EMPo rm e oeo
kF31(0
yJh
oai
David
B.
Davidson
Dept.
E E
EngineeringUniversity
of
Stellenbosch
Stellenbosch
7600,
South
Africa
(+27)
21
808
4458
(+27)
21
808
4981 Fax)
davidson@ing.sun.ac.za
(email)
Foreword
by the
Editor
This
issue's
column continues the
theme
of
the columns
of
October, 2004
[1]
and June,
2006
[2],
providing implementations
for
various canonical problems
of
electromagnetic scattering the
ory.
The present contribution,
again
using
MA
TLAB,
extends
the
previously
implemented analytical solutions
to
further include
a
number
of
asymptotic solutions. Additionally, solutions
of
some
other
oncanonical
objects
are
also addressed.
Once
again, thisis
likely
to
prove most useful
to code
developers
and
those whovalidate codes,
and
we thank the authors
for
this followup paper.
References
1.
V.
Demir,
A.
Z.
Elsherbeni,
D.
Worasawate,
and
E.
Arvas,
A
Graphical User Interface
(GUI)
for
Plane Wave Scattering from
a
Conducting, Dielectric or
a
Chiral Sphere,
IEEE
Antennas and
Propagation
Magazine,
46,
5,
October 2004,
pp.
9499.
2.
J.
P.
Swartz,
A
Python Toolbox
for
Computing Solutions
to
Canonical
Problems
in
Electromagnetics,
IEEE
Antennas
and
Propagation
Magazine,
48,
3,
June
2006,
pp.
78

8
1.
A
Graphical
User
Interface
(GUI)
for
Electromagnetic
Scattering
from
Two
and
ThreeDimensional Canonical
and
NonCanonical
Objects
Mohamed
At
Sharka
WY,
Veysel Demirl
Atef
Elsherbenil
and
Bassem
Mahatza
2
'The
Center
of
Applied
Electromagnetic
Systems Research
(CASER),
Electrical Engineering Department
The
University
of
Mississippi,
University,
MS
38677
USA
Email:
malshark@olemiss.edu; vdemir@olemiss.edu; atef@olemiss.edu
2
deciBel Research
Inc.
Huntsville,
AL
35806
USA
Email:
bmahafza@dbresearch.net
Abstract
Various
numerical
techniques
have
been
developed for
modeling
electromagneticfield
propagation
in
conducting
and
dielectric
media. The
validity
of
these techniques
is
usually verified
by
comparison to the exact
or
asymptotic solutions of
canonicalor noncanonical problems
of
wellknown solutions. This paper presents
a
software package designed
as
an
educational
and
IEEE
Antennas and
Propagationl Magazine
Vol.
48,
No.
6,
December
2006
135
validation
tool
for the purpose
of
visualizing
the
physical phenomena
of
electromagnetic scattering
from
some canonical
and
oncanonical objects. The package
is
constructed
to
provide
solutions
for dielectric
and
conductive
materials whereverppropriate,
and
it
calculates
and
displays
the
near
and
far
fields due
to an
excitation
from
a
line source or
a
plane
wave.
Keywords: Graphical user interfaces; electromagnetic scattering; radar cross sections; software verification
and
validation;boundary value problems
1.
ntroduction
Tn
electromagnetic education, the fundamentals
of
electromag
J.netic
scattering
theory
are
usually taught through solutions
of
scattering from
some
canonical objects
due
to
excitations
by
incident
plane,
cylindrical,
or spherical
waves.
In
general, these solu
tions
are
available
in
closed
mathematical
forms, which in
many
cases are hard
to
visualize,
and
it
can be
difficult
to
extract from
these solutions
the
physical characteristics
of
the
scattering proc
ess.
Therefore,
it is
important
to
have
such
canonical
solutionsprogrammed
and arranged
in an
easytouse
tool for the
purpose
of
visualizing
the physical
phenomena
of
scattering
from these
objects.
Thus, the
availability
of
such
programs
that
solve
thesetypes
of
canonical
problems
on the
widely available personal computers
and
workstations
provides
students with
a
better
under
standing
of
electromagnetic scattering
theories.
