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Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition

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Author

Summary, in English

We find effective, or homogenized, material parameters for Maxwell's equations when the microscopic scale becomes small compared to the scale induced by the frequencies of the imposed currents. After defining a singular value decomposition of the non-self-adjoint partial differential operator, we expand the electromagnetic field in the modes corresponding to the singular values and show that only the smallest singular values make a significant contribution to the total field when the scale is small. The homogenized material parameters can be represented with the mean values of the singular vectors through a simple formula, which is valid for wavelengths not necessarily infinitely large compared to the unit cell.

Publishing year

2005

Language

English

Pages

760-789

Publication/Series

Multiscale Modeling & Simulation

Volume

4

Issue

3

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • Maxwell's equations
  • singular value decomposition
  • homogenization
  • Bloch waves
  • dispersive media

Status

Published

ISBN/ISSN/Other

  • ISSN: 1540-3459