In this study, the edge diffraction of a TM-polarized electromagnetic plane wave by two-dimensional dielectric wedges has been analyzed. An asymptotic solution for the radiation field has been derived from equivalent electric and magnetic currents which can be determined by the geometrical optics (GO) rays. This method may be regarded as an extended version of physical optics (PO). The diffracted field has been represented in terms of cotangent functions whose singularity behaviors are closely related to GO shadow boundaries. Numerical calculations are performed to compare the results with those by other reference solutions, such as the hidden rays of diffraction (HRD) and a numerical finite-difference time-domain (FDTD) simulation. Comparisons of the diffraction effect among these results have been made to propose additional lateral waves in the denser media.

An interpretation method of inversion phenomena is newly proposed for backward transient scattered field components for both E- and H-polarizations when an ultra-wideband (UWB) pulse wave radiated from a line source is incident on a two-dimensional metal cylinder covered with a lossless dielectric medium layer (coated metal cylinder). A time-domain (TD) asymptotic solution, which is referred to as a TD saddle point technique (TD-SPT), is derived by applying the SPT in evaluating a backward transient scattered field which is expressed by an integral form. The TD-SPT is represented by a combination of a direct geometric optical ray (DGO) and a reflected GO (RGO) series, thereby being able to extract and calculate any backward transient scattered field component from a response waveform. The TD-SPT is useful in understanding the response waveform of a backward transient scattered field by a coated metal cylinder because it can give us the peak value and arrival time of any field component, namely DGO and RGO components, and interpret analytically inversion phenomenon of any field component. The accuracy, validity, and practicality of the TD-SPT are clarified by comparing it with two kinds of reference solutions.

In this study, edge diffraction of an electromagnetic plane wave by two-dimensional conducting wedges has been analyzed by the physical optics (PO) method for both E and H polarizations. Non-uniform and uniform asymptotic solutions of diffracted fields have been derived. A unified edge diffraction coefficient has also been derived with four cotangent functions from the conventional angle-dependent coefficients. Numerical calculations have been made to compare the results with those by other methods, such as the exact solution and the uniform geometrical theory of diffraction (UTD). A good agreement has been observed to confirm the validity of our method.

The problem of E-polarized plane wave diffraction by a thin material strip is analyzed using the Wiener-Hopf technique together with approximate boundary conditions. Exact and high-frequency asymptotic solutions are obtained. Our final solution is valid for the case where the strip thickness is small and the strip width is large in comparison to the wavelength. The scattered field is evaluated asymptotically based on the saddle point method and a far field expression is derived. Numerical examples on the radar cross section (RCS) are presented for various physical parameters and the scattering characteristics of the strip are discussed in detail.

The diffraction by a thin material strip is analyzed for the H-polarized plane wave incidence using the Wiener-Hopf technique together with approximate boundary conditions. An asymptotic solution is obtained for the case where the thickness and the width of the strip are small and large compared with the wavelength, respectively. The scattered field is evaluated asymptotically based on the saddle point method and a far field expression is derived. Scattering characteristics are discussed in detail via numerical results of the radar cross section.

A frequency-domain (FD) uniform asymptotic solution (FD-UAS) which is useful for engineering applications is newly derived for the two-dimensional scattered magnetic field by a coated conducting cylinder covered with a thin lossy medium. The FD-UAS is uniform in the sense that it remains valid within the transition region adjacent to the shadow boundary, and it smoothly connects a geometric optical ray (GO) solution and a geometrical theory of diffraction (GTD) solution exterior to the transition region, respectively. We assume that the thickness of a coating medium is thin as compared with one wavelength of a cylindrical wave radiated from a magnetic line source. This uniform asymptotic solution is represented by a combination of scattered field component solutions, namely, the GO solution composed of a direct GO (DGO) and a reflected GO, the extended uniform GTD (extended UTD) solution made up of a DGO and a pseudo surface diffracted ray (pseudo SD), the modified UTD solution representing SD series, and the GTD solution for a lowest order SD. The FD-UAS is valid for a source point and/or an observation point located either near the coating surface or in the far-zone. The effectiveness and usefulness of the FD-UAS presented here are confirmed by comparing with both the exact solution and the conventional UTD shadow region solution.

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.

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 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.

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).

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.