Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Definition of Effective Permittivity and Permeability For Thin
  Composite Layers   The problem of definition of effective material parameters (permittivity and
permeability) for composite layers containing only one-two parallel arrays of
complex-shaped inclusions is discussed. Such structures are of high importance
for the design of novel metamaterials, where the realizable layers quite often
have only one or two layers of particles across the sample thickness. Effective
parameters which describe the averaged induced polarizations are introduced. As
an explicit example, we develop an analytical model suitable for calculation of
the effective material parameters $\epsilon_{\rm{eff}}$ and $\mu_{\rm{eff}}$
for double arrays of electrically small electrically polarizable scatterers.
Electric and magnetic dipole moments induced in the structure and the
corresponding reflection and transmission coefficients are calculated using the
local field approach for the normal plane-wave incidence, and effective
parameters are introduced through the averaged fields and polarizations. In the
absence of losses both material parameters are purely real and satisfy the
Kramers-Kronig relations and the second law of thermodynamics. We compare the
analytical results to the simulated and experimental results available in the
literature. The physical meaning of the introduced parameters is discussed in
detail.

30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an