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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - S. S. Girgel
TI  - Kummer--Gaussian scalar astigmatic three-dimensional light beams
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2013
SP  - 19
EP  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2013_1_a2/
LA  - ru
ID  - PFMT_2013_1_a2
ER  - 
%0 Journal Article
%A S. S. Girgel
%T Kummer--Gaussian scalar astigmatic three-dimensional light beams
%J Problemy fiziki, matematiki i tehniki
%D 2013
%P 19-23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2013_1_a2/
%G ru
%F PFMT_2013_1_a2
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/

[1] A. M. Goncharenko, Gaussovy puchki sveta, Nauka i tekhnika, Mn., 1977, 142 pp.

[2] Yu. A. Ananev, Opticheskie rezonatory i problema raskhodimosti lazernogo izlucheniya, Nauka, M., 1990, 264 pp.

[3] A. P. Kiselev, “Novye struktury paraksialnykh gaussovykh puchkov”, Opt. i spektr., 96:4 (2004), 533–535

[4] A. E. Siegman, “Hermite-gaussian function of complex argument as optical-beam eigenfunction”, JOSA, 63:9 (1973), 1093–1094 | MR

[5] R. Pratesi, L. Ronchi, “Generalized gaussian beams in free space”, JOSA, 17:9 (1977), 1274–1276

[6] M. A. Bandres, J. C. Guttierres-Vega, “Cartesian beams”, Optics Letters, 32:23 (2007), 3450–3461

[7] S. S. Girgel, “Fizicheskie svoistva skalyarnykh 2D puchkov Kummera–Gaussa”, Problemy fiziki, matematiki i tekhniki, 2011, no. 4 (9), 19–23 | Zbl

[8] S. S. Girgel, “Svoistva skalyarnykh 2D puchkov Kummera–Gaussa”, Problemy fiziki, matematiki i tekhniki, 2010, no. 1 (2), 7–11 | Zbl

[9] N. N. Lebedev, Spetsialnye funktsii i ikh prilozheniya, GITTL, M., 1953, 379 pp.

[10] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979, 830 pp. | MR

[11] E. Yanke, F. Emde, F. Lesh, Spetsialnye funktsii, Nauka, M., 1977, 342 pp.

[12] A. Torre, “A note on the general solution of paraxial wave equation: a Lie algebra view”, Journ. Opt. A, 10:8 (2008), 055006–055020 | MR