Furthermore,
such
tools
can be
used
as
benchmarks
for
a
wide
range
of
researcherswho
are
developing numerical electromagnetic techniques,
and
these
researchers would
be able
to
have
immediate
access
to
solu
tions to
a
variety
of
test
cases
to
verify
their
techniques. With these
needs
in mind,
a
graphical
user
interface
(GUI)
has
been developed
to
calculate and
display
the
scattering from
two and
threedimen
sional
canonical
objects,
based
on exact
boundaryvalue solutions.
In
addition
to
canonical objects,
this
user interface
also
includes
some
simple noncanonical objects where
the
presented scatteringparameters
are
based
on
approximations
and
asymptotic solutions.Many configurations
are
considered
in
this
software package:
a
thin
strip,
circular cylinder, capped wedge,
truncated cone,. linesource above
a
ground plane, sphere, triangular and circular
flat
plates,
and
ellipsoid.
The
package
is
constructed
to
provide solutions
for
both
dielectric and conductive materials, wherever
appropriate.
It
calculates the
far and
nearfield components due
to
an
excitation
from a line
source
or
a
plane wave
[14].
In
the two
dimensional
problems,
the
TE
and
TM cases
are
treated
separately.
Electromagneticanalysis
software packages
are
judged
not
only
by
their computational efficiency
and
adaptability,
but also
by
their
ease
of
use
and
the
friendless
of
their user
interfaces.
A
graphical user interface was developed
for each
object considered
here,
in
order
to
provide the
object s
parameters
and the
excitation
type and
parameters,
and to
display
the computed
near
and/or
farfield
results,
and any
other appropriate
output
parameters.
Since the
computations
are fast,
the user interface
is
organized
such that
the
user
can
interactively
observe
the
effect
of
changing any
of
the
physical
or electrical
parameters on
the
resulting
farfield
patterns
and
parameters
in
near
real time.
2.
Software
Description
A
graphical user interface
was
developed using
MATLAB® in
order
to
provide
a
userfriendly
environmnent
for the
calculation
and
visualization
of
scatteredfield results
from
canonical
objects.
Eachobject
was
programmed
in
a
separate module,
and
the package
caneasily
be extended
to
include new
objects,
as
shown
in
Figure
1.
136
Nearfield
calculations take some time,
but
farfield calculations
are fast
enough
to
get results almost instantaneously.
The
scatteringgeometries included
in
the
package
will be
described
in
the
fol
lowing
paragraphs.
2.1
Thin
Strip
Scattering
from
a
thin,
perfectly
conducting
strip due to
a
normally
incident
plane wave
is
calculated.
The
plane
wave can
be
TE
or
TM
polarized.
The
monostatic
RCS
and
bistatic RCS
can be
calculated
and
displayed
either
in
polar
or
Cartesian coordinates.
For
this
module,
the
input
parameters
that
the user
can
tweak
and
change
are
the
strip s
width, the
operating
frequency, and the
inci
dent
angle
of
the
planewave excitation.
An
asymptotic solution,such
as
Physical Optics,
is
considered
to
provide
a
solution
for this
problem.
Equations
(1)
and
(2)
present
the
bistatic
RCS
for
TM
and
TE
polarizations, respectively,
while
Equation
(3)
presents
the
monostatic
RCS for
both polarizations,
TM
and
TE;
furthermathematical
details are
described
in
[1]. A
snapshot
of
this
mod
ule s
geometry,
along with
a
sample
RCS
pattern,
are shown
in
Figure
2.
('T2D(bistatic)
=
lim
2Js
,00
E
)
2rW
2
fsi
F
in
(X)
12
2
~
X
jJ
(1)
X=
aw CosOS
+
Cos
),
Th
i r
S
f
nTrw
7ajýe
ore
(Fustium)
Lmpi
ou~rre
~vmtpj e
I
Tiru~
Fiat
P~at,
Figure 1.
A
snapshot
of
the
main
module.
IEEE
Antennas
and Propagation Magazine
Vol. 48, No.
6,
December
2006
Figure
2. A
snapshot
of
the
Thin Strip
module.
`2D
(bistatic)
lim
7rp
2
HA
X
22
2,rw
Fi()I
E
=
Es
E
P74FEsin
~h
sin
0
ej8pý
(4)
where
I,
is the
linesource magnitude,
77
is
he
free space
ntr ns
impedance,
0S
s
the observation
angle,
p
is
the
plane wave
posi
tion
in
the farfield
region,
and
h
is
the
distance from the
linesource
to
the ground
plane.
