As a method of analyzing the wave scattering from a finite periodic surface, this paper introduces a periodic approach. The approach first considers the wave diffraction by a periodic surface that is a superposition of surface profiles generated by displacing the finite periodic surface by every integer multiple of the period . It is pointed out that the Floquet solution for such a periodic case becomes an integral representation of the scattered field from the finite periodic surface when the period goes to infinity. A mathematical relation estimating the scattering amplitude for the finite periodic surface from the diffraction amplitude for the periodic surface is proposed. From some numerical examples, it is concluded that the scattering cross section for the finite periodic surface can be well estimated from the diffraction amplitude for a sufficiently large .

We have discussed a ray tracing method to estimate the scattering characteristics from random rough surface. It has been shown from the traced rays that the diffracted rays dominate over the reflected rays. For the field evaluation, we have used the Fresnel function for the diffracted coefficient and the Fresnel's reflection coefficients. Numerical examples have been carried out for the scattering characteristics of an ocean wave-like rough surface and the delay spared characteristics of a building-like surface. In the present work we have demonstrated that the ray tracing method is effective to numerical analysis of a rough surface scattering.

The diffraction problem of a Gaussian beam by finite number of periodic slots in a parallel-plate waveguide filled with a homogeneous dielectric is considered. The integro-differential equation for the unknown equivalent surface magnetic current density over the slots is derived and solved by the method of moments (piecewise sinusoidal Galerkin method). From some theoretical results for the angular diffraction pattern, the present geometry is observed to simulate well the previous rectangular groove geometry from the viewpoint of scattering behaviour. In addition, two types (resonance and non-resonance types) of Bragg blazing phenomena are discussed. Simultaneous Bragg and off-Bragg blazing is also demonstrated.

The capability of frequency-swept cross-borehole radar to detect an empty rectangular cylinder embedded in a dielectric medium is simulated numerically by employing the boundary element method. The frequency loci providing the strongest double dips in the received signal pattern are plotted as functions of the observation distance and the cross-sectional width. It is found that, regardless of the shape of the rectangular cross-section, the strongest double dips become double nulls in the near-field region.

A novel method for image reconstruction of a microwave hologram synthesized from one-dimensional data is proposed. In the data acquisition, an emitting antenna is shifted along a line. At every position of the emitting antenna, the amplitude and phase of diffraction fields are measured with a detecting antenna along a line perpendicular to the shifted direction. An equivalent two-dimensional diffraction field is synthesized from the one-dimensional data sets. The conventional reconstruction method applied to the one-dimensional configuration was the Fresnel approximation method. In this paper, an equivalent diffraction is introduced in order to obtain better images than the Fresnel approximation. An experiment made at 10 GHz shows the usefulness of the proposed method.

The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.

Diffraction pattern functions of an E-polarized scattering by a wedge composed of perfectly conducting metal and lossless dielectric with arbitrary permittivity are analyzed by applying an improved physical optics approximation and its correction. The correction terms are expressed into a complete expansion of the Neumann's series, of which coefficients are calculated numerically to satisfy the null-field condition in the complementary region.

Simple approximate formulas are obtained for the mutual impedance and admittance by using a product of radiation patterns of antennas. The formulas come from a stationary expression of the reaction integral between two antennas where far-field approximations are employed. The theory deals with antennas in free space as well as under the presence of a wedge. Two applications are given for microstrip antennas with experimental verifications.

This paper presents a prediction of the millimeter-wave multipath propagation characteristics in the typical urban environment. To analyze the propagation in an outdoor environment, the three dimensional model based on the geometrical optics and the uniform geometrical theory of diffraction is employed. Prediction by the three dimensional ray tracing method needs a detailed map, which records locations and shapes of obstacles surrounding a transmitter and a receiver. It is usually difficult to create a complete map because tremendous data is necessary to describe the area structure. We propose, in this report, a three dimensional propagation model to predict the millimeter wave propagation characteristics by using the information available from only a map on the market. This approach gives us much convenience in the actual design. The modeled results are demonstrated and furthermore comparison are made between the simulated results and the experimental data.

