Geodesic
Solutions of the wave equation in parabolic rotary coordinates. I. 3D Kummer–Kummer light beams with the continuous angular index
Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 13-17

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Analytical expressions in the closed form for nonparaxial and paraxial 3D Kummer–Kummer (K-K) beams with continuous angular index $m$ in parabolic rotary coordinates are offered and analyzed. Physical restrictions on possible values of the free parameters of such beams are formulated.
Keywords: nonparaxial beams, paraxial beams, parabolic beams, Kummer–Kummer beams. 
S. S. Girgel. Solutions of the wave equation in parabolic rotary coordinates. I. 3D Kummer–Kummer light beams with the continuous angular index. Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 13-17. http://geodesic.mathdoc.fr/item/PFMT_2020_3_a1/
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[1] S.S. Girgel, “Bezdifraktsionnye asimmetrichnye volnovye polya Besselya nepreryvnogo poryadka”, Problemy fiziki, matematiki i tekhniki, 2017, no. 1 (30), 13–16

[2] S.S. Girgel, “Obobschennye puchki Besselya–Gaussa nepreryvnogo poryadka”, Problemy fiziki, matematiki i tekhniki, 2015, no. 4(25), 11–15

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

[4] S.S. Girgel, “Tsirkulyarnye 3D svetovye puchki Kummera–Gaussa s nepreryvnym uglovym spektrom”, Problemy fiziki, matematiki i tekhniki, 2019, no. 1(38), 4–7

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

[6] S.S. Girgel, “Opticheskie puchki Vebera–Gaussa s nepreryvnym uglovym spektrom”, Problemy fiziki, matematiki i tekhniki, 2018, no. 4(37), 1–5

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

[8] F.M. Mors, G.M. Feshbakh, Metody teoreticheskoi fiziki, Per. s angl., v. 2, IL, M., 1960, 886 pp.

[9] D. Deng et al., “Three-dimensional nonparaxial beams in parabolic rotational coordinates”, Optics Letters, 38:19 (2013), 3934–3936 | DOI

[10] L.C. Woon, L.Y. Willartzen, “Helmholtz equation in parabolic rotation coordinates application to wave problems in quantum mechanics and acoustics”, Mathematics and Computers in simulation, 65 (2004), 337–349 | DOI | MR

[11] W. Miller, “Lie theory and separation of variables. II. Parabolic coordinates”, Siam J. Math. Anal., 5:5 (1974), 822–836 | DOI | MR | Zbl

[12] A.A. Kovalev, V.V. Kotlyar, “Lazernye puchki Khankelya–Besselya”, Kompyuternaya optika, 35:3 (2011), 297–304 | Zbl

[13] Abramovits M., Stigan I. (red.), Spravochnik po spetsialnym funktsiyam, Per. s angl., Nauka, M., 1979, 832 pp.

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

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