Frequency-domain and time-domain novel uniform asymptotic solutions for the scattered fields by an impedance cylinder and a dielectric cylinder, with a radius of curvature sufficiently larger than the wavelength, are presented in this paper. The frequency-domain novel extended UTD and the modified UTD solutions, derived by retaining the higher-order terms in the integrals for the scattered fields, may be applied in the deep shadow region in which the conventional UTD solutions produce the substantial errors. The novel time-domain uniform asymptotic solutions are derived by applying the saddle point technique in evaluating the inverse Fourier transform. We have confirmed the accuracy and validity of the uniform asymptotic solutions both in the frequency-domain and in the time-domain by comparing those solutions with the reference solutions calculated from the eigenfunction expansion (frequency-domain) and from the hybrid eigenfunction expansion and fast Fourier transform (FFT) method (time-domain).

The problem of a Gaussian beam that is incident on a plane dielectric interface from a denser dielectric medium to a rarer one and is reflected at the interface has been important research subjects studied by many researchers. In this paper, we have obtained a novel uniform asymptotic solution for reflection and beam shift of the Gaussian beam that is incident on the interface from the denser medium. The uniform asymptotic solution consists of the geometrically reflected beam, the lateral beam if any, and the newly derived transition beam which plays an important role in the transition region near the critical angle of the total reflection. We have confirmed the validity of the uniform asymptotic solution by comparing with the reference solution obtained numerically from the integral representation. We have shown that, in addition to the Goos-Hanchen shift and the angular shift, the Gaussian beam is shifted to either direction by the interference of the geometrically reflected beam and the lateral beam near the critical angle of the total reflection.

Novel high-frequency asymptotic solutions for the scattered fields by a dielectric circular cylinder with a radius of curvature sufficiently larger than the wavelength are presented in this paper. We shall derive the modified UTD (uniform Geometrical Theory of Diffraction) solution, which is applicable in the transition regions near the geometrical boundaries produced by the incident ray on the dielectric cylinder from the tangential direction. Also derived are the uniform geometrical ray solutions applicable near the geometrical boundaries and near the caustics produced by the ray family reflected on the internal concave boundary of the dielectric cylinder. The validity and the utility of the uniform solutions are confirmed by comparing with the exact solution obtained from the eigenfuction expansion.

In this paper, we have derived a novel integral representation for the ground wave propagation over land-to-sea mixed-paths by applying the Helmholtz-Kirchhoff integral theorem. By using the method of stationary phase applicable uniformly as the stationary phase point approaches the endpoint of the integral, we have derived the asymptotic solution for the scattered fields consisting of the first-order and the second-order diffraction terms. We show that the asymptotic solution thus derived agrees with the asymptotic solution derived by applying the aperture field method (AFM) and the method of stationary phase. We have confirmed the validity and the utility of the novel integral representation and its asymptotic solution by comparing with the widely used mixed-path theorem and the experimental measurement performed in Kanto area and Tokyo bay.

In this paper, we have derived the new solution for the medium-frequency and the high-frequency ground wave propagation in a surface duct over mixed-paths. We have shown newly that the solution for the ground wave propagation in a standard atmosphere can be obtained directly from the solution for the surface duct problem by applying the analytic continuation from the negative equivalent radius of curvature of the earth to the positive one. Through the theoretical and experimental studies, it is confirmed that the radio wave propagating over the sea in the land-to-sea mixed-paths is enhanced by the recovery effect. It is clarified that the ground wave is also enhanced in the surface duct in a long range propagation. It is shown that the unexpected attenuation and the anomalous variation with distance are appeared in the propagation in the urban area due to the emergence of the slow-wave type trapped surface wave.

We have derived the novel extended UTD (Uniform Geometrical Theory of Diffraction) solution and the novel modified UTD solution for the back scattering of an incident whispering gallery (WG) mode on the edge of a cylindrically curved conducting sheet. By comparing with the reference solution obtained from the integral representation of the scattered field by integrating numerically along the integration path, we have confirmed the validity and the utility of the novel asymptotic solutions proposed in the present study. It is shown that the extended UTD solution can be connected smoothly to the modified UTD solution on the geometrical boundary separating the edge-diffracted ray and the surface-diffracted ray.

In this paper, we have obtained the integral representation for the ground wave propagation over land-to-sea mixed-paths which uses the equivalent current source on an aperture plane. By extending the integral to the complex plane and deforming the integration path into the steepest descent path, we have derived a simple integral representation for the mixed-path ground wave propagation. We have also derived the hybrid numerical and asymptotic representation for an efficient calculation of the ground wave and for easy understanding of the diffraction phenomena. By using the method of the stationary phase applicable uniformly as the stationary phase point approaches the endpoint, we have derived the high-frequency asymptotic solution for the ground wave propagation over the mixed-path. We have confirmed the validity of the various representations by comparing both with the conventional mixed-path theory and with the experimental results performed in Kanto areas including the sea near Tokyo bay. By examining the asymptotic solution in detail, we have found out the cause or the mechanism of the recovery effect occurring on the portion of the sea over the land-to-sea mixed-path.

We study the high-frequency asymptotic analysis methods for the scattered fields by a cylindrically curved conducting surface excited by the incident wave on the curved surface from the convex side. We first derive the novel hybrid ray-mode solution for the scattered fields near the concave surface by solving a canonical problem formulated under the assumption that the cylindrically curved conducting surface possesses only one edge. Then by applying the ray tracing technique and the idea of Keller's GTD (Geometrical Theory of Diffraction), the solutions derived for the canonical problem are extended to account for the problem of the radiation from and the scattering by the other edge of the cylindrically curved surface. We confirm the validity of the novel asymptotic representations proposed in the present study by comparing both with the numerical results obtained from the method of moment and the experimental results performed in the anechoic chamber.

When a cylindrically curved concave conducting surface is terminated abruptly at the edge, the whispering gallery (WG) mode propagating toward the edge direction is radiated into the free space from the aperture plane at the edge. In this paper, by applying the new analysis method, we shall derive a uniform geometrical theory of diffraction solution (UTD) for the electric-type WG mode radiation field applicable in the transition region near the geometrical boundaries produced by the incident modal ray on the edge of the curved surface. The UTD is represented by the summation of the solution for the geometrical ray converted from the modal ray of the WG mode and the solution for the uniform edge diffracted ray scattered at the cylindrically curved edge. By comparing with the reference solution obtained numerically from the integral representation of the radiation field, we will confirm the validity and the utility of the UTD proposed in this paper.