Wave propagation in metamaterial structures and retrieval of homogenization parameters
Author
Ircı, Erdinç
Advisor
Ertürk, Vakur B.
Date
2007Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
Electromagnetic wave propagation in metamaterial structures (metamaterial
slabs, metamaterial cylinders, metamaterial coated conducting cylinders etc.)
are investigated. Scattered and transmitted electromagnetic fields by these structures
due to electric line sources or plane wave illuminations are found. A generic
formulation of these wave propagation problems is done, enabling any kind of
metamaterial or conventional material to be used, having any sign combination
of constitutive parameters and having any electric and/or magnetic losses.
For one of these propagation problems i.e., metamaterial coated conducting
cylinders illuminated normally with plane waves, achieving transparency and
maximizing scattering are investigated thoroughly. It is found out that, rigorous
derivation of transparency and resonance (scattering maximization) conditions
for PEC core cylinder case under the sub-wavelength limitations yields the same
conditions of two electrically small concentric layers of conjugately paired cylinders,
given in the literature (when the inner core layer is also taken to the PEC
limit). These transparency and resonance conditions are found to be heavily dependent on the permittivity of the metamaterial coating (for TE polarization)
and the ratio of core-shell radii. The relations between the permittivity
of the coating and the ratio of core-shell radii are investigated for achieving
transparency and scattering maximization. Numerical results show that these
analytical relations are quite successful and work better when the cylindrical
scatter is electrically very small.
A novel homogenization method for the retrieval of effective constitutive parameters
of metamaterials is proposed and implemented. The method is based
on the simple idea that the total reflection coefficient from a finite metamaterial
structure has to resemble the reflection from an homogeneous equivalent.
While implementing the method, 1, 2, . . ., 20 unit cells of the same metamaterial
structure are stacked and their reflection coefficients are collected. The
homogenization quality of the metamaterial is evaluated in terms of various factors,
which showed that the method is very successful to retrieve the effective
constitutive parameters of the metamaterial.
Finally, another method has been proposed for the retrieval of surface wave
propagation constants on any periodic or non-periodic grounded slab medium. As
a preliminary, the method is applied to grounded dielectric slabs. The numerical
results generally show good agreement with their theoretical counterparts.
Keywords
MetamaterialsWave propagation
Scattering
Transmission
Metamaterial cylinders
Metamaterial coated conducting cylinders
Transparency
Resonance
Radar cross section
Homogenization
Parameter retrieval
Surface waves
Grounded Slabs