Stable computations of the spherically layered media theory with high lossy media by using scaled Bessel functions

Jia-Hui Wang; Bo O. Zhu

doi:10.1016/j.jnlest.2024.100291

Journal of Electronic Science and Technology ›› 2025, Vol. 23 ›› Issue (1) :100291 DOI: 10.1016/j.jnlest.2024.100291

research-article

Stable computations of the spherically layered media theory with high lossy media by using scaled Bessel functions

Jia-Hui Wang
, Bo O. Zhu ^*

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School of Electronic Science and Engineering, Nanjing University, Nanjing, 210023, China

^* E-mail addresses: wangjh677@163.com (J.-H. Wang),

bzhu@nju.edu.cn (B.O. Zhu).

Jia-Hui Wang was born in 1999 in Henan, China. He received the B.S. degree from North University of China in Taiyuan, Taiyuan, China in 2021. Currently, he is pursuing the M.S. degree with the School of Electronic Science and Engineering, Nanjing University (NJU), Nanjing, China. His research interest Mainly focuses on computational electromagnetics.

Bo O. Zhu received the Ph.D. degree in electrical engineering from NJU in 2010. In 2009, he was a visiting student at the Department of RF and Optical, Institute for Infocomm Research (I2R), Singapore, Singapore. From 2010 to 2012, he was a postdoctoral researcher with the Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, China. Since 2012, he has been an associate researcher first, and then an associate professor with the School of Electronic Science and Engineering, NJU. His research interests include computational electromagnetics, metasurfaces, antennas, and electromagnetic compatibility devices. He has published more than 30 scientific journal papers as the first author or corresponding author, and has presented more than 50 conference papers. Dr. Zhu is a member of the IEEE Antennas and Propagation Society (AP-S). He also serves as the reviewer of electromagnetics related primary journals, including IEEE Transactions on Antennas & Propagation, Advanced Materials series, OSA journals, IET Microwaves, Antennas & Propagation, and Chinese Physics B.

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Abstract

The spherically layered media theory has wide applications for electromagnetic wave scattering analysis. Due to the involved Bessel functions, the conventional formulations of the spherically layered media theory suffer from numerical overflow or underflow when the Bessel function's order is large, the argument is small, or the argument has a large imaginary part. The first two issues have been solved recently by employing small-argument asymptotic formulas of Bessel functions, while the third issue remains unsolved. In this paper, the Bessel functions in the conventional formulation of the theory are replaced by scaled Bessel functions which have good numerical properties for high lossy media, and stable formulas are derived. Numerical tests show that this approach can work properly with very high lossy media. Also, this approach can be seamlessly combined with the stable computation method for cases of small argument and large order of Bessel functions.

Keywords

Lossy media / Scaled Bessel function / Spherically layered media theory / Numerical stability

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Jia-Hui Wang, Bo O. Zhu. Stable computations of the spherically layered media theory with high lossy media by using scaled Bessel functions. Journal of Electronic Science and Technology, 2025, 23(1): 100291 DOI:10.1016/j.jnlest.2024.100291

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CRediT authorship contribution statement

Jia-Hui Wang: Writing – original draft, Derivation, Coding, Investigation, Formal analysis, Data curation. Bo O. Zhu: Conceptualization, Review & editing, Validation, Supervision, Project administration.

Declaration of competing interest

The authors declare that there are no competing interest.

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	H.A. Atwater, A. Polman, Plasmonics for improved photovoltaic devices, Nat. Mater. 9 (3) (2010) 205-213.

[2]	X.-F. Fan, W.-T. Zheng, D.J. Singh, Light scattering and surface plasmons on small spherical particles, Light Sci. Appl. 3 (2014) 1-14.

[3]	K.L. Kelly, E. Coronado, L.-L. Zhao, G.C. Schatz, The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment, J. Phys. Chem. B 107 (3) (2003) 668-677.

[4]	N.J. Halas, S. Lal, W.-S. Chang, S. Link, P. Nordlander, Plasmons in strongly coupled metallic nanostructures, Chem. Rev. 111 (6) (2011) 3913-3961.

[5]	J.V. Martins, P. Artaxo, C. Liousse, J.S. Reid, P.V. Hobbs, Y.J. Kaufman, Effects of black carbon content, particle size, and mixing on light absorption by aerosols from biomass burning in Brazil, J. Geophys. Res. Atmos. 103 (D24) (1998) 32041-32050.

[6]	S. Arslanagic, R.W. Ziolkowski, Cylindrical and spherical active coated nanoparticles as nanoantennas: active nanoparticles as nanoantennas, IEEE Antenn. Propag. Mag. 59 (6) (2017) 14-29.

[7]	G. Mie, Beiträge zur optik trüber medien, speziell kolloidaler metallösungen, Ann. Phys.-Berlin 330 (3) (1908) 377-445.

[8]	A.L. Aden, M. Kerker, Scattering of electromagnetic waves from two concentric spheres, J. Appl. Phys. 22 (10) (1951) 1242-1246.

[9]	M. Kerker, The Scattering of Light and Other Electromagnetic Radiation, Academic Press, New York, USA, (1969).

[10]	W.C. Chew, Waves and Fields in Inhomogeneous Media, IEEE Press, New York, USA, (1995).

[11]	L.-W. Li, P.S. Kooi, M.S. Leong, T.S. Yee, Electromagnetic dyadic Green’s function in spherically multilayered media, IEEE T. Microw. Theory 42 (12) (1994) 2302-2310.

[12]	E.L. Tan, S.Y. Tan, A unified representation of the dyadic Green’s functions for planar, cylindrical and spherical multilayered biisotropic media-abstract, J. Electromagnet. Wave. 12 (10) (1998) 1315-1316.

[13]	C.T. Tai, Dyadic Green Functions in Electromagnetic Theory, (second ed.), IEEE Press, Piscataway, (1994).

[14]	M. Majic, E.C. Le, Numerically stable formulation of Mie theory for an emitter close to a sphere, Appl. Opt. 59 (5) (2020) 1293-1300.

[15]	H.-Y. Yuan, W. Zhu, B.O. Zhu, Numerically stable calculations of the spherically layered media theory, IEEE Trans. Antenn. Propag. 71 (6) (2023) 5178-5188.

[16]	H.-Y. Yuan, W. Zhu, B.O. Zhu, Asymptotic approach for stable computations of the spherically layered media theory with large orders and small arguments, Opt Express 32 (3) (2024) 3062-3075.

[17]	J.W. Eaton, D. Bateman, S. Hauberg, R. Wehbring, GNU Octave Version 3.8.1 Manual: A High-Level Interactive Language for Numerical Computations, CreateSpace Independent Publishing Platform, (2014).

[18]	G.-Y. Wang, Z.-X. Li, C. Hu, G.-Y. Yang, X.-J. Yang, B. Liu, Deep learning-driven Mie scattering prediction method for radially varying spherical particles, Opt Laser. Technol. 177 (2024) 111170.

[19]	M.A. Ali, A. Alqaraghuli, A survey on the significance of artificial intelligence (AI) in network cybersecurity, Babylonian J. Net. 2023 (2023) 21-29.