ISSN 1027-4510, Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques, 2017, Vol. 11, No. 4, pp. 885–889. © Pleiades Publishing, Ltd., 2017.
Original Russian Text © V.V. Syshchenko, A.I. Tarnovsky, E.A. Larikova, 2017, published in Poverkhnost’, 2017, No. 8, pp. 109–112.
On Electromagnetic-Wave Scattering by a Dielectric Cylinder
V. V. Syshchenko*, A. I. Tarnovsky, and E. A. Larikova
Belgorod State National Research University, Belgorod, 308015 Russia
Received October 27, 2016
Abstract—An approximate method that is analogous to the eikonal approximation in quantum scattering the-
ory is developed to solve the problem оf the scattering of an electromagnetic wave in the case of its oblique
incidence onto an infinite circular cylinder. The limits of applicability of the method include, in particular,
the X-ray range. It is shown that inclusion of the finiteness of the cylinder thickness leads to significant asym-
metry of the angular distribution of the scattered radiation. The results can be used to improve the kinetic the-
ory of radiation propagation in a system of parallel fibers.
Keywords: electromagnetic wave, light scattering, fiber-like target, eikonal approximation
The problem of the scattering of an electromag-
netic wave in the case of its oblique incidence onto an
infinite homogeneous circular cylinder is well known
in optics; however, its generalized solution in the form
of an infinite series  has an extremely cumbersome
form, which leads to the necessity to construct various
approximate solutions. Thus, the author of  pro-
posed an approximation that is analogous to the Born
approximation in quantum scattering theory.
In this paper, to solve the problem under consider-
ation, we propose an approach that is analogous to the
eikonal approximation in quantum scattering theory
. The preliminary results corresponding to a per-
mittivity of the cylinder material of were
described in ; here, we consider the case of in
detail; it occurs, in particular, in the X-ray range.
The electric field of the monochromatic wave
E(r)exp(‒iωt) in a homogeneous medium with the
permittivity ε(r) is described by the equations
following from the Maxwell equations . The asymp-
totics of the solution of these equations corresponding
to the problem of scattering at large distances from a
local nonhomogeneity (a target) can be represented in
accordance with  and , in which a similar
approach was used in transition radiation theory for
where the first term describes a plane wave incident on
the target ( is its polarization vector), the second
term describes the field of the scattered wave at large
distances from the target, and are the wave vec-
tors of the incident and scattered waves, and
The time-averaged density of the wave energy f lux
scattered into the solid angle element related to the
intensity of the incident wave gives the scattering cross
However, the field in expression (4) contains
the total electric field in a region of space in which the
permittivity is nonzero, i.e., in the target. Thus, the
representation of Eqs. (1), (2) in form (3) is the rep-
resentation in the integrated form. Nevertheless,
such a representation offers the possibility of con-
structing various approximate solutions of the scat-
The author of  showed that, either under the
=− − ⋅
Er e I k k I
1 ε( ) ( ) .
1 εω 1ac− !