Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theory and numerical modeling of photonic resonances: Quasinormal Modal
  Expansion -- Applications in Electromagnetics   The idea of the modal expansion in electromagnetics is derived from the
research on electromagnetic resonators, which play an essential role in
developments in nanophotonics. All of the electromagnetic resonators share a
common property: they possess a discrete set of special frequencies that show
up as peaks in scattering spectra and are called resonant modes. These resonant
modes are soon recognized to dictate the interaction between electromagnetic
resonators and light. This leads to a hypothesis that the optical response of
resonators is the synthesis of the excitation of each physical-resonance-state
in the system: Under the excitation of external pulses, these resonant modes
are initially loaded, then release their energy which contributes to the total
optical responses of the resonators. These resonant modes with complex
frequencies are known in the literature as the Quasi-Normal Mode (QNM).
Mathematically, these QNMs correspond to solutions of the eigenvalue problem of
source-free Maxwell's equations. In the case where the optical structure of
resonators is unbounded and the media are dispersive (and possibly anisotropic
and non-reciprocal) this requires solving non-linear (in frequency) and
non-Hermitian eigenvalue problems. Thus, the whole problem boils down to the
study of the spectral theory for electromagnetic Maxwell operators. As a
result, modal expansion formalisms have recently received a lot of attention in
photonics because of their capabilities to model the physical properties in the
natural resonance-state basis of the considered system, leading to a
transparent interpretation of the numerical results. This manuscript is
intended to extend the study of QNM expansion formalism, in particular, and
nonlinear spectral theory, in general. At the same time, several numerical
modelings are provided as examples for the application of modal expansion in
computations.

5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
37
The categories of this paper are: supr-con