Electromagnetics in deterministic and stochastic bianisotropic media
Electromagnetics in deterministic and stochastic bianisotropic media
Electromagnetics in deterministic and stochastic bianisotropic media
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Assumption<br />
Homogenisation (determ<strong>in</strong>istic <strong>media</strong>)<br />
The medium exhibits small scale periodicity, i.e.,<br />
Aor = A ɛ or(x) = A per<br />
�<br />
x<br />
�<br />
or ,<br />
ɛ<br />
Gd = G ɛ d(x) = G per<br />
�<br />
x<br />
�<br />
d ,<br />
ɛ<br />
where A per<br />
or (·), G per<br />
d (·) are periodic matrix-valued functions on the<br />
parallelepided Y = [0, ℓ1] × [0, ℓ2] × [0, ℓ3] ⊂ R 3 <strong>and</strong> 0 < ɛ ≪ 1.<br />
(37)<br />
The set Y may be considered as the fundamental cell of the medium; the<br />
whole medium structure can be generated by repeat<strong>in</strong>g the structure <strong>in</strong> Y<br />
us<strong>in</strong>g translations.<br />
To ease notation, we drop the superscript “per” from Aper Aɛ � �<br />
or(x) = Aor <strong>and</strong> Gɛ d(x) = Gd <strong>in</strong>stead.<br />
� x<br />
ɛ<br />
� x<br />
ɛ<br />
or <strong>and</strong> G per<br />
d<br />
<strong>and</strong> use<br />
I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 44 / 95
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