A correction of the physical optics approximation by accounting for the presence of specific currents concentrated near shadow boundaries on the surface of a convex non-metallic scatterer is analysed by considering a canonical problem of diffraction of a plane electromagnetic wave incident normally to the axis of an infinite circular cylinder with impedance boundary conditions. The analysis focuses on the development of Fock-type asymptotic representations for magnetic field tangent components on the surface of the scatterer. The Fock-type representation of the surface field is uniformly valid within the penumbra region, providing a continuous transition from the geometrical optics formulas on the lit portion of the surface to the creeping waves approximation in the deep shadow region. A new numerical procedure for evaluating Fock-type integrals is proposed that extracts rapidly varying factors and approximates the rest, slowly varying coefficients via interpolation. This allows us to obtain accurate and simple representations for the shadow boundary currents that can be directly inserted into the radiation integral and effectively integrated. We show that accounting for the shadow boundary currents considerably improves the traditional PO analysis of the high-frequency electromagnetic fields scattered from smooth and convex non-metallic obstacles, particularly near the forward scattering direction.

We present an experimental and theoretical study of multiple diffraction rings of a cw Ar+ laser beam from a nitrobenzene solution of BDN (bis-(4-dimethylaminodithiobenzil)-nickel) caused by the spatial self-phase modulation. We examine in detail the effect of the intensity and phase shift profiles of the beam in the nonlinear medium by comparing the measured ring patterns with the theoretical results based on the Fraunhofer diffraction. Although the thickness of the sample is only 180 µm in our experiment, it is found that the intensity and phase shift profiles are broadened owing to the self-defocusing effect. It is also found that the phase shift profile is further broadened by the thermal diffusion. These two effects become remarkable when the focused beam is used.

It is shown from the Hilberts theory that if the real function Π(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factor π+(θ) and its complex conjugate π-(θ)(=). This factorization is tested to decompose a real far-zone field pattern having zeros. To this end, the factorized factors are described in terms of bicomplex mathematics. In our bicomplex mathematics, the temporal imaginary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i2=-1 and j2=-1.

The H-polarized diffraction by a wedge consisting of perfect conductor and lossless dielectric is investigated by employing the dual integral equations. Its physical optics diffraction coefficients are expressed in a finite series of cotangent functions weighted by the Fresnel reflection coefficients. A correction rule is extracted from the difference between the diffraction coefficients of the physical optics field and those of the exact solution to a perfectly conducting wedge. The angular period of the cotangent functions is changed to satisfy the edge condition at the tip of the wedge, and the poles of the cotangent functions are relocated to cancel out the incident field in the artificially complementary region. Numerical results assure that the presented correction is highly effective for reducing the error posed in the physical optics solution.

In this paper, a quite general systematic procedure is presented for defining incremental field contributions, that may provide effective tools for describing a wide class of scattering and diffraction phenomena at any aspect, whthin a unitary, self-consistent framework. This is based on a generalization of the localization process for cylindrical canonical problems with elementary source illumination and arbitrary observation aspects. In particular, it is shown that the spectral integral formulation of the exact solution may also be represented as a spatial integral convolution along the axis of the cylinder. Its integrand is then directly used to define the relevant incremental field contribution. This procedure, that will be referred to as a ITD (Incremental Theory of Diffraction) Fourier transform convolution localization process, is explicitly applied to both wedge and circular cylinder canonical configurations, to define incremental diffiraction and scattering contributions, respectively. These formulations are asymptotically approximated to find closed form high-frequency expression for the incremental field contributions. This generalization of the ITD lacalization process may provide a quite general, systematic procedure to find incremental field contributions that explicitly satisfy reciprocity and naturally lead to the UTD ray field representation, when it is applicable.

