2010/05/31 by Guillaume Dupont, Sébastien Guenneau, Sebastien Guenneau +2 · 13 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Antenna and Metasurface Technologies #Anisotropy #Cloaking #Electromagnetic Scattering and Analysis #Geometry #Mathematical analysis #Mathematics #Metamaterial #Metamaterials and Metasurfaces Applications #Optics #Physics #Plane (geometry) #Regular polygon #Singularity #Tensor (intrinsic definition) #physics.comp-ph #physics.optics
paper · pdf · doi:10.1103/physreva.82.033840
published in Physical Review A 82(3) (American Physical Society) · 6 pages, 6 figures, Current Status of Manuscript: 19Apr10 26May10-Sent on appeal;report rcvd 29Dec09 13Apr10-Ed. decision and/or ref. comments to author;response rcvd 04Dec09 21Dec09-Ed. decision and/or ref. comments to author;response rcvd 01Dec09-Transferred from PRL to PRA 18Aug09 30Nov09-Ed.decision and/or ref. comments to author;response rcvd 14Aug09 - Correspondence sent to author
arxiv created 2010/05/31 · openalex publication_date 2010/09/30 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive the expressions for the anisotropic heterogeneous tensors of permittivity and permeability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map an arbitrary region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components. Moreover, a reduced set of parameters leads to nonmagnetic two-dimensional carpets in p polarization (i.e., for a magnetic field orthogonal to the plane containing the carpet). Such an arbitrarily shaped carpet is shown to work over a finite bandwidth when it is approximated by a checkerboard with 190 homogeneous cells of piecewise constant anisotropic permittivity. We finally perform some finite element computations in the full vector three-dimensional case for a plane wave in normal incidence and a Gaussian beam in oblique incidence. The latter requires perfectly matched layers set in a rotated coordinate axis which exemplifies the role played by geometric transforms in computational electromagnetism.