A Canonical UTD Solution for Electromagnetic Scattering by an Electrically Large Impedance Circular Cylinder Illuminated by an Obliquely Incident Plane Wave

Abstract

Abstract-A uniform geometrical theory of diffraction (UTD) solution is developed for the canonical problem of the electromagnetic (EM) scattering by an electrically large circular cylinder with a uniform impedance boundary condition (IBC), when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transform, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TE¡. and TM¡. waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the geometrical optics (GO) or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution.

Modeling Human Blockage at 5G Millimeter-Wave Frequencies

“…When the scattering problem extends to 3D as oblique incidence of a plane wave to consider, e.g., scenarios with different heights of TX and RX antennas, closed form solutions of the scattering field do not exist. It is necessary to rely on a numerical electromagnetic field solver [17] and more extensive numerical integration [21] in this case.…”

Geometrical Theory of Diffraction Formulation for On-Body Propagation

“…Note that [19] has a sign error in the coefficient named c n as pointed out in [9]. The problem has also previously been solved for a IBC cylinder [11]. The notation of [11] is used.…”

“…A GTD/UTD formulation for the Impedance Boundary Condition (IBC) was done in [11], [12] and for dielectric coated cylinders in [13], [14]. These approximations would be more appropriate to use for on-body propagation than the PEC assumption.…”

“…Therefore, it is relevant to find a formulation valid for human tissue. However, the approaches used in [11]- [14] are useful.…”

An Efficient Numerical Technique to Calculate the High Frequency Diffracted Fields From the Convex Scatterers With the Fock-Type Integrals

“…Section 2 gives a vivid depiction about the traveling of rays and introduces the UTD solution in a scalar form. The situation for the electromagnetic scattered by a PEC and impedance circular cylinder is illuminated by an incident plane wave [25] which contains both TM and TE Pekeris functions. In Section 3, the quadrature scheme for these Pekeris functions and the numerical results of the integrals are presented.…”