Efficient Higher Order FullWave Numerical Analysis of 3D Cloaking Structures
 Slobodan V. Savić,
 Ana B. Manić,
 Milan M. Ilić,
 Branislav M. Notaroš
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Highly efficient and versatile computational electromagnetic analysis of 3D transformationbased metamaterial cloaking structures based on a hybridization of a higher order finite element method for discretization of the cloaking region and a higher order method of moments for numerical termination of the computational domain is proposed and demonstrated. The technique allows for an effective modeling of the continuously inhomogeneous anisotropic cloaking region, for cloaks based on both linear and nonlinear coordinate transformations, using a very small number of large curved finite elements with continuous spatial variations of permittivity and permeability tensors and highorder prefined field approximations throughout their volumes, with a very small total number of unknowns. In analysis, there is no need for a discretization of the permittivity and permeability profiles of the cloak, namely for piecewise homogeneous (layered) approximate models, with material tensors replaced by appropriate piecewise constant approximations. Numerical results show a very significant reduction (three to five orders of magnitude for the simplest possible 6element model and five to seven orders of magnitude for an hrefined 24element model) in the scattering cross section of a perfectly conducting sphere with a metamaterial cloak, in a broad range of wavelengths. Given the introduced explicit approximations in modeling of the spherical geometry and continuous material tensor profiles (both by fourthorder Lagrange interpolating functions), and inherent numerical approximations involved in the finite element and moment method techniques and codes, the cloaking effects are shown to be predicted rather accurately by the fullwave numerical analysis method.
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 Title
 Efficient Higher Order FullWave Numerical Analysis of 3D Cloaking Structures
 Journal

Plasmonics
Volume 8, Issue 2 , pp 455463
 Cover Date
 20130601
 DOI
 10.1007/s1146801294100
 Print ISSN
 15571955
 Online ISSN
 15571963
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Numerical analysis
 3D invisibility cloaks
 Transformation optics
 Scattering
 Metamaterials
 Higher order methods
 Industry Sectors
 Authors

 Slobodan V. Savić ^{(1)}
 Ana B. Manić ^{(2)}
 Milan M. Ilić ^{(1)} ^{(2)}
 Branislav M. Notaroš ^{(2)}
 Author Affiliations

 1. School of Electrical Engineering, University of Belgrade, Belgrade, 11120, Serbia
 2. Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, 805231373, USA