Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Small Beams with Large Topological Charge   Light beams can carry a discrete, in principle unbounded amount of angular
momentum. Examples of such beams, the Laguerre-Gauss modes, are frequently
expressed as solutions of the paraxial wave equation. There, they are
eigenstates of the orbital angular momentum (OAM) operator. The paraxial
solutions predict that beams with large OAM could be used to resolve
arbitrarily small distances - a dubious situation. Here we show how to solve
that situation by calculating the properties of beams free from the paraxial
approximation. We find the surprising result that indeed one can resolve
smaller distances with larger OAM, although with decreased visibility. If the
visibility is kept constant (for instance at the Rayleigh criterion, the limit
where two points are reasonably distinguishable), larger OAM does not provide
an advantage. The drop in visibility is due to a field in the direction of
propagation, which is neglected within the paraxial limit.

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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: astro-ph