A mathematically correct and numerically stable method (MAR; Method of Analytical Regularization) of solving the two-dimensional problem of wave diffraction by curved strips is suggested. This method is based on the reduction of initial boundary value problem with complex frequencies to the corresponding dual series equations, which are regularized by means of the solution of the Riemann-Hilbert problem. As a result we obtained an infinite system of linear algebraic equations of the second kind. It enables us to solve the initial diffraction and spectrum problems with any accuracy required. We also present some numericl results illustrating the possible applications of the method

View full abstract

Electromagnetic plane wave diffraction by a perfectly conducting strip has been analyzed for both H and E polarizations by utilizing high frequency asymptotic method. Formulation is based on the Geometrical Theory of Diffraction (GTD), by which simple physical interpretations can be given and higher order edge diffraction effects are easily included.
In order to clarify the deficiency of the GTD and to correct it, Equivalent Source Method (ESM) has also introduced here. Asymptotic expansion form of the total scattering cross section is derived analytically, and the result is found to agree with those by other methods. Then numerical calculation of the total scattering cross section, as well as far field scattering patterns are made for various strip width, and these results are compared with the exact solutions. The agreement seems to be excellent even for small strip width.

View full abstract

The problem of plane wave diffraction by a perfectly conducting strip is re-examined for both E and H polarizations based on the Wiener-Hopf technique. The starting point of the analysis here is in the formal exact solution obtained by the authors in the previous papers, which is expressed in terms of an integral equation in the complex domain. A new approach for solving the integral equation asymptotically is presented, and the high-frequency asymptotic solution including all the higher order terms is obtained for the width of the strip large compared with the wavelength. Numerical examples of the monostatic and bistatic radar cross sections (RCS) as well as the total scattering cross section are shown and the scattering characteristics of the strip are discussed in detail. Some comparisons with the exact solution based on separation of variables in elliptic coordinates are also given and the accuracy of the present approach is demonstrated.

View full abstract

The exact solutions of the diffraction and scattering of electromagnetic waves by a twodimensional conducting elliptic cylinder for both E and H wave polarizations are derived by the use of elliptic cylinder coordinates and Mathieu functions, and we obtain diffraction and scattering electromagnetic fields by a conducting strip with applying the above results whose ratio of minor axis to major axis tends to zero. In case of numerical solutions, the convergence conditions for the series of Mathieu functions are confirmed by several examples.
Corner reflector antennas are analyzed by a mode-expanding method. Applying these results, the radiation and scattering of electromagnetic fields by a two-dimensional strip are obtained as a special case of corner reflector which has 180° corner angle. Also in this case, the convergence conditions for the series of Bessel, Hankel functions are confirmed by the numerical results.

View full abstract

The scattering of plane wave incident on a conducting strip is analyzed by a new technique of point matching method. In the formulation of analysis, the exact edge condition is introduced into the conventional point matching method, in addition, the order of simulataneous equations has been reduced to one-fourth using the four-phase symmetrical coordinate method.
Main results are (1) the total scattering cross section shows a good agreement with accurate results by other method for both TE and TM waves and (2) the relative errors of this technique for the total scattering cross section and the scattering fields are 2 or 3 digits smaller than those of the conventional point matching method even for large values of wave number up to ka=50 (k: wavenumber, (2a): width of a strip) and the scattering level less than -30dB.

View full abstract

The diffraction of a plane electromagnetic wave by an inclined parallel plate grating with finite thickness is treated by using the Wiener-Hopf technique. The Wiener-Hopf equations and a representation of the scattered wave are obtained. Since the width and the thickness of the plate are finite, it is difficult to carry out rigorously the decomposition in the solution of the Wiener-Hopf equations. Therefore the characteristic of the sampling function is used for expansion of the unknown function on strip into a series so that the Wiener-Hopf equations are reduced to a set of simultaneous equations. For evaluation of the convergence and the errors in the numerical results, the relative error with respect to the extrapolated value and the power error for the power balance are computed. From comparison of the numerical results of the present method with the conventional mode-matching method, it is found that the present method provides us accurate results. The transmission characteristics of the grating are discussed.

