Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness in inverse diffraction grating problems with infinitely many
  plane waves at a fixed frequency   This paper is concerned with the inverse diffraction problems by a periodic
curve with Dirichlet boundary condition in two dimensions. It is proved that
the periodic curve can be uniquely determined by the near-field measurement
data corresponding to infinitely many incident plane waves with distinct
directions at a fixed frequency. Our proof is based on Schiffer's idea which
consists of two ingredients: i) the total fields for incident plane waves with
distinct directions are linearly independent, and ii) there exist only finitely
many linearly independent Dirichlet eigenfunctions in a bounded domain or in a
closed waveguide under additional assumptions on the waveguide boundary. Based
on the Rayleigh expansion, we prove that the phased near-field data can be
uniquely determined by the phaseless near-field data in a bounded domain, with
the exception of a finite set of incident angles. Such a phase retrieval result
leads to a new uniqueness result for the inverse grating diffraction problem
with phaseless near-field data at a fixed frequency. Since the incident
direction determines the quasi-periodicity of the boundary value problem, our
inverse issues are different from the existing results of [Htttlich & Kirsch,
Inverse Problems 13 (1997): 351-361] where fixed-direction plane waves at
multiple frequencies were considered.

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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: cs