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. 
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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/

[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.