Diffraction of an obliquely incident plane wave by a two‐face impedance half plane: Wiener‐Hopf approach

Lüneburg, E.; Serbest, A.H.

doi:10.1029/2000rs002372

Cited by 9 publications

(6 citation statements)

References 39 publications

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“…Notice that the known closed form solutions available in the literature are relative only to the case of a PEC or a PMC half plane; these solutions involve the factorization of (2 × 2) matrices. At skew incidence, that is for α 0 ≠ 0, the factorization of these matrices is often simplified by the transformation [ Senior , 1978; Lüneburg and Serbest , 2000]

For example, in case of a PMC half plane immersed in a chiral medium, one has to factorize the matrix ( + ) (see ), with

Thus factorization is accomplished by factorizing the scalars χ 1 χ 2 , and ( k 1 χ 2 + k 2 χ 1 ). Similar considerations apply to the PEC case, exhaustively studied by Przezdziecki [2000].…”

Section: Special Cases With Closed‐form Solutionsmentioning

confidence: 99%

“…Notice that the known closed form solutions available in the literature are relative only to the case of a PEC or a PMC half plane; these solutions involve the factorization of (2 Â 2) matrices. At skew incidence, that is for a 0 6 ¼ 0, the factorization of these matrices is often simplified by the transformation [Senior, 1978;Lüneburg and Serbest, 2000] t…”

Section: Isotropic and Bi-isotropic Mediamentioning

confidence: 99%

“…The first rigorous studies of the diffraction by a perfect electric conducting (PEC) half plane immersed in a homogeneous isotropic medium are by Poincaré [1892] and Sommerfeld [1896]. Noticeable progress in the solution of these problems is attributed to the introduction and use of the Sommerfeld‐Malyuzhinets (SM) technique and the Wiener‐Hopf (WH) technique [ Senior , 1978; Hurd and Luneburg , 1985; Budaev , 1995; Senior and Volakis , 1995; Lüneburg and Serbest , 2000; Daniele , 2003; Antipov and Silvestrov , 2006; Lyalinov and Zhu , 2006; Daniele and Lombardi , 2006]. In particular, we observe that the WH technique can deal with the most general problem of a half plane immersed in an anisotropic or bianisotropic medium, whereas the SM method cannot deal with it, as yet.…”

Section: Introductionmentioning

confidence: 99%

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Diffraction by an imperfect half plane in a bianisotropic medium

Daniele

Graglia

2007

Radio Science

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[1] A general theory to study the electromagnetic diffraction by imperfect half planes immersed in linear homogeneous bianisotropic media is presented. The problem is formulated in terms of Wiener-Hopf equations by deriving explicit spectral domain expressions for the characteristic impedances of bianisotropic media, which allow one to exploit their analytical properties. In the simpler case of perfect electric conducting and perfect magnetic conducting half planes, the Wiener-Hopf equations involve matrices of order 2, which can be factorized in closed form if the constitutive tensors of the bianisotropic material are of special form. Four of these special cases are discussed in detail. In order to deal with the more general problem, a technique to numerically factorize the Wiener-Hopf matrix kernels is presented. Our numerical approach is discussed on one example, by considering the previously unsolved problem of a perfect electric conducting half plane in a gyrotropic medium. The reported numerical results show that the diffracted field contribution is obtained by use of the saddle point integration method.Citation: Daniele, V., and R. D. Graglia (2007), Diffraction by an imperfect half plane in a bianisotropic medium, Radio Sci., 42, RS6S05,

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For example, in case of a PMC half plane immersed in a chiral medium, one has to factorize the matrix ( + ) (see ), with

Thus factorization is accomplished by factorizing the scalars χ 1 χ 2 , and ( k 1 χ 2 + k 2 χ 1 ). Similar considerations apply to the PEC case, exhaustively studied by Przezdziecki [2000].…”

Section: Special Cases With Closed‐form Solutionsmentioning

confidence: 99%

“…Notice that the known closed form solutions available in the literature are relative only to the case of a PEC or a PMC half plane; these solutions involve the factorization of (2 Â 2) matrices. At skew incidence, that is for a 0 6 ¼ 0, the factorization of these matrices is often simplified by the transformation [Senior, 1978;Lüneburg and Serbest, 2000] t…”

Section: Isotropic and Bi-isotropic Mediamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Diffraction by an imperfect half plane in a bianisotropic medium

Daniele

Graglia

2007

Radio Science

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“…However, the vectors ± (s) = T ± (s)φ ± (s) have to be continuous through these lines. Therefore the functions φ ± 1 (s) and φ ± 2 (s) solve the following system of two scalar difference equations: 10) subject to the Riemann-Hilbert boundary conditions on the cuts C…”

Section: Riemann-hilbert Problem For Two Even Functions On a System Omentioning

confidence: 99%

“…The steepest descent method applied to (2.4) for kρ → ∞ yields the diffracted field 10) where the diffraction coefficients D e (θ) and D h (θ) are expressed through the spectral functions S 1 (s) and S 2 (s) as follows: …”

Section: Normal Incidencementioning

confidence: 99%

Electromagnetic scattering from an anisotropic impedance half-plane at oblique incidence: the exact solution

Antipov

Silvestrov

2006

The Quarterly Journal of Mechanics and Applied Mathematics

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SummaryScattering of a plane electromagnetic wave from an anisotropic impedance half-plane at skew incidence is considered. The two matrix surface impedances involved are assumed to be complex and different. The problem is solved in closed form. The boundary-value problem reduces to a system of two first-order difference equations with periodic coefficients subject to a symmetry condition. The main idea of the method developed is to convert the system of difference equations into a scalar Riemann-Hilbert problem on a finite contour of a hyperelliptic surface of genus 3. A constructive procedure for its solution and the solution of the associated Jacobi inversion problem is proposed and described in detail. Numerical results for the edge diffraction coefficients are reported.

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2020

Scattering and Diffraction by Wedges 2

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Diffraction of an obliquely incident plane wave by a two‐face impedance half plane: Wiener‐Hopf approach

Cited by 9 publications

References 39 publications

Diffraction by an imperfect half plane in a bianisotropic medium

Diffraction by an imperfect half plane in a bianisotropic medium

Electromagnetic scattering from an anisotropic impedance half-plane at oblique incidence: the exact solution

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