The scattered
field
can
be
displayed either
in
polar
or Cartesian
coordinates,
where the
user
has
the ability
to
specify
and
change the values
of
the
operating frequency,
as
well
as
the distance
between the linesource
position
and the
infinite groundplane.
A
snapshot
of
this
module s
geometry with
a
sample
far
field
pattern
is
shown
in
Figure
3.
2.3
Capped
Wedge
Scattering
from
a
wedge loaded
with
a
cylindrical
cap at its
sharp edge
is
calculated based
on
the exact,
closedform
solution
given
in
[2].
The
excitation
can
be due
either
to
an
incident plane
wave or
a
line source.
The cappedwedge
material can be
either
a
dielectric
or
a
conductor,
or
it
can be
simply
eliminated
by
eitherreducing
the
cap
radius
to zero or
by
setting the
relative
dielectricconstant
to
that
of
the
surrounding media.
If
the
user chooses
a
dielectriccapped
wedge, the
user then has
to
specify the values ofthe relative
permittivity
and
permeability
of
the
capped wedge. Thecappedwedge module
was
generated
to
accept
different
angles
between the infinite
sides
of
the
wedge
and
the
reference
axis,
thus
providing
a
more
general
configuration.
In
this
case, the
user
has
the ability
of
choosing among
equal angles,
different angles,
oreven
having
one
of
the
wedge s
sides
coincide with
the
reference
axis. The
nearfield distribution can be displayed,
and
the
far fieldcan
be plotted.
A
snapshot
of
his module
is
shown
in
Figure
4.
The corresponding
farfield and
nearfield results
are
shown
(2)
in Figures
5
and
6,
respectively,
for
a
capped
wedge
excited
by
a
line source
having
the
parameters shown
in
Figure
4
for the
cappedwedge module.
(3)
Y=/Jwcosgi
(3),
where
w
is
the strip',s
width,
0.
is
the
scattering
angle,
i
is
the
incident
angle,
8
is
the wave
number,
and
A
is the
wavelength.
Es
and
H
are the scattered electric and
magnetic
field compo
nents, respectively, while
E
and
H
are
the
corresponding
incident fields.
2.2
Line
Source
Above
a
Ground
Plane
The
scattered
fiel
from
ine
source
located
bove round
plane
is
calculated based
on the asymptotic
solution
given
in
[1].
The
final
expression
for the total electric field
(Et)
is
shown
in
Equation
(4).
IEEE
Antennas and
Propagation Magazine
Vol. 48,
No.
6
December
2006
El1lrm14~
ScatRin
aý
ap W*I
cp
~MW
q'
0Dwwric
C ',
udaao Nonm
pk
C
g
Rea
enc
a..
1
a
POrc
of
PlaaaWn
yN
*~$~
Q~)
~PI~t
Figure
4. A
snapshot
of
the
Capped
Wedge module
137
30
T
RCSm
ýý=
12120
.. ............
.................
M
40
0
20
40
W
so
100
incdent.4,11e
1210 140
160
lao
M~
Total
Far
Field
(Ez)
[Line source
excitation]
0.8
6
0
.4
. .......... ...
0
80
120 190
240 300
3600
Observation
angle
+0
Figure
5.
The farfield results
for
the
input
parameters
shown
.n
Figure
4.
Figure
7.
A
snapshot
of the
Circular
Cylinder
module.
Far
field
on
a
Dielectric
cylinder excited
by
a
TMz
Plane wave
2
~
.
10 .
/
0 50
120 180
240 300
350
t,
(degrees)
Figure
8.
The farfield results for
the
input
parameters
shown
in
Figure
7.
138
2.4
Circular
Cylinder
Scattering
from
a
circular
cylinder
is
calculated based
on
the
exact, closedform
solution
given
in
[ 1,
2,
5].
The
excitation
can
be
due either
to an
incident plane
wave or
a
line source. The
planewave
can be
TE
or TM
polarized.
The
cylinder material
can
be
a
dielectric or
a
conductor.
The
nearfield
distribution
can
be dis
played,
and the
far
field
can
be
plotted.
