Publication: Scattering of plane electromagnetic waves by radially inhomogeneous spheres: Asymptotics and special functions
Issued Date
2016-01-01
Resource Type
ISSN
21941017
21941009
21941009
Other identifier(s)
2-s2.0-85013270550
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Mahidol University
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SCOPUS
Bibliographic Citation
Springer Proceedings in Mathematics and Statistics. Vol.157, (2016), 383-417
Suggested Citation
Michael A. Pohrivchak, John A. Adam, Umaporn Nuntaplook Scattering of plane electromagnetic waves by radially inhomogeneous spheres: Asymptotics and special functions. Springer Proceedings in Mathematics and Statistics. Vol.157, (2016), 383-417. doi:10.1007/978-3-319-31323-8_17 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/40925
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Title
Scattering of plane electromagnetic waves by radially inhomogeneous spheres: Asymptotics and special functions
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Abstract
© Springer International Publishing Switzerland 2016. A brief historical introduction to the visual and wave-theoretic consequences of high frequency electromagnetic scattering by large spheres is given, with special emphasis on backscattering. Exact electromagnetic solutions for radially inhomogeneous dielectric lenses are unavailable for many functional dependences of the refractive index on the radial distance, so the high-frequency behavior based on an asymptotic analysis of the exact solution has been obtained in very few cases. In this chapter existing results for the asymptotic behavior of backscattered radiation are extended to a broader class of refractive index profiles. Additionally, by exploiting some known results from quantum mechanics, asymptotic solutions for two scalar problems (decoupled from the electromagnetic cases) are derived for the case of small variations in the refractive index across the scattering sphere. By using a Liouville transformation the electromagnetic wavenumber-dependent scattering potential is converted to a wavenumber-independent form, and the resulting inverse problem is solved for several refractive index profiles.