Uniform Diffraction Coefficient for Electromagnetic
Scattering by Flat and Curved Plates
Divyabramham Kandimalla and Arijit De
Department of Electronics and Electrical Communication Engineering,
Indian Institute of Technology Kharagpur, Kharagpur-721302, West Bengal, India.
divyabramham@gmail.com
Abstract—A diffraction coefficient is being proposed for plane-
wave scattering by a straight edge in both planar and curved
screens which is valid uniformly for all aspect angles. This new
form of diffraction coefficient is obtained via Uniform
Asymptotic Theory of Diffraction (UAT), where the arguments of
the Fresnel integrals of the traditional Uniform Theory of
Diffraction (UTD) coefficients are redefined by the Phase Detours
(PDs) of the UAT formulations. The proposed coefficient is
supported with the monostatic RCS predictions of flat plate and
curved plate for soft polarization case. These predictions are
compared with existing diffraction coefficients, full-wave
simulation and with the available experimental results. This new
diffraction coefficient shows superior nature over the existing
coefficients when applied to the curved plate problem.
I. INTRODUCTION
The Geometrical theory of diffraction (GTD) [1] is a simple
and a powerful tool to address the problems involving
electrically large complex structures at high frequency ranges.
The wide range of its applicability to diffraction problems
forced the researchers to introduce its extensions to overcome
its defects at the incident and reflection shadow boundaries.
The most popular GTD extensions are Uniform Theory of
Diffraction (UTD) [2] and Uniform Asymptotic Theory of
Diffraction (UAT) [3]. It is well known that UTD overcomes
this defects by introducing Fresnel integrals (FIs) in its
diffraction coefficient (DC), whereas UAT modifies its
Geometrical Optics (GO) fields itself. Both these methods
provide uniform description of fields in the transition regions
around the shadow boundaries. A detailed comparison of these
methods was discussed by Boersma and Rahmat-samii [4]
using cylindrical wave diffraction by a half-plane, and
discussed that the UAT solution agrees with asymptotic
expansions of the Van der Waerden type whereas the UTD
solution can be obtained as the leading term of the asymptotic
expansion of the Pauli-Clemmow type. Though fundamentally
different, the two methods agree with each other from a
numerical point of view.
The traditional UTD diffraction coefficients due to their
simplicity are quite popular, provide reasonably accurate
scattered fields for flat plate, but however fail for the case of
curved plate as will be demonstrated later. In this paper, a
modified diffraction coefficient is being proposed which is
valid for diffraction by both flat and curved plates. Unlike in
UTD, the proposed coefficient is derived by using the concept
of phase detours (PD), i.e. the difference between the phase of
the diffracted field and the phase of the incident (reflected)
field, as in the UAT formulations in the arguments of the
Fresnel Integrals of the traditional UTD DCs.
The proposed coefficient is quite simple to use and has
been successfully applied to obtain the monostatic Radar
Cross-Section (RCS) of both flat plates and curved plates for
normal incidence case with electric field parallel to edge (soft
polarization case). The coefficient has also been extended for
hard polarization case but the scope of this paper is limited to
soft polarization case only.
II. PROPOSED DIFFRACTION COEFFICIENT
The proposed diffraction coefficient for a normal incident
plane-wave diffraction by a straight edge in planar and
cylindrically curved screens is derived by employing the PDs
of the the UAT [3] formulations, as the arguments of the
Fresnel Integrals [2] as,
exp 4
, sec sec
2 2 2 2
d i d r
j
D F F
s
k
kS S kS S
(1)
where, the angles , ׳are defined as in Fig. 1. S
i
, S
r
and S
d
are phase of the incident, reflected and diffracted rays
respectively. Note that, k(S
d
-S
i
) is the incident field PD and
k(S
d
-S
r
) is the reflected field PD. The FI is given as,
2
2 exp exp
X
F X j X jX j d
(2)
A. Phase Detours of the Plane screen
The incident and the reflected field PDs for a planar screen
[3, (3.8)], as given in terms of the incident (φ) and the
diffraction (φ) angles defined in Fig. 1(a) is,
1 cos
d i
kS S kd
(3a)
1 cos
d r
kS S kd
(3b)
2
1
2
1
r
S s ma
cos
d
o
S d a p
p
a
s
d
2
o
P
o
B
d i
S S BO OP
d
(a) (b) (c)
Fig. 1 (a) 2D view of planar screen; 2D view of a curved
screen and its associated Phase Detours: (b) Reflected field,
and (c) Incident field.
504 978-1-4799-7815-1/15/$31.00 ©2015 IEEE AP-S 2015