Geometrical Theory of Diffraction Formulation for On-Body Propagation

Abstract

A geometrical theory of diffraction model for on-body propagation is developed in this paper. The exact solution to the canonical problem of a plane wave incident on an infinitely long cylinder, with arbitrary constitutive parameters, is found. The same is done for a magnetic and an electric infinitesimal dipole source of any orientation, located on the surface of the cylinder. The exact solutions are transformed with the Watson transformation to yield asymptotic expressions that are valid in the deep shadow region. These asymptotic expressions are validated by comparison to the numerically evaluated exact solution. It is found that the expressions are valid as long as the object is opaque, with a geometry down to the size of (κ/κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + τ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) > λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /2, and the rays not too torsional τ/κ <; 2, where κ and τ are the curvature and torsion of the local geometry, respectively. The asymptotic expressions are found to approximate the exact solution significantly better than the asymptotic expression of an equivalent perfect electric conductor geometry. The same is the case for the impedance boundary condition asymptotic approximation for low dielectric constant materials. Finally, the asymptotic expressions are generalized so they can be applied to any convex geometry of the human body or an opaque lossy dielectric of electrically large size.