Generalized Bessel–Gaussian beams of continuous order
Problemy fiziki, matematiki i tehniki, no. 4 (2015), pp. 11-15 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The new solutions of the parabolic equation featuring the generalized Bessel–Gaussian beams of the continuous order are offered. They are characterized by three free continuous parameters and possess a spiral wave front. Restrictions on these parameters at which the explored fractional beams transfer terminating power are discovered. Graphic simulation of such beams is held.
Keywords: fractional beams, beams of Bessel–Gaussian, square integrability.
@article{PFMT_2015_4_a1,
     author = {S. S. Girgel},
     title = {Generalized {Bessel{\textendash}Gaussian} beams of continuous order},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {11--15},
     year = {2015},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_4_a1/}
}
TY  - JOUR
AU  - S. S. Girgel
TI  - Generalized Bessel–Gaussian beams of continuous order
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2015
SP  - 11
EP  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/PFMT_2015_4_a1/
LA  - ru
ID  - PFMT_2015_4_a1
ER  - 
%0 Journal Article
%A S. S. Girgel
%T Generalized Bessel–Gaussian beams of continuous order
%J Problemy fiziki, matematiki i tehniki
%D 2015
%P 11-15
%N 4
%U http://geodesic.mathdoc.fr/item/PFMT_2015_4_a1/
%G ru
%F PFMT_2015_4_a1
S. S. Girgel. Generalized Bessel–Gaussian beams of continuous order. Problemy fiziki, matematiki i tehniki, no. 4 (2015), pp. 11-15. http://geodesic.mathdoc.fr/item/PFMT_2015_4_a1/

[1] A. P. Kiselev, “Lokalizovannye svetovye volny: paraksialnye i tochnye resheniya volnovogo uravneniya (obzor)”, Optika i spektroskopiya, 102:4 (2007), 661–681

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

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

[4] 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, 8 pp.

[5] Shao Hua Tao, Woei Ming Lee, Xiaocong Yuan, “Experimental study of holographic generation of fractional Bessel beams”, Applied Optics, 43:1 (2004), 122–126 | DOI

[6] J. Durnin, “Exact solutions for nondiffracting beams. I: The scalar theory”, JOSA A, 4:4 (1987), 651–654 | DOI

[7] F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss beams”, Optics Communications, 64:6 (1987), 491–495 | DOI

[8] V. Bagini et al., “Generalized Bessel–Gauss beams”, Journal of Modern Optics, 43:6 (1996), 1155–1166 | MR | Zbl

[9] C. Palma et al., “Imaging of generalized Bessel–Gauss beams”, Journal of Modern Optics, 43:11 (1996), 2269–2277 | DOI | MR

[10] M. Santarsiero, “Propagation of general Bessel–Gauss beams throught ABCD optical systems”, Optics Communications, 132 (1996), 1–7 | DOI

[11] S. S. Girgel, “Polyarizatsionnye svoistva bessel-gaussovykh puchkov sveta. Problemy vzaimodeistviya izlucheniya s veschestvom”, Izvestiya Gomelskogo gosuniversiteta im. F. Skoriny, 2001, no. 6(9), 150–154

[12] S. S. Girgel, “Polyarizatsionnye i energeticheskie svoistva vektornykh bessel-gaussovykh svetovykh puchkov”, Izvestiya Gomelskogo gosuniversiteta im. F. Skoriny, 2006, no. 6(39), Ch. 1, 49–52 | MR

[13] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. II, Nauka, M., 1974, 295 pp. | MR

[14] U. Miller, Simmetriya i razdelenie peremennykh, Mir, M., 1981, 342 pp. | MR

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

[16] E. G. Abramochkin, V. G. Volosnikov, “Spiralnye puchki sveta”, UFN, 174:12 (2004), 1273–1300 | DOI

[17] Dzh. A. Stretton, Teoriya elektromagnetizma, OGIZ. GITTL, M., 1948, 539 pp.

[18] C. J. R. Sheppard, T. Wilson, “Gaussian-beam theory of lenses with annular aperture”, IEEE J. Microwaves, Optics and Acoustics, 2 (1978), 105–112 | DOI

[19] 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

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

[21] C. C. Girgel, “Svoistva vektornykh paraksialnykh svetovykh puchkov. II: Neodnorodnaya polyarizatsiya”, Problemy fiziki, matematiki i tekhniki, 2012, no. 1(10), 11–14

[22] C. C. Girgel, “Svoistva vektornykh paraksialnykh svetovykh puchkov. I: Odnorodnaya polyarizatsiya”, Problemy fiziki, matematiki i tekhniki, 2011, no. 1(6), 20–24