Techniques based on the method of modal expansions, the Rayleigh-Stevenson expansion in inverse powers of the wavelength, and also the method of moments solution of integral equations are essentially restricted to the analysis of electromagnetic radiating structures which are small in terms of the wavelength. It therefore becomes necessary to employ approximations based on “high-frequency techniques” for performing an efficient analysis of electromagnetic radiating systems that are large in terms of the wavelength.

Techniques for High-Frequency Problems

The geometrical theory of diffraction and its application

An asymptotic solution for the electromagnetic diffraction by a perfectly conducting strip illuminated at grazing incidence is obtained by an extension of the uniform GTD. Uniform expressions for the scattered field are given for plane, cylindrical, and spherical wave illuminations. Outside the transition regions these essentially reduce to results obtained by an ordinary application of the uniform GTD augmented by slope diffraction. In the case of plane wave illumination a very simple closed form expression is provided for the scattered far field. Numerical results are presented and compared with those calculated from a moment method solution.

A uniform GTD solution for the diffraction by strips illuminated at grazing incidence

A tunnel is modeled as congregates of walls, with the wall being approximated by a uniform impedance surface. The aim is to get a solution for a canonical problem of a wedge with uniform impedance surface. The diffraction by a right-angle wedge with different impedance boundary conditions at its two surfaces is first considered. A functional transformation is used to simplify the boundary conditions. The eigenfunction solutions for the transformed functions are replaced by integral representations, which are then evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. The asymptotic solution is interpreted ray optically to obtain the diffraction coefficient for the uniform geometrical theory of diffraction (UTD). The obtained diffraction coefficients are related directly to the Keller diffraction coefficients in the uniform version. The total field is continuous across the shadow of the geometrical optics fields.

/pdf/ray-optical-prediction-of-radio-wave-propagation-47i80sz15a.pdf

Ray-optical prediction of radio-wave propagation characteristics in tunnel environments. 1. Theory

The canonical problem of evaluating the scattered field at a finite distance from the edge of an impedance wedge which is illuminated by a line source is considered. The presentation of the results is divided into two parts. In this first part, reciprocity and superposition of plane wave spectra are applied to the left far-field response of the wedge to a plane wave, to obtain exact expression for the diffracted field and the surface wave contributions. In addition, a high-frequency solution is given for the diffracted field contribution. Its expression, derived via a rigorous asymptotic procedure, has the same structure as that of the uniform geometrical theory of diffraction (UTD) solution for the field diffracted by a perfectly conducting wedge. This solution for the diffracted field explicitly exhibits reciprocity with respect to the direction of incidence and scattering. >

High-frequency scattering from a wedge with impedance faces illuminated by a line source. I. Diffraction

: A ray-fixed coordinate system is introduced and used to derive a new, compact form of the dyadic diffraction coefficient for an electromagnetic wave incident on a perfectly-conducting wedge. This diffraction coefficient is merely the sum of two dyads; furthermore, with the use of simple correction factors which have the same form for plane, cylindrical, conical or spherical waves incident on the edge, the dyadic diffraction coefficient is valid in the transition regions of the shadow and reflection boundaries.

/pdf/the-dyadic-diffraction-coefficient-for-a-perfectly-dxjd531wjb.pdf

P. H. Pathak

Papers

The dyadic diffraction coefficient for a perfectly conducting wedge