Physical properties of scalar 2D beams of Kummer -- Gauss
Problemy fiziki, matematiki i tehniki, no. 4 (2011), pp. 19-23.

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The unified formalism allowing to deduce common expressions for paraxial two-dimensional Gaussian-like light Kummer – Gaussian beams and discover correlations between them is developed. Сonditions of their physical realizability are explored in details. New types of Kummer – Gaussian beams are discovered. Such beams are presented as Gaussian product on Kummer function of complex argument and a $n$ integer index.
Keywords: paraxial beams, Hermite – Gaussian beams, Kummer – Gaussian beams, Gaussian-like beams, square integrability.
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S. S. Girgel. Physical properties of scalar 2D beams of Kummer -- Gauss. Problemy fiziki, matematiki i tehniki, no. 4 (2011), pp. 19-23. http://geodesic.mathdoc.fr/item/PFMT_2011_4_a3/

[1] Yu. A. Ananev, Opticheskie rezonatory i lazernye puchki, Nauka, M., 1990, 264 pp.

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

[3] S. S. Girgel, “Skalyarnye paraksialnye dvumernye gaussovopodobnye puchki”, Problemy fiziki, matematiki i tekhniki, 2010, no. 1 (2), 7–11 | Zbl

[4] M. A. Bandres, J. C. Gutierres-Vega, “Cartesian beams”, Optics Letters, 32:23 (2007), 3459–3461 | DOI

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

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

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

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

[9] A. D. Polyanin, Spravochnik po lineinym uravneniyam matematicheskoi fiziki, Fizmatlit, M., 2001, 576 pp.

[10] Z. Flyugge, Zadachi po kvantovoi mekhanike, v. 2, Mir, M., 1974, 418 pp.

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

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

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

[14] E. Karimi et al., “Hypergeometric-Gaussian modes”, Optics Letters, 32:21 (2007), 3053–3055 | DOI

[15] E. Karimi et al., “Improved focusing with Hypergeometric-Gaussian type-II optical modes”, Optics Express, 16:25 (2008), 21069–21075 | DOI

[16] V. V. Kotlyar i dr., “Gipergeometricheskie mody”, Kompyuternaya optika, 2006, no. 3, 16–22