Integral-Equation Analysis of 3-D Metallic Objects Arranged in 2-D Lattices Using the Ewald Transformation

Stevanović, I.; Crespo-Valero, P.; Blagovic, K.; Bongard, F.; Mosig, J. R.

doi:10.1109/tmtt.2006.882876

Cited by 70 publications

(60 citation statements)

References 32 publications

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“…The first part of this section generalizes this formulation to periodic systems, and shows that the EFIE and MFIE are restricted to the unit cell with periodic boundary conditions. The EFIE and MFIE involve the pseudo-periodic dyadic Green's function, whose evaluation can be accelerated with Ewald's method [19,[22][23][24]. The MoM is used to discretize and solve the integral equations for the equivalent surface currents.…”

Section: Surface Integral Formulation For Electromagnetic Scattering mentioning

confidence: 99%

Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation

Gallinet¹,

Martin²

2010

Photonics and Nanostructures - Fundamentals and Applications

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The surface integral formulation is a flexible, multiscale and accurate tool to simulate light scattering on nanostructures. Its generalization to periodic arrays is introduced in this paper. The general electromagnetic scattering problem is reduced to a discretizated model using the Method of Moments on the surface of the scatterers in the unit cell. The study of the resonances of an array of bowtie antennas illustrates the main features of the method. When placed into an array, the bowtie antennas show additional resonances compared to those of an individual antenna. Using the surface integral formulation, we are able to investigate both nearfield and far-field properties of these resonances, with a high level of accuracy. #

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Section: Surface Integral Formulation For Electromagnetic Scattering mentioning

confidence: 99%

Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation

Gallinet¹,

Martin²

2010

Photonics and Nanostructures - Fundamentals and Applications

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“…Although SIE methods generate dense matrices, the fact that they scale with only the second power of the lateral dimension makes them very efficient for homogeneous scatterers. Very popular in the microwave community, SIE methods based on the method of moments (MoM) [12,26] have also been extensively used in the microwave regime for periodic lossy [21,[27][28][29] or metallic [30] systems. Recently, it has been successfully introduced to optics to simulate individual high permittivity and plasmonic scatterers [25].…”

Section: Introductionmentioning

confidence: 99%

Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach

2010

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A surface integral formulation for light scattering on periodic structures is presented. Electric and magnetic field equations are derived on the scatterers' surfaces in the unit cell with periodic boundary conditions. The solution is calculated with the method of moments and relies on the evaluation of the periodic Green's function performed with Ewald's method. The accuracy of this approach is assessed in detail. With this versatile boundary element formulation, a very large variety of geometries can be simulated, including doubly periodic structures on substrates and in multilayered media. The surface discretization shows a high flexibility, allowing the investigation of irregular shapes including fabrication accuracy. Deep insights into the extreme near-field of the scatterers as well as in the corresponding far-field are revealed. This method will find numerous applications for the design of realistic photonic nanostructures, in which light propagation is tailored to produce novel optical effects.

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“…Its convergence can be accelerated by different techniques (such as Ewald transformations), which have been a subject of extensive research over the past years [6,7,8]. where Ej^(r) is the corresponding Bloch component of the incident field E°(r).…”

Section: Dyadic Green's Function For Periodic Structuresmentioning

confidence: 99%

Electromagnetic Scattering of Finite and Infinite 3D Lattices in Polarizable Backgrounds

Gallinet¹,

Martin

2009

AIP Conference Proceedings

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Abstract. A novel method is elaborated for the electromagnetic scattering from periodical arrays of scatterers embedded in a polarizable background. A dyadic periodic Green's function is introduced to calculate the scattered electric field in a lattice of dielectric or metallic objects. The method exhibits strong advantages: discretization and computation of the field are restricted to the volume of the scatterers in the unit cell, open and periodic boundary conditions for the electric field are included in the Green's tensor, and finally both near and far-fields physics are directly revealed, without any additional computational effort. Promising applications include the design of periodic structures such as frequency-selective surfaces, photonic crystals and metamaterials.Keywords: Electromagnetic Scattering, Dyadic Green Function, Periodic Structures PACS: 42.70. Qs,78.67.Bf,02.70.Pt Recent developments in the fabrication of periodic structures with tailored optical periodic structures call for specific modeUng tools. Most real structures are threedimensional but still very few techniques are able to simulate them without considerable computational efforts [1,2]. There is therefore a need to seek for a general method supporting full 3D vectorial calculations, enabling the investigation of both near and far-fields physics. Our approach is based on the volume integral equation for scattering in free space and at surfaces [3].We first develop the Bloch modes calculations in lattices using the Green's tensor formalism. The method exhibits strong advantages, especially about the restriction of the discretization and the minimal computational efforts required to reveal both near and far-field physics. Then two examples of calculations are reported to illustrate some physical effects that can be simulated: grating effects, propagation in multi-dimensional finite and infinite size lattices. Promising appUcations include the design of periodic structures such as frequency-selective surfaces, photonic crystals, and metamaterials. DYADIC GREEN'S FUNCTION FOR PERIODIC STRUCTURESThe scalar Green's function has been previously reported for energy bands calculations using Schrodinger's equation in a periodic potential [4]. Our objective is to deduct its dyadic form in electromagnetism for a lattice of point sources. Consider a scattering system described by a dielectric function e(r) embedded in an infinite homogeneous background medium EB. Nonmagnetic materials and harmonic fields with an exp(-/a)f) dependance are assumed. When this system is illuminated by an incident field E°(r) propagating in the background medium, the total electric field (incident plus scattered field) is a solution of the vectorial wave equation:where feg = ap-/c^ is the vacuum wave number The permittivity e(r) is assumed to have a spatial periodicity: e(r + l) = e(r), where 1 = wai +ma2 + pa3 {m,n,p integers) is a translation vector of the lattice and ai, a2, as are the translation primitive vectors. The volume of the unit cell is called Q.. If t...

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Integral-Equation Analysis of 3-D Metallic Objects Arranged in 2-D Lattices Using the Ewald Transformation

Cited by 70 publications

References 32 publications

Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation

Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation

Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach

Electromagnetic Scattering of Finite and Infinite 3D Lattices in Polarizable Backgrounds

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