On solution of the light scattering problem for a spheroid in the TM and TE modes when using spheroidal bases
Farafonov V. G. 1, Il'in V. B. 1,2,3, Turichina D.G. 2,3
1Saint-Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia
2St. Petersburg State University, St. Petersburg, Russia
3Pulkovo Astronomical Observatory, Russian Academy of Sciences, St. Petersburg, Russia
Email: far@aanet.ru, ilin55@yandex.ru, t.dasha5@mail.ru

Light scattering by spheroids plays an important role in various applications. The most efficient algorithm to calculate the optical properties of spheroids implies the field expansions in a special spheroidal basis, but its application is limited by three problems - difficulties of computations of the spheroidal functions of complex argument, the absent transition to the standard T-matrix, and loss of precision in complicated calculations for one case of the incident radiation polarization (TE mode). The first two difficulties have been recently overcome to a large extent, and in this work we solve the last problem - by using T-matrix transformations, we find the way of expressing the TE mode solution through the more simple and stable TM mode solution. Numerical calculations performed by us demonstrate that the suggested approach improves the result accuracy by several orders, accelerates solution in several times and significantly extends its applicability range (up to the diffraction parameters exceeding 100). Keywords: light scattering, T-matrix, spheroidal scatterers.
  1. A. Sihvola. J. Nanomater., 2007, 45090 (2007). DOI: 10.1155/2007/45090
  2. Thermo Fisher Scientific [Electronic source]. URL: https://www.thermofisher.com /ru/ru/home/life-science/cell-culture/organoids-spheroids-3d-cell-culture.html
  3. R. Hogg. KONA Powder Part. J., 32, 227 (2015). DOI: 10.14356/kona.2015014
  4. M.M. Bukharin, V.Ya. Pecherkin, A.K. Ospanova et al. Sci. Rep., 12, 7997 (2022). DOI: 10.1038/s41598-022-11733-4
  5. O. Dubovik, A. Sinyuk, T. Lapyonok et al. J. Geophys. Res. Atmos., 111, D11208 (2006). DOI: 10.1029/2005JD006619
  6. S. Merikallio, H. Lindqvist, T. Nousiainen, M. Kahnert. Atmos. Chem. Phys., 11, 5347 (2011). DOI: 10.5194/acp-11-5347-2011
  7. H. Tang, X.-X. Li. Int. J. Num. Meth. Heat Fluid Flow., 24, 1762 (2014). DOI: 10.1108/HFF-04-2013-0105
  8. L. Mukherjee, P.-W. Zhai, Y. Hu, D.M. Winker. Opt. Expr., 26, A124 (2018). DOI: 10.1364/OE.26.00A124
  9. B. Vandenbroucke, M. Baes, P. Camps et al. Astron. Astrophys., 653, A34 (2021). DOI: 10.1051/0004-6361/202141333
  10. H. Chen-Chen, S. Perez-Hoyos, A. Sanchez-Lavega. Icarus, 354, 114021 (2021). DOI: 10.1051/0004-6361/202141333
  11. S. Hofer, H. Mutschke, Th.G. Mayerhofer. Astron. Astrophys., 646, A87 (2021). DOI: 10.1051/0004-6361/202038931
  12. B.T. Draine. Astrophys. J., 926, 90 (2022). DOI: 10.3847/1538-4357/ac3977
  13. B.S. Hensley, B.T. Draine. Astrophys. J., in press (2022) (arXiv-preprint 2208.12365). DOI: 10.48550/arXiv.2208.12365
  14. M. Min, J.W. Hovenier, A. de Koter. Astron. Astrophys., 404, 35--46 (2003). DOI: 10.1051/0004-6361:20030456
  15. V.G. Farafonov, V.B. Il'in, M.S. Prokopjeva, A.R. Tulegenov, V.I. Ustimov. Opt. Spectrosc., 126, 360 (2019). DOI: 10.1134/S0030400X19040076
  16. M.I. Mishchenko, J.W. Hovenier, L.D. Travis. Light scattering by nonspherical particles (Academic Press, San Diego, 2000)
  17. B. Sun, G.W. Kattawar, P.Yang, X. Zhang. Appl. Sci., 8, 2686 (2018). DOI: 10.3390/app8122686
  18. F.M. Kahnert. J. Quant. Spectrosc. Rad. Transf., 79-80, 775 (2003). DOI: 10.1016/S0022-4073(02)00321-7
  19. V.G. Farafonov, V.B. Il'in. Light Scatt. Rev., 1, 125 (2006). DOI: 10.1007/3-540-37672-0_4
  20. P.C. Waterman. Proc. IEEE, 53, 805 (1965). DOI: 10.1109/PROC.1965.4058
  21. M.I. Mishchenko. J. Quant. Spectrosc. Rad. Transf., 242, 106692 (2020). DOI: 10.1016/j.jqsrt.2019.106692
  22. M.I. Mishchenko, L.D. Travis. Opt. Commun., 109, 16 (1994). DOI: 10.1016/0030-4018(94)90731-5
  23. W.R.C. Somerville, B. Auguie, E.C. Le Ru. J. Quant. Spectrosc. Rad. Transf., 160, 29 (2015). DOI: 10.1016/j.jqsrt.2015.03.020
  24. S. Asano, G. Yamamoto. Appl. Opt., 14, 29 (1975). DOI: 10.1364/AO.14.000029
  25. N.V. Voshchinnikov, V.G. Farafonov. Astrophys. \& Space Sci., 204, 19 (1993). DOI: 10.1007/BF00658095
  26. V.G. Farafonov, N.V. Voshchinnikov. Appl. Opt., 51, 1586 (2012). DOI: 10.1364/AO.51.001586
  27. V.G. Farafonov. Diff. Equat., 19, 1765 (1983)
  28. V.G. Farafonov. Light Scatt. Rev., 8, 189 (2013). DOI: 10.1007/978-3-642-32106-1_5
  29. A.L. van Buren. arXiv-preprints, math/2009.01618 (2020)
  30. A.L. van Buren. Mathieu and spheroidal wave functions. [Electronic resource]. URL: http://www.mathieuandspheroidalwavefunctions.com
  31. V.G. Farafonov, V.B. Il'in, D.G. Turichina. Opt. Spectrosc., 130, 259 (2022). DOI: 10.21883/EOS.2022.02.53686.2893-21
  32. C. Bohren, D. Huffman. Absorption and scattering of light by small particles (John Wiley \& Sons, New York, 1983). DOI: 10.1002/9783527618156
  33. G. Mie. Ann. Phys., 330, 377 (1908). DOI: 10.1002/andp.19083300302
  34. P.W. Barber, S.C. Hill. Light scattering by particles: computational methods (World Scientific, Singapore, 1990). DOI: 10.1142/0784
  35. M.I. Mishchenko, L.D. Travis, A.A. Lacis. Scattering, absorption and emission of light by small particles (Cambridge Univ. Press, Cambridge, 2002)
  36. V.G. Farafonov, A.A. Vinokurov, V.B. Il'in. Opt. Spectrosc., 102, 927 (2007). DOI: 10.1134/S0030400X07060203
  37. C. Flammer. Spheroidal wave functions (Stanford Univ. Press, 1957)
  38. D.G. Turichina, V.G. Farafonov, V.B. Il'in. In: 2022 Days on Diffraction, ed. by O.V. Motygin (IEEE, Danvers, 2022), p. 130. DOI: 10.1109/DD55230.2022.9960958

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