Electromagnetic analysis of arbitrarily shaped pinched carpets

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.033840· OSTI ID:21456969

Dupont, Guillaume; Guenneau, Sebastien; Enoch, Stefan ^[1]

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1. Institut Fresnel, CNRS, Aix-Marseille Universite, Campus Universitaire de Saint-Jerome, 13013 Marseille (France)

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.

• OSTI ID: 21456969
• Journal Information: Physical Review. A, Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevA.82.033840; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANISOTROPY
COORDINATES
ELECTROMAGNETISM
FINITE ELEMENT METHOD
LAYERS
MAGNETIC FIELDS
MAGNETIC SUSCEPTIBILITY
PERMITTIVITY
POLARIZATION
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
WAVE PROPAGATION
CALCULATION METHODS
DIELECTRIC PROPERTIES
ELECTRICAL PROPERTIES
MAGNETIC PROPERTIES
MAGNETISM
MATHEMATICAL SOLUTIONS
NUMERICAL SOLUTION
PHYSICAL PROPERTIES