Application of the modern spheroidal T-matrix method for calculating the optical properties of silver nanospheroids with a dielectric coating

Farafonov, V.G., Iliin, V.B., Bespyatyy G.Y., Arefyev A.V.

For Russian citation (Opticheskii Zhurnal):

Фарафонов В.Г., Ильин В.Б., Беспятый Г.Ю., Арефьев А.В. Применение современного метода сфероидальной T-матрицы для вычисления оптических свойств серебряных наносфероидов с диэлектрическим покрытием // Оптический журнал. 2026. Т. 93. № 4. С. 38–45. http://doi.org/10.17586/1023-5086-2026-93-04-38-45

Farafonov V.G., Il′in V.B., Bespyatyy G.Y., Arefyev A.V. Application of the modern spheroidal T-matrix method for calculating the optical properties of silver nanospheroids with a dielectric coating [in Russian] // Opticheskii Zhurnal. 2026. V. 93. № 4. P. 38–45. http://doi.org/10.17586/1023-5086-2026-93-04-38-45

For citation (Journal of Optical Technology):

Abstract:

Subject of study. Optical properties of coated metal nanoparticles. The spheroidal T-matrix method. Aim of study. To investigate the applicability of the spheroidal T-matrix method to silver nanoparticles with a dielectric coating and to illustrate the capabilities of this method. Method. The optical properties of nanospheroids with a silver (Ag) core and a non-confocal dielectric shell were calculated using an exact T-matrix method recently developed by the authors. This method employs field expansions in spheroidal bases and utilizes the relations between similar field expansions in different bases, also previously found by the authors. Main results. A comparison was made between the results obtained using the spheroidal T-matrix method and the data derived within the Rayleigh approximation. A significant dependence of the optical absorption cross-sections of nanoparticles on the shape of the Ag core (which is non-confocal with the shell) and on the size of such particles was demonstrated. Practical significance. It is noted that the proposed method not only allows for the consideration of highly elongated nanospheroids with an aspect ratio a/b >> 10 but also facilitates the calculation of characteristics for randomly oriented particles and enables the use of possible multilayer structures for a more adequate representation of nanoparticle coatings. It is concluded that the approaches used in this work will allow the extension of the Rayleigh and Improved Electrostatic Approximations to nanospheroids with non-confocal layers.

Keywords:

optical properties of nanoparticles, T-matrix method, layered spheroids, Rayleigh approximation

Acknowledgements:

the authors thank Turichina D.G. for the opportunity to use the SoMSP program. They are also grateful to the reviewer and Professor Vartanyan T.A. for their remarks

OCIS codes: 050.005, 260.026

References:

1. Prasher P., Sharma M. Silver nanoparticles: synthesis, functionalization and applications. Singapore: Bentham Science Publishers, 2022. 132 p. https://doi.org/10.2174/97898150505301220101
2. Fahmy H.M., Mosleh A.M., Elghany A.A., ShamsEldin E. et al. Coated silver nanoparticles: synthesis, cytotoxicity, and optical properties // Roy. Soc. Chem. Advances. 2019. V. 27. № 9. P. 20118–20136. https://doi.org/10.1039/c9ra02907a
3. Zhuo Х., Henriksen-Lacey M., de Aberasturi D.J. et al. Shielded silver nanorods for bioapplications // Chemistry of Materials. 2020. V. 32. № 13. P. 5879–5889. https://doi.org/ 10.1021/acs.chemmater.0c01995
4. Dos Santos P.S., Mendes J.P., Pastoriza-Santos I. et al. Gold-coated silver nanorods on side-polished singlemode optical fibers for remote sensing at optical telecommunication wavelengths // Sensors and Actuators B. 2025. V. 425. P. 136936. https://doi.org/10.1016/j.snb.2024.136936
5. Li J.Z., Li X.N., Chen J. et al. Extinction behavior and near-field enhancement of 3D hybrid nanostructures consisting of Ag-Coated SiO2 nanorods // Plasmonics. 2025. V. 20. P. 211–220. https://doi.org/10.1007/s11468-024-02267-8
6. Климов В.В. Оптические нанорезонаторы // Успехи физических наук. 2023. Т. 193. № 3. С. 279–304. https://doi.org/10.3367/UFNr.2022.02.039153
Klimov V.V. Optical nanoresonators // Physics-Uspekhi. 2023. V. 33. № 3. P. 263–287. https://doi.org/10.3367/UFNe.2022.02.039153
7. Khlebtsov N.G., Zarkov S.V. Analytical modeling of coated plasmonic particles // Journal of Physical Chemistry C. 2024. V. 128. № 36. P. 15029–15040. https://doi.org/10.1021/acs.jpcc.4c03126
8. Kahnert F.M. Numerical methods in electromagnetic scattering theory // Journal of Quantitative Spectroscopy and Radiative Transfer. 2003. V. 79–80. P. 775–824. https://doi.org/10.1016/S0022-4073(02)00321-7
9. Flatau P.J., Draine B.T. Fast near-field calculations in the discrete dipole approximation for regular rectilinear grids // Optics Express. 2012. V. 20. P. 1247–1252. https://doi.org/10.1364/OE.20.001247
10. Электронный ресурс URL: https://github.com/adda-team/adda/ (Yurkin MA. ADDA — light scattering simulator based on the discrete dipole approximation)

URL: https://github.com/adda-team/adda/ (Yurkin MA. ADDA — light scattering simulator based on the discrete dipole approximation)
11. Farafonov V.G., Il’in V.B. Single light scattering: computational methods // Light scattering reviews. 2006. V. 1. P. 125–177. http://doi.org/10.1007/3-540-37672-0_4
12. Farafonov V.G., Il’in V.B., Ustimov V.I., Volkov E.V. Analysis of Waterman’s method in the case of layered scatterers // Advances in Mathematical Physics. 2017. V. 2017. P. 7862462. https://doi.org/10.1155/2017/7862462
13. Onaka T. Light scattering by spheroidal grains // Annals of Tokyo Astronomical Observatory. 1980. V. 18. P. 1–54.
14. Han Y., Zhang H., Sun X. Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries // Applied Physics. 2006. V. 84. P. 485–492. https://doi.org/10.1007/s00340-006-2298-7
15. Фарафонов В.Г., Ильин В.Б., Лазневой С.И., Туричина Д.Г. Расчет оптических свойств двухслойных сфероидов с несофокусными границами оболочки // Оптика и спектроскопия. 2024. Т. 132. № 6. C. 620–636. https://doi.org/10.61011/OS.2024.06.58639.6665-24
Farafonov V.G., Il’in V.B., Laznevoy S.I., Turichina D.G. Calculation of the optical properties of twolayer spheroids with non-confocal shell boundaries // Optics and Spectroscopy. 2024. V. 132. № 6. P. 620–636. https://doi.org/10.61011/OS.2024.06.58639.6665-24
16. Il’in V.B., Turichina D.G., Farafonov V.G., Laznevoi S.I., Gontcharov G.A., Marchuk A.A., Mosenkov A.V., Poliakov D.M., Savchenko S.S., Smirnov A.A., Prokopjeva M.S. A new practical approach to light scattering by spheroids with the use of spheroidal and spherical function bases // Journal of Quantitative Spectroscopy and Radiative Transfer. 2023. V. 311. P. 108759. https://doi.org/10.1016/j.jqsrt.2023.108759
17. Электронный ресурс URL: https://github.com/Kifye/SoMSP (Turichina D.G. A codes for light scattering on a multilayered spheroidal particle)

URL: https://github.com/Kifye/SoMSP (Turichina D.G. A codes for light scattering on a multilayered spheroidal particle)
18. Электронный ресурс URL: https://github.com/MathieuandSpheroidalWaveFunctions (van Buren A.L. Mathieu and spheroidal wave functions)
URL: https://github.com/MathieuandSpheroidalWaveFunctions (van Buren A.L. Mathieu and spheroidal wave functions)
19. Электронный ресурс URL: https://refractiveindex.info/ (Refractive index database)
URL: https://refractiveindex.info/ (Refractive index database)
20. Bohren С., Huffman D. Absorption and scattering of light by small particles. New York: John Wiley & Sons Inc, 1983. 544 p.
21. Farafonov V.G., Ustimov V.I., Il’in V.B. Relations between spheroidal harmonics and the Rayleigh approximation for multilayered nonconfocal spheroids // Journal of Mathematical Sciences. 2021. V. 252. P. 702–730. https://doi.org/10.1007/s10958-021-05192-x
22. Farafonov V.G., Voshchinnikov N.V., Somsikov V.V. Light scattering by a сore-mantle spheroidal particle // Applied Optics. 1996. V. 35. P. 5412–5426. https://doi.org/10.1364/AO.35.005412