TY - CHAP
T1 - Scattering of plane electromagnetic waves by radially inhomogeneous spheres
T2 - Asymptotics and special functions
AU - Pohrivchak, Michael A.
AU - Adam, John A.
AU - Nuntaplook, Umaporn
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Asymptotic expansions
KW - Back-scattering
KW - Bessel’s equation
KW - Born approximation
KW - EM scattering
KW - Hypergeometric equation
KW - Liouville transformation
KW - Maxwell Fish-Eye
KW - Radial Debye potentials
KW - Rainbow
KW - Refractive index profiles
KW - Riccati-Bessel functions
KW - Scattering potentials
KW - TE/TM modes
KW - Watson transform
KW - Whittaker’s equation
UR - https://www.scopus.com/pages/publications/85013270550
U2 - 10.1007/978-3-319-31323-8_17
DO - 10.1007/978-3-319-31323-8_17
M3 - Chapter
AN - SCOPUS:85013270550
T3 - Springer Proceedings in Mathematics and Statistics
SP - 383
EP - 417
BT - Springer Proceedings in Mathematics and Statistics
PB - Springer New York LLC
ER -