This paper deals with the scattering and diffraction of a plane wave by a randomly rough half-plane by three tools: the small perturbation method, the Wiener-Hopf technique and a group theoretic consideration based on the shift-invariance of a homogeneous random surface. For a slightly rough case, the scattered wavefield is obtained up to the second-order perturbation with respect to the small roughness parameter and represented by a sum of the Fresnel integrals with complex arguments, integrals along the steepest descent path and branch-cut integrals, which are evaluated numerically. For a Gaussian roughness spectrum, intensities of the coherent and incoherent waves are calculated in the region near the edge and illustrated in figures, in terms of which several characteristics of scattering and diffraction are discussed.

Electromagnetic field diffracted by conducting circular disk and circular hole in the conducting plate is formulated by the method of Kobayashi potential. The field is expressed by linear combination of functions which satisfy the required boundary conditions except on the disk or hole. Thus the functions may be regarded as eigen functions of the configuration. By imposing the remaining boundary conditions, we can derive the matrix equations for the expansion coefficients. It may be verified readily that each eigen function satisfies edge conditions for induced current on the disk and for aperture field distribution on the hole. It may also be verified that the solutions for the disk and the hole satisfy Babinet's principle. Matrix elements of the equations for the expansion coefficients are given by two kinds of infinite integrals and the series solutions for these integrals are derived. The validity of these expressions are verified numerically by comparing with the results obtained from direct numerical integrations.

This paper deals with a probabilistic formulation of the diffraction and scattering of a plane wave from a periodic surface randomly deformed by a binary sequence. The scattered wave is shown to have a stochastic Floquet's form, that is a product of a periodic stationary random function and an exponential phase factor. Such a periodic stationary random function is then represented in terms of a harmonic series representation similar to Fourier series, where `Fourier coefficients' are mutually correlated stationary processes rather than constants. The mutually correlated stationary processes are written by binary orthogonal functionals with unknown binary kernels. When the surface deformations are small compared with wavelength, an approximate solution is obtained for low-order binary kernels, from which the scattering cross section, coherently diffracted power and the optical theorem are numerically calculated and are illustrated in figures.

A rigorous radar cross section (RCS) analysis is carried out for two-dimensional rectangular and circular cavities with double-layer material loading by means of the Wiener-Hopf (WH) technique and the Riemann-Hilbert problem (RHP) technique, respectively. Both E and H polarizations are treated. The WH solution for the rectangular cavity and the RHP solution for the circular cavity involve numerical inversion of matrix equations. Since both methods take into account the edge condition explicitly, the convergence of the WH and RHP solutions is rapid and the final results are valid over a broad frequency range. Illustrative numerical examples on the monostatic and bistatic RCS are presented for various physical parameters and the far field scattering characteristics are discussed in detail. It is shown that the double-layer lossy meterial loading inside the cavities leads to the significant RCS reduction.

A bicomplex representation for time-harmonic electromagnetic fields appearing in scattering and diffraction problems is given using two imaginary units i and j. Fieldsolution integral-expressions obtained in the high-frequency and low-frequency limits are shown to provide the new relation between high-frequency diffraction and low-frequency scattering. Simple examples for direct scattering problems are illustrated. It may also be possible to characterize electric or magnetic currents induced on the obstacle in terms of geometrical optics far-fields. This paper outlines some algebraic rules of bicomplex mathematics for diffraction or scattering fields and describes mathematical evidence of the solutions. Major discussions on the relationship between high-frequency and low-frequency fields are relegated to the companion paper which will be published in another journal.

The key concept of Physical Optics (PO), originally developed for a perfectly electric conductor (PEC), consists in that the high frequency fields on the scatterer surface are approximated by those which would exist on the infinite flat surface tangent to the scatterer. The scattered fields at arbitrary observation points are then calculated by integrating these fields on the scatterer. This general concept can be extended to arbitrary impedance surfaces. The asymptotic evaluation of this surface integration in terms of diffraction coefficients gives us the fields in analytical forms. In this paper, uniform PO diffraction coefficients for the impedance surfaces are presented and their high accuracy is verified numerically. These coefficients are providing us with the tool for the mechanism extraction of various high frequency methods such as aperture field integration method and Kirchhoff's method.