ABSTRACT
Within the frame of the effective medium approximation, numerous models can be used to retrieve εeff from the dielectric constants of the different elements of the effective medium (air, silicon, oxide, etc.). It is worth mentioning here that such models are usually used to describe isotropic heterogeneous materials with heterogeneities size much smaller than the wavelength of light. ree main models have been intensively used, namely Lorentz-Lorentz (LL), Maxwell Garnet (MG1 and MG2), and Bruggeman (EMA). All of them could be derived from the following generic formula (Aspnes et al. 1979):
(8.1) ε ε ε ε
ε ε
ε ε
ε ε
ε ε eff h
h wi−
+ =
−
+ +
−
+ +
2 2 21 1
2 v v th vii =∑ 1
where εh, ε1, ε2,... are, respectively, the complex dielectric constants of the host medium and the inclusions (type 1, 2,...) with a proportion in volume of v1, v2, ... Relations in the case of the LL (MG1), MG2, and EMA approximations can simply be derived for εh = 1, εh = εeff and εh = εi, respectively. e Sellmeyer model has also been used, and can simply be obtained by removing the denominator and taking εh = 1.
