Circular $3D$ Kummer--Gauss beams with the continuous angular index
Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 16-20.

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

Analytical expressions in the closed shape for circular $3D$ Kummer–Gauss beams $(cK-G)$ with the continuous angular coefficient $m$ are offered and analyzed. Physical restrictions on possible values of the free parameters of such beams are formulated. Pictorial modeling of beams $(cK-G)$ is fulfilled and shown that the continuous values of an angular coefficient $m$ and complex values of the free parameter $\nu$ are physically possible.
Keywords: paraxial beams, circular beams, Kummer–Gaussian beams.
@article{PFMT_2019_1_a2,
     author = {S. S. Girgel},
     title = {Circular $3D$ {Kummer--Gauss} beams with the continuous angular index},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {16--20},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2019_1_a2/}
}
TY  - JOUR
AU  - S. S. Girgel
TI  - Circular $3D$ Kummer--Gauss beams with the continuous angular index
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2019
SP  - 16
EP  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2019_1_a2/
LA  - ru
ID  - PFMT_2019_1_a2
ER  - 
%0 Journal Article
%A S. S. Girgel
%T Circular $3D$ Kummer--Gauss beams with the continuous angular index
%J Problemy fiziki, matematiki i tehniki
%D 2019
%P 16-20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2019_1_a2/
%G ru
%F PFMT_2019_1_a2
S. S. Girgel. Circular $3D$ Kummer--Gauss beams with the continuous angular index. Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 16-20. http://geodesic.mathdoc.fr/item/PFMT_2019_1_a2/

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

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

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

[4] M.A. Bandres, J.C. Gutierres-Vega, “Vector Helmholtz–Gauss and vector Laplace–Gauss beams”, Optics Letters, 30:16 (2005), 2155–2157 | DOI | MR

[5] F. Gori, G. Guattari, C. Padovani, “Bessel-Gaussian beams”, Opt. Communs., 64 (1987), 491–495 | DOI

[6] M.A. Bandres, J.C. Gutierrez-Vega, “Circular beams”, Optics Letters, 33:2 (2008), 177–179 | DOI

[7] M.A. Bandres, D. Lopez-Mago, J.C. Gutierrez-Vega, “Higher-order moments and overlaps of rotationally symmetric beams”, J. Opt., 12 (2010), 015706 | DOI

[8] D. Lopez-Mago, M.A. Bandres, J.C. Gutierrez-Vega, “Propagation of Whittaker–Gaussian Beams”, Proc. of SPIE, 7430, 2011, 743013, 8 pp. | DOI

[9] S.S. Girgel, “Bezdifraktsionnye asimmetrichnye volnovye polya Besselya nepreryvnogo poryadka”, Problemy fiziki, matematiki i tekhniki, 2017, no. 1 (30), 13–16

[10] S.S. Girgel, “Obobschennye asimmetrichnye volnovye puchki Besselya–Gaussa nepreryvnogo poryadka”, Problemy fiziki, matematiki i tekhniki, 2017, no. 2 (31), 10–14

[11] S.S. Girgel, “Puchki Kummera bez gaussovoi apodizatsii s perenosimoi konechnoi moschnostyu”, Problemy, fiziki, matematiki i tekhniki, 2015, no. 3 (24), 7–9

[12] U. Miller, Simmetriya i razdelenie peremennykh, Mir, M., 1981, 342 pp.

[13] R.A. Waldron, “A helical coordinate system and its applications in electromagnetic theory”, Quart. Journ. Mech. and Applied Math., XI:4 (1958), 438–461 | DOI | MR | Zbl

[14] P.L. Overfelt, “Scalar optical beams with helical symmetry”, Phys. Rev. A, 46:6 (1992), 3516–3522 | DOI | MR

[15] M.V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps”, Journal of Optics, 2003, no. 6, 259–268

[16] S.H. Tao, W.M. Lee, X. Yuan, “Experimental study of holographic generation of fractional Bessel beams”, Applied Optics, 43:1 (2004), 122–126 | DOI | MR

[17] J.C. Gutierrez-Vega, “Fractionalization of optical beams: I. Planar Analysis”, Optics Letters, 32:11 (2007), 1521–1523 | DOI

[18] J.C. Gutierrez-Vega, “Fractionalization of optical beams: II. Elegant Laguerre–Gaussian modes”, Optics Express, 15:10 (2007), 6300–6313 | DOI

[19] J.C. Gutierrez-Vega, C. Lopez-Mariscal, “Nondiffracting vortex beams with continuous orbital angular momentum order dependence”, J. Opt. A. Pure Appl. Opt., 2008, 10015009

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

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

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

[23] G. Vallone, “On the properties of Circular-Beams: normalization, Laguerre–Gauss expansion and free-space divergence”, Optics Letters, 40:8 (2015), 1717–1720 | DOI