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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Effective Maxwell&\;#39\;s equations in a geome
try with flat split-rings and wires - Agnes Lamac
z (Universität Duisburg-Essen)
DTSTART;TZID=Europe/London:20190610T143000
DTEND;TZID=Europe/London:20190610T153000
UID:TALK125755AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/125755
DESCRIPTION:Propagation of light in heterogeneous media is a c
omplex subject of research. Key research areas ar
e photonic crystals\, negative index metamaterials
\, perfect imaging\, and cloaking. \; The m
athematical analysis of negative index materials\,
which we want to focus on in this talk\, is conne
cted to a study of singular limits in Maxwell'\
;s equations. We present a result on homogenizati
on of the time harmonic Maxwell'\;s equations i
n a complex geometry. The homogenization process i
s performed in the case that \; many (order $\
\eta^{-3}$) small (order $\\eta^1$)\, flat (order
$\\eta^2$) and highly conductive (order $\\eta^{-3
}$) metallic split-rings are distributed in a doma
in $\\Omega\\subset \\mathbb{R}^3$. We determine t
he effective behavior of this metamaterial in the
limit $\\eta\\searrow 0$. For $\\eta>\;0$\, each
single conductor occupies a simply connected doma
in\, but the conductor closes to a ring in the lim
it $\\eta\\searrow 0$. This change of topology all
ows for an extra dimension in the solution space o
f the corresponding cell-problem. Even though both
original materials (metal and void) have the same
positive magnetic permeability $\\mu_0>\;0$\, w
e show that the effective Maxwell system exhibits\
, depending on the frequency\, a negative magnetic
response. Furthermore\, we demonstrate that combi
ning the split-ring array with thin\, highly condu
cting wires can effectively provide a negative ind
ex metamaterial.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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