Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition
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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-selfadjoint 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.
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-selfadjoint 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
2004
Language
English
Publication/Series
Technical Report LUTEDX/(TEAT-7124)/1-24/(2004)
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Document type
Report
Publisher
[Publisher information missing]
Topic
- Electrical Engineering, Electronic Engineering, Information Engineering
Status
Published
Report number
TEAT-7124
Research group
- Electromagnetic theory