Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrical aspects of first-order optical systems   We reconsider the basic properties of ray-transfer matrices for first-order
optical systems from a geometrical viewpoint. In the paraxial regime of scalar
wave optics, there is a wide family of beams for which the action of a
ray-transfer matrix can be fully represented as a bilinear transformation on
the upper complex half-plane, which is the hyperbolic plane. Alternatively,
this action can be also viewed in the unit disc. In both cases, we use a simple
trace criterion that arranges all first-order systems in three classes with a
clear geometrical meaning: they represent rotations, translations, or parallel
displacements. We analyze in detail the relevant example of an optical
resonator.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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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: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph