Doubly periodic volume–surface integral equation formulation for modelling metamaterials

Usner, B.C.; Sertel, Kubilay; Volakis, John L.

doi:10.1049/iet-map:20050344

Cited by 13 publications

(10 citation statements)

References 40 publications

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“…In Figure 2 we have plotted the power transmission coefficients based on 161 frequency computations, which corresponds to a used frequency step of 50 MHz. Results correspond well to those presented by Usner et al in [4].…”

Section: Periodic Materials Consisting Of Resonant Dielectric Spheressupporting

confidence: 93%

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SIE approach to scattered field computation for 2D periodic diffraction gratings in 3D space consisting of high permittivity dielectric materials and plasmonic scatterers

Jorna

Lancellotti

Beurden

2014

2014 International Conference on Electromagnetics in Advanced Applications (ICEAA)

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We describe a surface integral-equation (SIE) method suitable for reliable computation of electromagnetic fields scattered by 2D periodic gratings in homogeneous 3D space in which the gratings may consist of high permittivity dielectric materials and metals. More in particular we briefly describe the formulation, the discretization and efficient evaluation of the Quasi Periodic Green Function (QPGF) and its gradient using Ewald's method. We present a case study to illustrate the method's capability of handling high permittivity dielectric materials and a second case study to demonstrate the effectiveness and indispensability of interpolating the QPGF and its gradient using tables with precomputed values.

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Section: Periodic Materials Consisting Of Resonant Dielectric Spheressupporting

confidence: 93%

“…The periodic medium configurations under consideration have been defined by Usner et al in [4] and consequently we can compare our computations with their results. The periodic materials consist of a single and dual layer of periodic dielectric spheres of radius 1 mm and ε r = 100.…”

Section: Periodic Materials Consisting Of Resonant Dielectric Spheresmentioning

confidence: 84%

SIE approach to scattered field computation for 2D periodic diffraction gratings in 3D space consisting of high permittivity dielectric materials and plasmonic scatterers

Jorna

Lancellotti

Beurden

2014

2014 International Conference on Electromagnetics in Advanced Applications (ICEAA)

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“…The derived formulation given in (15) can be used to predict the cutoff frequency for each Floquet harmonic denoted by and for nonorthogonal lattice configurations (15) where , denotes light velocity in free space, and . Note that (14) can be converted into a matrix equation by sampling at frequencies points such that (16) where (17a)…”

Section: Mbpe Methods For Wideband Interpolation Of the Required Bimentioning

confidence: 99%

“…Although the MoM works primarily for metallic structures, the volume-surface integral equation (VSIE) formulas have been proposed to characterize arbitrarily complex designs of periodic metamaterial structures composed of high-contrast inhomogeneous and anisotropic material regions with metallic inclusions [15]. However, even with these improvements, MoM formulations are generally not efficiently applicable to structures containing bianisotropic and inhomogeneous materials with arbitrary metallic objects.…”

mentioning

confidence: 99%

Application of AIM and MBPE Techniques to Accelerate Modeling of 3-D Doubly Periodic Structures with Nonorthogonal Lattices Composed of Bianisotropic Media

Wang

Werner

Turpin

2014

IEEE Trans. Antennas Propagat.

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An efficient methodology is introduced for rapid analysis and design of three-dimensional (3-D) doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral (FEBI) methods. The 3-D doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily-shaped metallic patches. Based on Floquet theory and periodic boundary conditions, the original stated problem that involves infinite periodic structures can be converted into a single unit cell. Using the equivalence principle, the derived BI equation formulation is applied to the top and bottom surfaces of the unit cell, which results in a perfectly reflectionless boundary condition for the FE-based approach. Then, the unit cell was meshed using triangular prismatic volume elements, which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction. The adaptive integral method (AIM) was employed to accelerate the calculation of the matrix-vector product for the BI portion within the iterative solver. Furthermore, a model-based parameter estimation (MBPE) technique was proposed for the wide-band interpolation of the required impedance matrix elements in the BI part for near field components that were used in the AIM procedure. The accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results (e.g., in comparison with analytical solutions). Several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily-shaped metallic patches, bianisotropic materials, and nonorthogonal lattice configurations.Index Terms-Adaptive integral method (AIM), bianisotropic media, finite element, frequency selective surface (FSS), hybrid finite-element boundary integral (FEBI) methods, integral equation, model-based parameter estimation (MBPE), periodic structure, periodic structure with nonorthogonal lattice.

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“…It should be noted that MoM is usually implemented together with other integral methods, e.g., MoM-VIE (volume integral equation) [72], MoM-CG-FFT [73,74], MoM-FMM (fast multipole method) [75], and MoM-VSIE (volume-surface integral equation) [76]. That is because the electric and magnetic integral equations (13) and (14) cannot be solved analytically for anisotropic scatterers in noncanonical shape via the vector potential formulation.…”

Section: Cartesian Anisotropy Of Spheresmentioning

confidence: 99%

Light scattering from anisotropic particles: propagation, localization, and nonlinearity

Qiu

Gao

Joannopoulos

et al. 2010

Laser & Photonics Reviews

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Plasmon resonances and extraordinary light scatterings of a nanoparticle with radial anisotropy are studied and summarized. The coupling between localized surface plasmons and far-field quantities is discussed. It is found that the presence of radial anisotropy redistributes the localization of plasmons and also results in certain novel phenomena in the far zone, which provide the possibility of scattering control such as electromagnetic transparency, enhanced scattering cross section, etc. The nonlinear optical response is explored in order to yield deeper physical insight into the interaction between plasmons and incident light.Nondissipative damping in the dipolar mode in a radial anisotropic sphere when the transversal permittivity t = 2:1 is near the surface plasmon resonance with positive r (Ae < 0) at different scales.

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Doubly periodic volume–surface integral equation formulation for modelling metamaterials

Cited by 13 publications

References 40 publications

SIE approach to scattered field computation for 2D periodic diffraction gratings in 3D space consisting of high permittivity dielectric materials and plasmonic scatterers

SIE approach to scattered field computation for 2D periodic diffraction gratings in 3D space consisting of high permittivity dielectric materials and plasmonic scatterers

Application of AIM and MBPE Techniques to Accelerate Modeling of 3-D Doubly Periodic Structures with Nonorthogonal Lattices Composed of Bianisotropic Media

Light scattering from anisotropic particles: propagation, localization, and nonlinearity

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