Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Paraxial Wave Analysis of 3D Airy Beams   The 3D Airy beam (AiB) is thoroughly explored from a wave-theory point of
view. We utilize the exact spectral integral for the AiB to derive local
ray-based solutions that do not suffer from the limitations of the conventional
parabolic equation (PE) solution, and are valid far beyond the paraxial zone
and for longer ranges. The ray topology near the main lobe of the AiB
delineates a hyperbolic umilic diffraction catastrophe, consisting of a cusped
double-layered caustic, but this caustic is deformed in the far range where the
field loses its beam shape. The field in the vicinity of this caustic is
described uniformly by a hyperbolic umilic canonical integral which is
structured explicitly on the local geometry of the caustic as obtained from the
initial field distribution. In order to accommodate the finite-energy AiB we
also modify the canonical integral by adding a complex loss parameter. The
canonical integral is calculated using a series expansion and the results are
used to identify the validity zone of the conventional PE solution. The
analysis is performed within the framework of the non-dispersive AiB where the
aperture field is scaled with frequency such that the ray skeleton is
frequency-independent. This scaling enables an extension of the theory to the
ultra wide band (UWB) regime and ensures that the pulsed field propagates along
the curved beam trajectory without dispersion, as will be demonstrated in a
subsequent publication.

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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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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: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas