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For pt.I seeibid. vol.46, no.9, p.1328, (1998).The uniform theory of diffraction (UTD) developed in part 1 is used to predict narrow- and wide-band propagation characteristics in tunnels at 900- and 1800-MHz. Narrow-band propagation characteristics is shown in the spatial domain and wide-band propagation in the time domain. In empty straight-tunnel environments, propagation exhibits a break-point phenomenon and has very short time delay spread. In empty curved or branched tunnel environments, propagation suffers higher loss. Vehicles cause additional propagation loss and larger varying time delay spread in tunnels. The measured results have validated the accuracy of the theoretical model and provided important information on narrow-band and wide-band propagation characteristics in empty, branched and obstructed tunnels.

A theoretical approach based on the geometrical theory of diffraction is used to study the electromagnetic radiation from a narrow slot in a dielectric-covered perfectly-conducting surface terminated at an edge. The total far-zone field is composed of a geometrical optics field and a diffracted field. The geometrical optics field is the direct radiation from the slot to the field point. The slot also generates surface waves which are incident at the termination of the dielectric cover, where singly-diffracted rays and reflected surface waves are excited. The diffraction and reflection coefficients are obtained from the canonical problem of the diffraction of a surface wave by a right-angle wedge where the dielectric-covered surface is approximated by an impedance surface. This approximation is satisfactory for a very thin cover; however, the radiation from its vertical and faces cannot be neglected in treating the thicker dielectric cover. This is taken into account by using a Kirchhoff-type approximation, which contributes a second term to the diffraction coefficient previously obtained. The contributions from the geometrical optics field, the singly-diffracted rays and all significant multiply-diffracted rays are summed to give the total radiation. Calculated and measured patterns are found to be in good agreement.

Summary form only given. This article begins with an account of how Professor Robert E. Collin's work has impacted on the author's own teaching and research. Particular note is made of his contributions to dyadic Green's functions and to his book Field Theory of Guided Waves. It then moves on to a description of how an important discovery impacted on the author's research. In a paper by Keller (1953) edge and vertex diffracted rays were introduced using a generalization of Fermat's principle. But no expressions were given for the fields which propagate along the ray paths, so it was impossible to apply this intriguing method at the time. However, a few years later Keller published expressions for the fields of rays diffracted from a wedge in the scalar acoustic case and in the electromagnetic case when the wedge is perfectly conducting. He then referred to the method as the geometrical theory of diffraction (GTD). His expressions for the diffraction coefficients were accurate away from the shadow and reflection boundaries, but they failed at and near these boundaries. Clearly, new expressions were needed and they could be found from the solution of the canonical problem only if uniform asymptotic methods were used. The author and his graduate students derived uniform diffraction coefficients for plane, cylindrical, conical and spherical wave illumination of the wedge.

Summary form only given. In the first half of the last century there was relatively little work on high frequency diffraction. However all that changed in 1953 when Keller introduced the geometrical theory of diffraction (GTD) as an extension of geometrical optics to include diffracted rays. This was a very important development, because it made it possible to calculate the high frequency radiation from antennas and scatterers of a quite general shape and to understand the various radiation mechanisms involved. Also, the GTD motivated the asymptotic treatment of the numerous canonical problems to determine the fields diffracted from edges, vertices and smooth curved surfaces. Unfortunately the GTD diffracted fields failed at and near the shadow boundaries of the incident and reflected fields, so the uniform GTD (UTD) was developed to overcome this limitation. In the UTD the canonical problems are solved by uniform asymptotic methods, and the resulting diffracted field not only describes the field in the shadow region, it also compensates the discontinuities in the geometrical optics field at the shadow boundaries. In this paper the canonical problems which have been solved are reviewed and some of the work which remains to be done is described. In conclusion, the relationship of the UTD to other high frequency methods such as the physical theory of diffraction and the method of incremental edge diffraction is discussed.

Summary form only given. The author presented a brief history of the UTD (uniform theory of diffraction) for the diffraction by edges in perfectly conducting surfaces. Particular attention was given to the three-dimensional case for the perfectly conducting wedge; a reexamination of the solution to the canonical wedge problem; and double diffraction, where a second edge is illuminated by a field from the first edge which is not ray optical. >

In this paper the geometrical theory of diffraction is extended to treat the radiation from apertures or slots in convex perfectly conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is represented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres, and spheroids.

The conditions for radar cross-section measurement are given in terms of permissible variations in the amplitude and phase of the incident field at the target. A number of minimum range conditions are listed and discussed. The minimum range associated with the uniform square aperture antenna is analyzed and its relationship to the sensitivity of measurement is determined. Measurements of small targets in the near zones of focused and unfocused apertures are examined. The substantial range reduction possible with the use of a suitable microwave lens, when measuring large and medium size targets, is indicated.

In recent years the geometrical theory of diffraction (GTD) has developed rapidly as a practical tool for calculating the radiation from complex shapes. At the present time it has progressed beyond the treatment of simple examples to the construction of user-oriented computer programs for antenna and scattering problems of engineering interest.

An integral of the type which commonly occurs in radiation theory is evaluated by the method of steepest descent to optain a well-known asymptotic expansion. The coefficients of the first three terms of this expansion are given in terms of functions and derivatives of functions which appear in the integrand; the coefficient of the third term does not appear to have been given previously.

A power conservation principle for electromagnetic fields in the presence of moving boundaries is stated and applied to an example which illustrates its usefulness. The present interpretation of power conservation is seen to differ from that given earlier by Pauli.