Geodesic
Kummer--Gaussian scalar astigmatic three-dimensional light beams
Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 19-23

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The formalism for the description of paraxial $3D$ Gaussian-like light Kummer–Gaussian beams by a simple astigmatism is offered. Conditions of their physical realizability are formulated. New types of Kummer–Gaussian beams are found. Such beams are presented by Gaussian product on Kummer function of a complex argument and a nonnegative integer index $n$.
Keywords: paraxial beams, Hermite–Gaussian beams, Kummer–Gaussian beams, Gaussian-like beams. 
@article{PFMT_2013_1_a2,
     author = {S. S. Girgel},
     title = {Kummer--Gaussian scalar astigmatic three-dimensional light beams},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {19--23},
     publisher = {mathdoc},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2013_1_a2/}
}
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S. S. Girgel. Kummer--Gaussian scalar astigmatic three-dimensional light beams. Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 19-23. http://geodesic.mathdoc.fr/item/PFMT_2013_1_a2/