Akira Matsushima

Singular integral equation approach to plane wave diffraction by an infinite strip grating at oblique incidence

An accurate numerical solution of the plane wave diffraction by an infinite strip grating is presented, where the incident wave propagates in an arbitrary direction and is arbitrarily polarized. We derive a set of singular integral equations and solve it by the moment method, where the Chebyshev polynomials are chosen for the basis and the testing functions. The edge condition is incorporated in the expansion of the unknown functions in order to accelerate the convergence. A decomposition of the kernel into a singular and a regular part enables us to avoid the relative convergence phenomenon. Numerical results show the accuracy of the present method. Some numerical examples are presented for the polarization discrimination characteristics and surface current distributions.

Singular Integral Equation Approach to Electromagnetic Scattering from a Finite Periodic Array of Conducting Strips

An accurate numerical solution for the electromagnetic scattering from a periodic array of a finite number of conducting strips is presented, where the incident plane wave propagates in an arbitrary direction. Both TM and TE polarizations are treated. First, the boundary value problem is formulated into the solution of a set of Fredholm integral equations of the first kind with singular kernels. Then it is regularized to a set of the second kind equations which is numerically solved by the moment method. The present method is much more effective than the moment solution of the first kind equations. This is because the kernel functions of the resulting second kind equations are bounded and smooth, and because the edge condition is automatically taken into account in the course of the regularization. Some numerical examples are shown for the total scattering cross-sections, surface current distributions, and the far-zone scattered fields. The near zone fields are compared with the experimental data.

Application of Integral Equation Method to Metal-Plate Lens Structures

The present paper concerns the design, numerical analysis, and measurement for simple metal-plate lens structures. The power of electromagnetic waves can be concentrated by arranging flat strips parallel to one another and adjusting the transverse and longitudinal length of the waveguide regions. The simple designing procedures are described for the lenses with plane, concave, and convex profiles. These steps are practically applied to construct the lenses for the X band. In order to discuss the dependence of focusing properties on the lens and source types, we numerically analyze the scattering problems using the integral equations combined with the moment method. The lenses are made up by aluminum plates, and the field amplitude in the transmission region is measured. We confirm the formation of the focus near the design point.

Effect of temperature and multiple scattering on rain attenuation of electromagnetic waves by a simple spherical model

Speciflc rain attenuation is discussed from the viewpoint of numerical solution for scattering and absorption of electromagnetic waves related to dielectric spheres. Special attention is paid to the quantitative evaluations considering the change of temperature and the existence of multiple scattering efiect. The analysis is based on the set of Strattons vector spherical wave functions and its addition theorem, which lead to the simultaneous linear equations for the expansion coe-cients with adaptively selected truncation numbers. Computed extinction cross sections lead directly to the speciflc rain attenuation, where the Weibull raindrop distribution model is used. It is discussed how the dependence of the permittivity of water on temperature and frequency afiects the attenuation property. Furthermore, the efiect of multiple scattering is evaluated in terms of the root mean square of attenuation deviation from the simple superposition of single scattering (Mies) coe-cients. Contrary to general belief, this deviation is the highest at around the boundary between microwave and millimeter wave bands.

Efficient numerical approach to electromagnetic scattering from three-dimensional periodic array of dielectric spheres using sequential accumulation

An effective numerical solution is presented for the plane wave scattering by multilayered periodic arrays of dielectric spheres. The treated structure is a fundamental model of photonic crystals having three-dimensional periodicity. The problem is analyzed by the mode matching method, where the electromagnetic fields in the air and dielectric regions are approximated by using the Floquet harmonics and vector spherical wave functions, respectively. They are matched on the junction surfaces in the least squares sense. Introduction of sequential accumulation in the process of QR decomposition reduces the computation time from O(Q 3 )t oO(Q 1 ) and the memory requirement from O(Q 2 )t oO(Q 1 ), with Q being a number of sphere layers. Numerical results are given for CPU time, speed of convergence, and some band gap characteristics.

Integral Equation Analysis of Plane Wave Scattering From Multilayered Resistive Strip Gratings

An accurate and efficient numerical solution is presented for the two-dimensional electromagnetic wave scattering from multilayered resistive strip gratings. Both E- and H-waves are treated. The method is based on the integral equations combined with the moment method with regularization procedure. The numerical experiment reveals the criteria for the truncation numbers. The reflected, transmitted, and absorbed powers are computed for various grating parameters and frequencies. Special attention is paid to maximizing the absorption into the strips, and thereby the relative absorbed power amounts to more than 90%.

