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Author Dupont, Guillaume ♦ Guenneau, Sebastien ♦ Enoch, Stefan
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword 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
Abstract 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.
ISSN 10502947
Educational Use Research
Learning Resource Type Article
Publisher Date 2010-09-15
Publisher Place United States
Journal Physical Review. A
Volume Number 82
Issue Number 3


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