Once the
user
selects the
nearfield distribution
for
either
excitation,
he
or she
then
has
to
specify' how
many
points
to
draw around
the
cylinder
in
both the
x
and
y
directions.
A
snapshot
of
this
module
is
shown
in
Figure
7.
Farfield
and
nearfield results
are
shown in Figures
8
and
9,
respectively,
for
a
dielectric
cylinder
excited
by
a
plane wave hav
ing
the
parameters shown
in
Figure
7
for the
circularcylinder
module.
2.5 Sphere
Scattering
from
a
sphere due
to
an
incident
plane
wave
is cal
culated based
on
the exact,
closedform solution presented
in
[4].
The
sphere s
material
can
be
a
dielectric
or
a
conductor. Copolarized
and
crosspolarized radar cross sections
can
be
plotted
and
saved
to
a
file.
A
snapshot
of
the
module
is
shown
in
Figure
10,
with the copolarized scattering cross section
of
a
dielectric
sphere.
2.6
Truncated
Cone
Scattering from
a
truncated
cone
(frustum)
due
to an
incidentplane wave
is
calculated based
on the
approximation
given
in
[3].
Equation
(5)
presents the
backscattered
RCS due
to
a
linearly
polarized
incident
wave.
Az
tan
a r~2
7small
end
j
tn9ar
large
end
8,sin9[a
( ±
(5)
h
r
tan
a
where
r
and
r
2
are
the
smallend
and largeend radii
of
the
cone s
base, respectively. The
parameter a
is
the
half
cone
angle,
0
is
the aspect angle with
respect
to the
frustum s
surface,
h
is
the
dis
tance between
the top and
bottom bases
of
the
frustum,
and
z
is
a
function
of
r
where
r
represents
either
r
or
r
2
,
depending
on
whether
the RCS
contribution
is
from the
small
or large end
of
thecone.
In
this
module,
the
user has
the
ability
to
tweak
the
values
of
the operating
frequency,
the smallend radius, the
largeend
radius,
and the
height
of
the frustum.
A
snapshot
of
the
module
is
shown
in
Figure
11,
along
with a
sample RCS pattern.
2.7
Triangular
Flat
Plate
Scattering
from
a
triangular
flat
plate
due
to
an
incident planewave
is
calculated based
on the
asymptotic solution given
in
[3].
In
IEEE
Antennas
and Propagation Magazine
Vol.
48,
No.
6,
December
2006
1 o~
dim
W
_z
0
~
F
ik
Veer
11et
Toots Ooaktme
ridu
H*Electromagnetic Scatteiing
from
a
Una
Source
above
Ground lane/
Calculation
Parameters
~
/
Frequency
0
Heighit
m
2
~
3
6')CanessePott
Total snd ncident ield
of
a
ine source bove ground lane
0
10
20
30
40
70
.80
90
100it11
i
0
20 40
60
80
1002
12
140
160
180
Figure
3.
A
snapshot of
the Scattering from
a
Line Source
above
a
Ground
Plane
module.
Ez
[Line
source excitation]
0.4
06
0.2
up
0.5j
1.5
i
New
field
on
a
Dielectric cylinder
excited
by
a
TMz
Plane
wave
I
A
1.3
1.2
0.50.5
OA
0.9
y
0 0.7
0.2
x
i
0.5
0.4
Figure
9.
The nearfield results
for
the
input
parameters
shown
in
Figure
7.
Plane wave scattering from
a
conductive
or
dielectric sphere
Sphere
Properties
radius
Intll
0
Ei
Permittivity
4
.
penneaibddy
I
Scattered Fields
frequency
1GHz]
distance
jntj
Op
degreenj
0
.
number of
terms
to
o
ev
etinc
Saoo lot ots
frequency
u s
9
ýScale
nd
NfdomtalizatiOn
0
(
0
01
de
,
I
j
Figure
6.
The nearfield results for
the
input parameters
shownin
Figure
4.
Figure
10.
A
snapshot
of the
Sphere
module.
IEEE
Antennas and Propagation
Magazine
Vol. 48,
No.
6,
December
200613
Incident
F
height
2
m
...... ............. ....... .. ....... .......... . ....
I
.......... .....
ý
......................... ................. ...... .. ..... ..........
.......
139