View full abstract

An efficient method of solution for problem of wave diffraction by a set of perfectly conducting flat strips is presented, where both E- and H-polarizations are treated. By using a spectral approach, the problem is reduced to a system of linear algebraic equations for the unknown Fourier coefficients of the current density function. A truncation of the infinite system of equations can yield the solution with any desired accuracy. Numerical results are presented for total cross sections of a single strip and strip resonators. By detailed examinations of the convergence in numerical computations, the criteria for truncation size are established. The limitation of this method on the strip width is also revealed.

View full abstract

An analytical method is presented for the plane wave scattering by an infinite strip grating. The effect of the finite metallization thickness of the strips can be taken into consideration by the introduction of the aperture fields as the source quantity, and the structures with multilayered media can be treated easily by using the simple recurrent relation and circuit theory. Efficient numerical calculation is available by employing the suitable basis functions, which incorporate the edge singularity. Simpler zero-thickness cases are analyzed based on the current-source formulation as well as the aperture-field formulation, and numerical examples are compared with available data to show the validity of the method. The metallization thickness effect of the strip grating with multilayered media is clarified for the E- and H-polarized incident waves for the first time.

View full abstract

An accurate numerical solution is presented for the excitation problem of guided modes of a slab waveguide at a plane wave incidence, where a finite periodic array of strips is used for excitation. This system is one of the typical models of grating couplers. The problem is two-dimensional and only the TE mode is treated. We derive a set of singular integral equations and solve it by the moment method, where the Chebyshev polynomials are successfully used as the basis and the testing functions. Numerical calculations are carried out under the condition that the error on the optical theorem is less than 0.1%. It is shown that the frequency which yields maximum excitation efficiency is somewhat different from one predicted by the Bragg condition. We also confirm that too many strips lead to deterioration of the efficiency. The calculations predict that the efficiency of the first even mode at its maximum is 37%.

View full abstract

A simple method is described for the analysis of a planar dielectric waveguide with periodic metal strips. The approach is a combination of the coupled-mode theory and the finite element method. The finite element method is used to calculate the dispersion characteristics of an infinite metal strip array. Coupling coefficients are then determined by matching the dispersion characteristics from the coupled-mode equations with those obtained by the finite element method. The solution of coupled-mode equations allows the determination of scattering coefficients of a planar dielectric waveguide with a finite metal strip array. Examples are computed for metal strips periodically placed in the middle or on the top of a dielectric slab waveguide.

View full abstract

Low density polyethylene (LDPE) is widely used as an electric insulating material in electric power cables. The generation of electrical treeing due to aging of LDPE may lose the reliability of its insulating capability. It is therefore important to suppress its treeing and to improve its electrical properties so that the reliability of cables can be improved. With this purpose, we prepared LDPE to which varius inorganic materials were added. Our investigation was particularly focused on lithium carbonate and quartz which were effective to suppress the treeing when added to LDPE. Lithium carbonate-added (0.25phr) showed in two hours of discharge the length of tree, 150μm shorter than that (560μm) of non-added LDPE, offering obvious suppressing effect on treeing generation. We found that this effect was more significant than quartz-added LDPE and even at elevated temperatures lithium carbonate added LDPE exhibited suppression of treeing. The thermal decomposition temperature at which lithium carbonate-added (1phr) LDPE loses 50% of its weight rose 100°C more than non-added LDPE and 60°C more than that of quartz-added LDPE, which evidenced improvement in heat resistance of LDPE.

View full abstract

The optical properties and the structure are investigated for phosphatidic acid (PA) Langmuir films adsorbing cyanine dyes from the aqueous solutlon at the air-water interface, and are also studied for PA LB films containing the dyes on substrates. ^H∗ aggregation of the dyes oriented perpendicular to the water surface is observed at pH5 of the subphase for the PA Langmuir films. The ^H∗ aggregation, however, is not observed after the LB films are deposited on the substrates, and ^J aggregate appears instead of it. Aggregation structures of the dyes in the PA Langmuim films and in the LB films are different from the structures of the dyes adsorbed in arachidic acid films, and the structures depend upon pH of the subphase. Furthermore, absorption peaks of the aggregates, calculated using an extended dipolar model, coincide with the experimental absorption spectra. The properties are of great interest for controlling characteristics of LB films adsorbing dyes and fabricating LB devices.

View full abstract