Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalised Hermite-Gaussian beams and mode transformations   Generalised Hermite-Gaussian modes (gHG modes), an extended notion of
Hermite-Gaussian modes (HG modes), are formed by the summation of normal HG
modes with a characteristic function $\alpha$, which can be used to unite
conventional HG modes and Laguerre-Gaussian modes (LG modes). An infinite
number of normalised orthogonal modes can thus be obtained by modulation of the
function $\alpha$. The gHG mode notion provides a useful tool in analysis of
the deformation and transformation phenomena occurring in propagation of HG and
LG modes with astigmatic perturbation.

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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg