ON THE SCATTERING OF SPHERICAL ELECTROMAGNETIC WAVES BY A LAYERED SPHERE by NIKOLAOS L. TSITSAS † and CHRISTODOULOS ATHANASIADIS ‡ (Department of Mathematics, University of Athens, Panepistimiopolis, GR 15784 Athens, Greece) [Received 4 April 2005. Revises 1 July and 16 August 2005. Accepted 25 August 2005] Summary A spherical electromagnetic wave is scattered by a layered sphere. The exact expressions of the scattered and interior fields are obtained by solving the corresponding boundary-value problem, by means of a combination of Sommerfeld’s and T-matrix methods. A recursive algorithm with respect to the number of layers is extracted for the computation of the fields in every layer. The far-field pattern and the scattering cross-sections are determined in terms of the physical and geometrical characteristics of the scatterer. As the point-source tends to infinity, the known results for plane wave incidence are recovered. Numerical results are presented for several cases and various parameters of the layered spherical scatterer. 1. Introduction A classic problem in scattering theory concerns the interaction of an incident wave with a bounded three-dimensional obstacle. The case of spherical wave scattering by a finite body has been investi- gated to some extent in the literature (see, for example, (1, 2)), although it is by far less studied than the scattering problem for plane wave incidence. Dassios and his co-workers introduced a normal- ized point-source field, reducing to a plane wave for point-sources at infinity, and obtained explicit results in the low frequency region for particular scattering geometries; see (3 to 5) for acoustic waves and (6) for elastic waves. Thus, this normalization can be used to recover related results for plane wave incidence. Furthermore scattering relations for point-sources are treated in (7) for acoustic and electromagnetic waves. The point-source scattering by layered bodies has interesting technological applications. A basic application is the interaction between mobile phone antennas and the human head (8). Since the an- tenna operates in close proximity to the head, the generated electromagnetic field is considered to be spherical. Several numerical techniques, regarding the interaction of dipoles with a layered sphere, which represents a simplified model of the human head, have been proposed; see, for example, (9). The determination of the total power absorbed by the human head gives important information about the biological effects of electromagnetic radiation. Besides, one meets several other applications of point-source scattering in underwater acoustics, non-destructive testing and evaluation techniques † 〈ntsitsas@esd.ntua.gr〉 ‡ Corresponding author 〈cathan@math.uoa.gr〉 Q. Jl Mech. Appl. Math, Vol. 59. No. 1 c  The Author 2005. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org Advance Access publication 16 November 2005. doi:10.1093/qjmam/hbi031 Downloaded from https://academic.oup.com/qjmam/article-abstract/59/1/55/1920521 by guest on 22 May 2020