Analysis of the electromagnetic scattering from a cavity

Ammari, Habib; Bao, Gang; Wood, Aihua W.

doi:10.1007/bf03167458

Cited by 86 publications

(106 citation statements)

References 9 publications

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“…It is known that the problem (2.1) has a unique solution whenever Im(k) ≥ 0 [2]. The mapping R(k) : f → u defines an operator-valued function which is holomorphic in Im(k) ≥ 0.…”

Section: γ 2 Dieletricmentioning

confidence: 99%

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Enhancement of Electromagnetic Fields Caused by Interacting Subwavelength Cavities

Babadjian¹,

Bonnetier²,

Triki³

2010

Multiscale Model. Simul.

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Abstract. This article is devoted to the asymptotic analysis of the electromagnetic fields scattered by a perfectly conducting plane containing two sub-wavelength rectangular cavities. The problem is formulated through an integral equation, and a spectral analysis of the integral operator is performed. Using the generalized Rouché theorem on operator valued functions, it is possible to localize two types of resonances, symmetric and anti-symmetric, in a neighborhood of each zero of some explicit function, associated to the limiting geometry. For the symmetric modes, the fields in the cavities interact in phase, and the system of two cavities essentially acts as a dipole. In the anti-symmetric case, the fields oscillate in anti-phase, and the system behaves like a quadripole. Asymptotic expansions of the resonances, the far-field and the near-field are given.

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“…It is known that the problem (2.1) has a unique solution whenever Im(k) ≥ 0 [2]. The mapping R(k) : f → u defines an operator-valued function which is holomorphic in Im(k) ≥ 0.…”

Section: γ 2 Dieletricmentioning

confidence: 99%

“…Moreover, if y = (wy 1 ± wd, wy 2 ) for some y 1 ∈ Γ and y 2 > 0, then u(wy 1 ± wd, wy 2 ) = u e (wy 1 ± wd, wy 2 …”

Section: Asymptotic Of the Field Umentioning

confidence: 99%

Enhancement of Electromagnetic Fields Caused by Interacting Subwavelength Cavities

Babadjian¹,

Bonnetier²,

Triki³

2010

Multiscale Model. Simul.

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show abstract

“…A variety of numerical methods, including the method of moments, finite difference, finite element, boundary element method, and hybrid methods [3,7,9,10], have been developed to characterize the scattering from cavities. Some mathematical analysis and numerical treatments on the open cavities can be found in [1,2,5].…”

Section: Introductionmentioning

confidence: 99%

A Fast High Order Method for Electromagnetic Scattering by Large Open Cavities

Zhao

Qiao

Tang

2011

JCM

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In this paper, the electromagnetic scattering from a rectangular large open cavity embedded in an infinite ground plane is studied. By introducing a nonlocal artificial boundary condition, the scattering problem from the open cavity is reduced to a bounded domain problem. A compact fourth order finite difference scheme is then proposed to discrete the cavity scattering model in the rectangular domain, and a special treatment is enforced to approximate the boundary condition, which makes truncation errors reach O(h 4 ) in the whole computational domain. A fast algorithm, exploiting the discrete Fourier transformation in the horizontal and a Gaussian elimination in the vertical direction, is employed, which reduces the discrete system to a much smaller interface system. An effective preconditioner is presented for the BICGstab iterative solver to solve this interface system. Numerical results demonstrate the remarkable accuracy and efficiency of the proposed method. In particular, it can be used to solve the cavity model for the large wave number up to 600π.Mathematics subject classification: 65N06, 78M20.

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“…Ammari, Bao & Wood [3], Bao & Dobson [9], Bonnet-Bendhia & Starling [10], Elschner & Schmidt [26], Elschner, Hinder, Penzel & Schmidt [27], Elschner & Yamamoto [28] and Kirsch [33]. In the case of elastic scattering by periodic surfaces, the variational approach is established by Elschner & Hu in [24,25] for the boundary value problems of the first, second, third and fourth kind as well as for transmission problems with non-smooth interfaces in R n (n = 2, 3).…”

Section: Introductionmentioning

confidence: 99%

Elastic Scattering by Unbounded Rough Surfaces

Elschner¹,

Hu²

2012

SIAM J. Math. Anal.

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We consider the two-dimensional time-harmonic elastic wave scattering problem for an unbounded rough surface, due to an inhomogeneous source term whose support lies within a finite distance above the surface. The rough surface is supposed to be the graph of a bounded and uniformly Lipschitz continuous function, on which the elastic displacement vanishes. We propose an upward propagating radiation condition (angular spectrum representation) for solutions of the Navier equation in the upper half-space above the rough surface, and establish an equivalent variational formulation. Existence and uniqueness of solutions at arbitrary frequency is proved by applying a priori estimates for the Navier equation and perturbation arguments for semi-Fredholm operators.

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Analysis of the electromagnetic scattering from a cavity

Cited by 86 publications

References 9 publications

Enhancement of Electromagnetic Fields Caused by Interacting Subwavelength Cavities

Enhancement of Electromagnetic Fields Caused by Interacting Subwavelength Cavities

A Fast High Order Method for Electromagnetic Scattering by Large Open Cavities

Elastic Scattering by Unbounded Rough Surfaces

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