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Proceedings ArticleDOI

Wiener-Hopf analysis of the diffraction by a thin material strip

22 Sep 2016-pp 557-560
TL;DR: In this article, the plane wave diffraction by a thin material strip is analyzed using the Wiener-Hopf technique and approximate boundary conditions and an asymptotic solution is obtained under the condition that the strip width is large compared with the wavelength.
Abstract: The plane wave diffraction by a thin material strip is analyzed using the Wiener-Hopf technique and approximate boundary conditions. An asymptotic solution is obtained under the condition that the strip width is large compared with the wavelength. Applying the saddle point method, the scattered far field is evaluated asymptotically. Numerical results on the radar cross section (RCS) are presented.
Citations
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Proceedings ArticleDOI
01 Jan 2014
TL;DR: Nagasaka and Kobayashi as discussed by the authors analyzed plane wave diffraction by a thin material strip for both H and E polarizations using the Wiener-Hopf technique together with the two different approximate boundary conditions.
Abstract: TPID5179783. Volakis analyzed the H-polarized plane wave diffraction by a thin material strip using the dual integral equation approach and the extended spectral ray method together with approximate boundary conditions [1]. In [1], Volakis first solved rigorously the diffraction problem involving a single material halfplane, and subsequently obtained a high-frequency solution to the original strip problem by superposing the singly diffracted fields from the two independent half-planes and the doubly/triply diffracted fields from the edges of the two half-planes. Therefore his analysis is not rigorous from the viewpoint of boundary value problems, and may not be applicable unless the strip width is relatively large compared with the wavelength. In this paper, we shall consider the same problem as in Volakis [1], and analyze plane wave diffraction by a thin material strip for both H and E polarizations using the Wiener-Hopf technique together with the two different approximate boundary conditions [2], [3]. Main results of this paper are published in Nagasaka and Kobayashi [4], [5].

6 citations


Cites result from "Wiener-Hopf analysis of the diffrac..."

  • ...The results presented in this paper provide an important extension of our earlier analysis of the same problem (Koshikawa and Kobayashi, 2000; Nagasaka and Kobayashi, 2013)....

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DOI
TL;DR: In this paper , the authors proposed a semianalytical spectral method based on an original extension of the Wiener-Hopf (WH) technique that uses the concept of characteristic Green's function and the Fredholm factorization technique.
Abstract: In this article, we study the scattering problem of a truncated grounded slab illuminated by an arbitrarily incident $E_{\text{z}}$ -polarized plane wave. We present a solution using the novel semianalytical spectral method based on an original extension of the Wiener–Hopf (WH) technique that uses the concept of characteristic Green’s function and the Fredholm factorization technique. The combination of these mathematical tools allows to extend the capabilities of classical WH method to a new set of problems. One of the main benefits of the proposed semianalytical solution is that it allows the computation of field components similar to what is done with closed-form spectral solutions when available. Physical phenomena, such as the reflection, diffraction, and excitation of surface/leaky waves, are reported. Numerical results validate the proposed methodology.

3 citations

References
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Book
01 Jan 1995
TL;DR: In this article, the authors describe a variety of methods for the approximate simulation of material surfaces, and provide the first comprehensive treatment of boundary conditions in electromagnetics, including impedance, resistive sheet, conductive sheet and generalised (or higher order) and absorbing (or non-reflecting) boundary conditions.
Abstract: Non-metallic materials and composites are now commonplace in modern vehicle construction, and the need to compute scattering and other electromagnetic phenomena in the presence of material structures has led to the development of new simulation techniques. This book describes a variety of methods for the approximate simulation of material surfaces, and provides the first comprehensive treatment of boundary conditions in electromagnetics. The genesis and properties of impedance, resistive sheet, conductive sheet, generalised (or higher order) and absorbing (or non-reflecting) boundary conditions are discussed. Applications to diffraction by numerous canonical geometries and impedance (coated) structures are presented, and accuracy and uniqueness issues are also addressed, high frequency techniques such as the physical and geometrical theories of diffraction are introduced, and more than130 figures illustrate the results, many of which have not appeared previously in the literature. Written by two of the authorities m the field, this graduate-level text should be of interest to all scientists and engineers concerned with the analytical and numerical solution of electromagnetic problems.

641 citations


"Wiener-Hopf analysis of the diffrac..." refers background or methods in this paper

  • ...If the strip thickness is small compared with the wavelength, the material strip can be replaced by a strip of zero thickness satisfying the second order boundary conditions [4]....

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  • ...Volakis [1] analyzed the plane wave diffraction by a thin material strip using the dual integral equation approach [2] and the extended spectral ray method [3] together with approximate boundary conditions [4]....

