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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 (2003) In Technical Report LUTEDX/(TEAT-7119)/1-27/(2003)
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 non-vanishing Bloch waves, providing a new means of

homogenization. The representation is valid for an arbitrary wave vector in

the first Brillouin zone.
Please use this url to cite or link to this publication:
author
; ; ; and
organization
publishing date
type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7119)/1-27/(2003)
publisher
Department of Electroscience, Lund University
report number
TEAT-7119
language
English
LU publication?
yes
additional info
Published version: Multiscale Modeling & Simulation, Vol. 4, No. 1, pp. 149-171, 2005.
id
64778400-7ddb-40fa-b12e-918559efc429 (old id 530371)
date added to LUP
2016-04-04 14:39:12
date last changed
2023-03-24 12:20:52
@techreport{64778400-7ddb-40fa-b12e-918559efc429,
  abstract     = {{Using Bloch waves to represent the full solution of Maxwell’s equations in<br/><br>
periodic media, we study the limit where the material’s period becomes much<br/><br>
smaller than the wavelength. It is seen that for steady-state fields, only a<br/><br>
few of the Bloch waves contribute to the full solution. Effective material<br/><br>
parameters can be explicitly represented in terms of dyadic products of the<br/><br>
mean values of the non-vanishing Bloch waves, providing a new means of<br/><br>
homogenization. The representation is valid for an arbitrary wave vector in<br/><br>
the first Brillouin zone.}},
  author       = {{Sjöberg, Daniel and Engström, Christian and Kristensson, Gerhard and Wall, David J.N. and Wellander, Niklas}},
  institution  = {{Department of Electroscience, Lund University}},
  language     = {{eng}},
  number       = {{TEAT-7119}},
  series       = {{Technical Report LUTEDX/(TEAT-7119)/1-27/(2003)}},
  title        = {{A Floquet-Bloch decomposition of Maxwell's equations, applied to homogenization}},
  url          = {{https://lup.lub.lu.se/search/files/6409532/624887.pdf}},
  year         = {{2003}},
}