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A Floquet-Bloch Decomposition of Maxwell's Equations Applied to Homogenization

Sjöberg, Daniel LU orcid ; Engström, Christian LU ; Kristensson, Gerhard LU ; Wall, David J.N. and Wellander, Niklas LU (2005) In Multiscale Modeling & Simulation 4(1). p.149-171
Abstract
Using Bloch waves to represent the full solution of Maxwell's equations in periodic media, we study the limit where the material's period becomes much smaller than the wavelength. It is seen that for steady state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the nonvanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.
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author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Multiscale Modeling & Simulation
volume
4
issue
1
pages
149 - 171
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • wos:000230501900005
  • scopus:33644684621
ISSN
1540-3459
DOI
10.1137/040607034
language
English
LU publication?
yes
id
4f5fe52e-9e1c-4fe6-b730-1d1ff4fb6d3a (old id 144345)
date added to LUP
2016-04-01 12:06:52
date last changed
2023-06-24 04:00:08
@article{4f5fe52e-9e1c-4fe6-b730-1d1ff4fb6d3a,
  abstract     = {{Using Bloch waves to represent the full solution of Maxwell's equations in periodic media, we study the limit where the material's period becomes much smaller than the wavelength. It is seen that for steady state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the nonvanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.}},
  author       = {{Sjöberg, Daniel and Engström, Christian and Kristensson, Gerhard and Wall, David J.N. and Wellander, Niklas}},
  issn         = {{1540-3459}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{149--171}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{Multiscale Modeling & Simulation}},
  title        = {{A Floquet-Bloch Decomposition of Maxwell's Equations Applied to Homogenization}},
  url          = {{https://lup.lub.lu.se/search/files/2787407/624995.pdf}},
  doi          = {{10.1137/040607034}},
  volume       = {{4}},
  year         = {{2005}},
}