Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier Optics treatment of Classical Relativistic Electrodynamics   In this paper we couple Synchrotron Radiation (SR) theory with a branch of
physical optics, namely laser beam optics. We show that the theory of laser
beams is successful in characterizing radiation fields associated with any SR
source. Both radiation beam generated by an ultra-relativistic electron in a
magnetic device and laser beam are solutions of the wave equation based on
paraxial approximation. It follows that they are similar in all aspects. In the
space-frequency domain SR beams appear as laser beams whose transverse extents
are large compared with the wavelength. In practical situations (e.g.
undulator, bending magnet sources), radiation beams exhibit a virtual "waist"
where the wavefront is often plane. Remarkably, the field distribution of a SR
beam across the waist turns out to be strictly related with the inverse Fourier
transform of the far-field angle distribution. Then, we take advantage of
standard Fourier Optics techniques and apply the Fresnel propagation formula to
characterize the SR beam. Altogether, we show that it is possible to
reconstruct the near-field distribution of the SR beam outside the magnetic
setup from the knowledge of the far-field pattern. The general theory of SR in
the near-zone developed in this paper is illustrated for the special cases of
undulator radiation, edge radiation and transition undulator radiation. Using
known analytical formulas for the far-field pattern and its inverse Fourier
transform we find analytical expressions for near-field distributions in terms
of far-field distributions. Finally, we compare these expressions with
incorrect or incomplete literature.

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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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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: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int