ARIMA Modeling of Tropical Rain Attenuation on a Short 28-GHz Terrestrial Link

This letter reports the result of modeling of the tropical rain attenuation at 28 GHz adopting the auto-regressive integrated moving average (ARIMA) model. The result obtained is useful for the evaluation of transmission system design in radio communications at millimeter-wave frequencies in tropical areas. In this research, radio power measurement on a 56.4-m link at 28 GHz was carried out in Surabaya, Indonesia, with a data acquisition system that recorded a sample once every second. Approximation of the data by ARIMA(p,d,q) models for every rain event was carried out in order to obtain a valid time series model. In the validation, comparisons were made of the distributions of attenuation from the models against those from direct measurement of attenuation and from estimation based on the synthetic storm method. Comparisons were also made of the attenuation slope distributions against that from the measurement. Each of rain attenuation time series obtained from events in February 2009 was found to be well approached by the ARIMA model with various sets of parameters (p,d,q). The best model was found to be ARIMA (0, 1, 1) , as indicated by the Akaike Information Criteria (AIC) and Schwarz Bayesian Criteria (SBC) test results. A procedure for generating rain events based on the model is presented.

A NUMERICAL ANALYSIS OF STOP BAND CHARACTERISTICS BY MULTILAYERED DIELECTRIC GRATINGS WITH SINUSOIDAL PROFILE

An effective computational method based on a conven- tional modal expansion approach is presented for handling a multilay- ered dielectric grating whose profiles are multilayered and sinusoidally modulated. This structure fabricated by dielectric material is one of the useful photonic crystals. The method is based on Yasuuras modal expansion, which is known as a least-squares boundary residual method or a modified Rayleigh method. In the extended method, each layer is divided into shallow horizontal layers. The Floquet modal func- tions and approximate solutions are defined in each shallow layer, and the latter are matched with boundary conditions in the least-squares sense. A huge-sized least-squares problem that appears in finding the modal coefficients is solved by the QR decomposition accompanied by sequential accumulation. This procedure makes it possible to treat the case where the groove depths are the same as or a little more than the grating period. As numerical example, we calculate a diffractive char- acteristic by a multilayered deep dielectric grating and confirm that a common band gap occurs for both polarizations.

Improved Numerical Method for Computing Internal Impedance of a Rectangular Conductor and Discussions of its High Frequency Behavior

An e-cient numerical solution is been developed to compute the impedances of rectangular transmission lines. Method of moments is applied to integral equations for the current density, where the cross section is discretized, to improve the convergence, by a nonuniform grid that obeys the skin efiect. Powerfulness of this approach up to rather high frequencies is verifled by comparing with asymptotic formulas and other references. Detailed discussion is given for the current density distribution and its efiect to the impedance, especially for a high frequency range.

A COMBINATION OF UP- AND DOWN-GOING FLOQUET MODAL FUNCTIONS USED TO DESCRIBE THE FIELD INSIDE GROOVES OF A DEEP GRATING

An effective computational method based on a conven- tional modal-expansion approach is presented for solving the problem of diffraction by a deep grating. The groove depth can be the same as or a little more than the grating period. The material can be a perfect conductor, a dielectric, or a metal. The method is based on Yasuuras modal expansion, which is known as a least-squares boundary residual method or a modified Rayleigh method. The feature of the present method is that: (1) The semi-infinite region U over the grating sur- face is divided into an upper half plane U0 and a groove region UG by a fictitious boundary (a horizontal line); (2) The latter is further di- vided into shallow horizontal layers U1 ,U 2, ··· ,U Q again by fictitious boundaries; (3) An approximate solution in U0 is defined in a usual manner, i.e., a finite summation of up-going Floquet modal functions with unknown coefficients, while the solutions in Uq (q =1 , 2, ··· ,Q ) include not only the up-going but also the down-going modal functions; (4) If the grating is made of a dielectric or a metal, the semi-infinite region L below the surface is partitioned similarly into L0 ,L 1, ··· ,L Q, and approximate solutions are defined in each region; (5) A huge-sized least squares problem that appears in finding the modal coefficients is solved by the QR decomposition accompanied by sequential accu- mulation. The method of solution for a grating made of a perfect conductor is described in the text. The method for dielectric gratings can be found in an appendix. Numerical examples include the results for perfectly conducting and dielectric gratings.