitrarily close to the edge is presented. The scattered field is expanded into an angular spectrum of GBs that emerge from the edge. We derive asymptotic expressions for the diffracted beams amplitudes, that are valid uniformly as a function of the distance of the incident beam from the edge and of the scattering beams angles. In the limiting cases when the incident GB hits far from the edge, these expressions reduce uniformly to a geometrical optics model plus a weak edge diffractions due to the off-axis beam field that hits the edge. Applications to GBS modeling of indoor propagation are discussed.

Phase Space Gaussian Beam Summation Analysis of Half Plane Diffraction

The canonical problem of scattering of an ultrawideband (UWB) plan wave by a perfectly conducting half plane is analyzed via the UWB frame-based Gaussian beam summation (GBS) formulation of . The scattered field is described as a sum of isodiffracting-Gaussian beams (ID-GB) that emerge from the edge in a discrete frequency-independent lattice of directions, plus beams that describe the geometrical optics reflections. Asymptotic expressions for the diffracted beams excitation amplitudes are derived, interpreted, and validated via a comparison with an exact numerical calculations. The beams that are strongly excited are those associated with the geometrical optics and the edge diffracted rays. As discussed in the conclusions to this paper, the quality of the present GBS scheme deteriorates for grazing incidence and/or observations, hence we propose an alternative GBS scheme that is expected to be more useful for edge diffraction problems. This issue will be presented in a future publication.

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

We present a beam summation (BS) representation for the field scattered by an impedance wedge illuminated by a general 3D electromagnetic Gaussian beam (EM-GB). The emphasis here is not only on the solution of the beam diffraction problem, but mainly on the BS representation. In this representation, the field is expressed as a beam optics (BO) term plus an edge field, described as a sum of diffracted EM-GBs emerging from a discrete set of points and directions along the edge. We introduce an edge-fixed set of EM-GBs that provides a basis for the edge field. The expansion coefficients (the beams excitation amplitudes) account in a dyadic format for the polarization of the incident beam and also for its direction, displacement from the edge, collimation, and astigmatism. We derive exact expressions for these coefficients as well as simpler approximations that are valid uniformly as a function of the incident beam distance from the edge. The results of this paper provide essential building blocks for a BS representation of EM fields in complex configurations, where the source excited field is described as a sum of beam propagators, and the diffracted fields generated by propagators that hit near edges are also described using beams.

Electromagnetic complex-source beam diffraction by the tip of a circular cone

The paper deals with the electromagnetic scattering and diffraction of a complex-source beam by a perfectly electrically conducting (PEC) semi-infinite circular cone. Particularly, we are interested in the diffraction by the tip of the circular cone as a function of various parameters (opening angle of the cone, angle of incidence, polarization). The results are important in the context of the application of asymptotic methods like GTD, UTD, or the complex-ray tracing (CRT) method.

Beam summation analysis of half plane diffraction

This scenario has been addressed within the analytical framework of the ultra wideband phase-space GBS method. In spite of the satisfactory field results, that formulation has been found to be inconvenient for the edge diffraction problem, mainly due to the fact that it utilizes a non-uniform angular lattice of beams that becomes increasingly denser for large tilt angles. To overcome these difficulty this paper analyzes a similar problem using the GBS scheme which is more convenient for localized scatterers. In this paper the spectral function that controls the GB2GB scattering matrix is derived and a numerical demonstration is presented

Converging and Diverging Beam Diffraction by a Wedge: A Complex-Source Formulation and Alternative Solutions

In a previous publication, the problem of 2-D beam diffraction by a wedge has been solved via the complex-source (CS) approach. However, the straightforward CS formulation may be applied only when the incident beam is diverging as it hits the edge, but not when it is converging as it hits the wedge. In this paper, we generalize the CS setup, so that it can address both problems. The surprising result is that the CS approach can be applied for the converging beam case, but only if the CS coordinates are defined in a specific fashion. We then formulate the angular harmonics and the spectral integral representations for both cases, and also derive uniform asymptotic expressions for beam diffraction by a wedge. The validity of the results is verified by calculating the diffracted field via each one of these formulations, and comparing them with yet another approach, wherein the field of the incident diverging or converging beam is synthesized using a plane-wave integral, and the diffracted field is then calculated via multipole expansion. The overall goal of this paper is the derivation of techniques for the analysis of 3-D beam diffraction by a cone.

Scattering and diffraction of an arbitrarily directed complex-source beam by a semi-infinite circular cone

The problem of an arbitrarily directed Gaussian beam (GB) illuminating an acoustically soft or hard semi-infinite circular cone is solved by using a complex source beam (CSB) whose waist and direction are defined by the real and imaginary parts of the source coordinate, respectively. The corresponding scalar boundary-value problem is solved by assigning a complex-valued source coordinate into the conventional spherical-multipole expression of the Greens function, thus converting it to the response to the incident CSB. The solution requires the calculation of the associated Legendre functions of the 1st kind for a complex-valued argument. Beside a numerical analysis of these calculations, we also present numerical results for the total near- and far-fields.