Appl Phys B (2009) 96: 105–109
DOI 10.1007/s00340-009-3482-3
Scattering of shaped beam by a conducting infinite cylinder
with dielectric coating
M. Wang ·H. Zhang ·Y. Han ·Y. Li
Received: 16 November 2008 / Revised version: 22 February 2009 / Published online: 2 April 2009
© Springer-Verlag 2009
Abstract Based on the generalized Lorenz–Mie theory
(GLMT), which provides the general framework and expan-
sion of the incident shaped beam in terms of cylindrical vec-
tor wave functions, an analytic solution to the electromag-
netic scattering by coated infinite cylinders is constructed
for arbitrary incidence of a shaped beam. As an example,
for a tightly focused Gaussian beam propagating perpendic-
ularly to the cylinder axis, the scattering characteristics that
obviously demonstrate the three-dimensional nature are de-
scribed in detail, and numerical results of the normalized
differential scattering cross section are evaluated.
PACS 42.25.Fx · 42.60.Jf · 42.79.Wc
1 Introduction
Exact solutions of electromagnetic wave scattering by some
objects exhibiting regular shapes such as spheres, spheroids
and infinite cylinders play an important role in the investi-
gation of scattering problems. Aside from providing exact
solutions for their respective geometries, they are a standard
of accuracy in the evaluation of approximate and numerical
M. Wang · Y. L i
Institute of E.M. Wave Propagation & Scattering, Xianyang
Normal College, Xianyang, Shaanxi 712000, China
H. Zhang (
)
School of Electronic Science and Technology, Anhui University,
Hefei, Anhui 230039, China
e-mail: hyzhang0905@163.com
Y. H a n
School of Science, Xidian University, Xi’an, Shaanxi 710071,
China
solutions. There is a rather large literature on the scattering
of a plane electromagnetic wave by a spherical, spheroidal
and infinite cylindrical particle [1–6]. For the case of an inci-
dent shaped beam, Gouesbet et al. published the generalized
Lorenz–Mie theory (GLMT) [7–9], which is effective for
describing the interaction of a shaped beam with a spheri-
cal particle, and has been extended to multilayered spheres
by Onofri et al. [10] and to spheroids by Han et al. [11–13].
By relying on the theory of distributions, Ren et al. have
carried out some investigations on the shaped beam scat-
tering by an infinite cylindrical particle, and have presented
quantitatively some main characteristics of the scattering of
a Gaussian beam by a circular infinite cylinder [14–17]. In
our previous papers, we have obtained the expansion of a
shaped beam in terms of cylindrical vector wave functions;
then, an analytic solution to the shaped beam scattering by
an infinite cylinder in the framework of the GLMT is avail-
able [18, 19]. As an implication of the GLMT in cylindrical
coordinates, this paper is devoted to the description of the
scattering of a shaped beam by an arbitrarily oriented con-
ducting infinite cylinder with dielectric coating.
The body of this paper proceeds as follows. In Sect. 2,the
theoretical procedure for the determination of the scattered
fields of a shaped beam by an arbitrarily oriented conducting
infinite cylinder with dielectric coating is given. Section 3
provides the numerical results for the scattering properties
of a tightly focused Gaussian beam normally incident on a
coated infinite cylinder. The work is summarized in Sect. 4.
2 Formulation
AsshowninFig.1, an incident shaped beam propagates
in free space, from the negative z
to the positive z
axis