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Journal ArticleDOI
TL;DR: In this paper, a simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of "dual" integral equations, which replaces the single integral equation of Schwinger's method.
Abstract: In the last few years Copson, Schwinger and others have obtained exact solutions of a number of diffraction problems by expressing these problems in terms of an integral equation which can be solved by the method of Wiener and Hopf. A simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of ‘dual’ integral equations, which replaces the single integral equation of Schwinger’s method. The unknown function in each of these dual integral equations is that defining the angular spectrum, and when this function is known the scattered field is presented in the form of a definite integral. As far as the ‘radiation’ field is concerned, this integral is of the type which may be approximately evaluated by the method of steepest descents, though it is necessary to generalize the usual procedure in certain circumstances. The method is appropriate to two-dimensional problems in which a plane wave (of arbitrary polarization) is incident on plane, perfectly conducting structures, and for certain configurations the dual integral equations can be solved by the application of Cauchy’s residue theorem. The technique was originally developed in connexion with the theory of radio propagation over a non-homogeneous earth, but this aspect is not discussed. The three problems considered are those for which the diffracting plates, situated in free space, are, respectively, a half-plane, two parallel half-planes and an infinite set of parallel half-planes; the second of these is illustrated by a numerical example. Several points of general interest in diffraction theory are discussed, including the question of the nature of the singularity at a sharp edge, and it is shown that the solution for an arbitrary (three-dimensional) incident field can be derived from the corresponding solution for a two-dimensional incident plane wave.

89 citations


"Wiener-Hopf analysis of the diffrac..." refers methods in this paper

  • ...Volakis [1] analyzed the plane wave diffraction by a thin material strip using the dual integral equation approach [2] and the extended spectral ray method [3] together with approximate boundary conditions [4]....

    [...]

Journal ArticleDOI
Kazuya Kobayashi1
TL;DR: In this paper, a generalized gamma function for two complex variables and a positive integer is introduced, and several important analytical properties are investigated in detail, which include regularity, asymptotic expansions and analytic continuations.
Abstract: As a generalization of the Gamma function defined for a single complex variable, a new special function called a generalized Gamma function, defined for two complex variables and a positive integer, is introduced, and several important analytical properties are investigated in detail, which include regularity, asymptotic expansions and analytic continuations. Furthermore, as a function closely related to a generalized Gamma function, a generalized incomplete Gamma function, which is a generalization of the incomplete Gamma function, is also introduced, and some fundamental properties are investigated briefly.

79 citations


"Wiener-Hopf analysis of the diffrac..." refers background in this paper

  • ...and ( , ) m Γ ⋅ ⋅ is the generalized gamma function [8] given by 1...

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Journal ArticleDOI
TL;DR: In this article, an asymptotic solution for the diffraction by a resistive strip is presented, which is useful in the simulation of thin dielectric layers, up to third-order diffraction terms are derived which include the surface wave field effects in a uniform manner.
Abstract: An asymptotic solution is presented for the diffraction by a resistive strip which is useful in the simulation of thin dielectric layers. Up to third-order diffraction terms are derived which include the surface wave field effects in a uniform manner. Extensions to the case of conductive and impedance strips are also given in Appendix C. The derivation of the higher order terms is based on the extended spectral ray method. New first-order diffraction coefficients for the impedance, resistive and conductive half planes are also presented. The last are uniform everywhere, including the surface wave field boundaries.

67 citations


"Wiener-Hopf analysis of the diffrac..." refers methods in this paper

  • ...Volakis [1] analyzed the plane wave diffraction by a thin material strip using the dual integral equation approach [2] and the extended spectral ray method [3] together with approximate boundary conditions [4]....

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors derived diffraction coefficients for a thin dielectric half plane and strip having arbitrary permittivity and permeability by modeling the thin material layer by a pair of modified resistive and conductive sheets.
Abstract: Diffraction coefficients are derived for a thin dielectric half plane and strip having arbitrary permittivity and permeability. This is accomplished by modeling the thin material layer by a pair of modified resistive and conductive sheets. By means of this model the dielectric half plane is first treated via the dual integral equation approach. By employing the half plane solution, up to third-order multiply diffracted fields are then derived for the case of a strip. These are obtained via the extended spectral ray method and include the surface wave diffraction effects in a uniform manner. Numerical results are also presented which validate the accuracy of the model and that of the derived diffraction coefficients.

37 citations


"Wiener-Hopf analysis of the diffrac..." refers background or methods or result in this paper

  • ...In [1], Volakis obtained a high-frequency asymptotic solution to the original strip problem by superposing the diffracted fields from the two independent material half-planes and the doubly/triply diffracted fields between the edges of the two half-planes....

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  • ...θ = ° Figure 3 shows comparison with Volakis’s results [1], where the strip dimension is 2 7 , 1....

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  • ...In this paper, we shall consider the same strip geometry as in Volakis [1] and analyze the plane wave diffraction using the Wiener-Hopf technique....

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  • ...Some comparisons with Volakis [1] are also shown....

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  • ...Volakis [1] analyzed the plane wave diffraction by a thin material strip using the dual integral equation approach [2] and the extended spectral ray method [3] together with approximate boundary conditions [4]....

    [...]