Abstract
This chapter explains how a composite material with a periodic microstructure can be modeled with effective material parameters in the low-frequency limit. In particular, we treat the problem of how to compute the material parameters when the scale of the microstructure is finite compared to the applied wavelength. For lossless anisotropic media, a self-adjoint eigenvalue problem can be formulated to compute the relevant material parameters, whereas a singular value decomposition of Maxwell’s equations can be used to treat the general lossy bianisotropic case. The fundamental idea is the number of degrees of freedom: homogenization is possible precisely when the electromagnetic field can only be excited (or observed) corresponding to the degrees of freedom possible in a homogeneous material. When the scale difference is not large, this requires spatial dispersion in the homogenized model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Sirenko, Y.K., Ström, S. (2010). Finite Scale Homogenization of Periodic Bianisotropic Structures. In: Sirenko, Y., Ström, S. (eds) Modern Theory of Gratings. Springer Series in Optical Sciences, vol 153. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1200-8_5
Download citation
DOI: https://doi.org/10.1007/978-1-4419-1200-8_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1199-5
Online ISBN: 978-1-4419-1200-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)