Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A mathematical theory for Fano resonance in a periodic array of narrow
  slits   This work concerns resonant scattering by a perfectly conducting slab with
periodically arranged subwavelength slits, with two slits per period. There are
two classes of resonances, corresponding to poles of a scattering problem. A
sequence of resonances has an imaginary part that is nonzero and on the order
of the width $\varepsilon$ of the slits; these are associated with Fabry-Perot
resonance, with field enhancement of order $1/\varepsilon$ in the slits. The
focus of this study is another class of resonances which become real valued at
normal incidence, when the Bloch wavenumber $\kappa$ is zero. These are
embedded eigenvalues of the scattering operator restricted to a period cell,
and the associated eigenfunctions extend to surface waves of the slab that lie
within the radiation continuum. When $0<|\kappa|\ll 1$, the real embedded
eigenvalues will be perturbed as complex-valued resonances, which induce the
Fano resonance phenomenon. We derive the asymptotic expansions of embedded
eigenvalues and their perturbations as resonances when the Bloch wavenumber
becomes nonzero. Based on the quantitative analysis of the diffracted field, we
prove that the Fano-type anomalies occurs for the transmission of energy
through the slab, and show that the field enhancement is of order
$1/(\kappa\varepsilon)$, which is stronger than Fabry-Perot resonance.

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The categories of this paper are: q-alg
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat