Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blowing up Light: A nonlinear amplification scheme for electromagnetic
  waves   We use blow-up solutions of nonlinear Helmholtz equations to introduce a
nonlinear resonance effect that is capable of amplifying electromagnetic waves
of particular intensity. To achieve this, we propose a scattering setup
consisting of a Kerr slab with a negative (defocusing) Kerr constant placed to
the left of a linear slab in such a way that a left-incident coherent TE wave
with a specific incidence angle and intensity realizes a blow-up solution of
the corresponding Helmholtz equation whenever its wavenumber $k$ takes a
certain critical value, $k_\star$. For $k=k_\star$, the solution blows up at
the right-hand boundary of the Kerr slab. For $k<k_\star$, the setup defines a
scattering system with a transmission coefficient that diverges as
$(k-k_\star)^{-4}$ for $k\to k_\star$. By tuning the distance between the slabs
we can use this setup to amplify coherent waves with a wavelength in an
extremely narrow spectral band. For nearby wavelengths the setup serves as a
filter. Our analysis makes use of a nonlinear generalization of the transfer
matrix of the scattering theory as well as properties of unidirectionally
invisible potentials.

21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
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The categories of this paper are: eess
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat