Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Turing Patterns in Nonlinear Optics   The phenomenon of pattern formation in nonlinear optical resonators is
commonly related to an off-resonance excitation mechanism, where patterns occur
due to mismatch between the excitation and resonance frequency. In this paper
we show that the patterns in nonlinear optics can also occur due to the
interplay between diffractions of coupled field components. The reported
mechanism is analogous to that of local activation and lateral inhibition found
in reaction-diffusion systems by Turing. We study concretely the degenerate
optical parametric oscillators. A local activator-lateral inhibitor mechanism
is responsible for generation of Turing patterns in form of hexagons.

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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin