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Abstract

Analytical solution is derived to the problem of scattering of electromagnetic plane wave by an array of dielectric spheres each coated with a dielectric shell. The incident, scattered and transmitted electric and magnetic fields are expressed in terms of the vector spherical wave functions. The vector spherical translation addition theorem is applied to impose the boundary conditions on the surface of various layers. Numerical results are computed and presented graphically for the radar cross sections of several configurations of spheres system with multi dielectric layers.
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ADP015062
TITLE:
Electromagnetic
Scattering by
a
System
of
Dielectric
Spheres
Coated
With
a
Dielectric
Shell
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TITLE:
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ADP015064
UNCLASSIFIED
ACES
JOURNAL, VOL.
18,
NO. 4,
NOVEMBER
2003
91
Electromagnetic
Scattering
by
a
System
of
Dielectric
Spheres Coated
With
a
Dielectric
Shell
A-K.
Hamid
M.
I.
Hussein
M.
Hamid
Department
of
Electrical and
Department
of
Electrical Engineering
Department
of
Electrical
Engineering
Computer
Engineering
United
Arab
Emirates
University University
of
South
Alabama
University
of
Sharjah
P.O.
Box
17555,
Al-Ain,
United
Arab
Mobile,
AL 36688, U.S.A
P.O.
Box
27272,
Sharj
ah,
U.A.E
Emirates
email: mhamid(@.usouthal.edu
email:
akhamidt@Shariah.ac.ae
email:
MIHussein(uaeu.ac.ae
Abstract
with
a
dielectric layer.
In
this
paper,
we
extend
the
solution
of
scattering by
two
dielectric
spheres
covered
with
a
Analytical
solution
is
derived
to the
problem
of
scattering
of
dielectric
shell
[9]
to the
case
of
scattering by
a
system
of
electromagnetic plane wave
by
an
array
of
dielectric
spheres dielectric spheres each
covered with
a
dielectric
shell.
The
each
coated
with
a
dielectric
shell.
The incident,
scattered
solution
to
this
problem
has
many
practical
applications
and
transmitted
electric
and
magnetic fields
are
expressed
in
since,
for
example,
it
may be
used
to
study
the scattering
by
terms
of
the
vector
spherical
wave
functions.
The
vector complex
objects simulated
by
a
collection
of
spheres
[12],
spherical
translation addition theorem
is
applied
to
impose
and
it
may
also
be
used
to
check
the
accuracy
of
numerical
the
boundary conditions
on
the
surface
of
various
layers.
solutions.
Numerical results
are
computed
and
presented
graphically
From
the
design
point
of
view, the
backscattering
cross
for the
radar cross
sections
of
several
configurations
of
section
of
an
array
of
N
dielectric
coated
spheres
can
be
spheres
system with multi dielectric
layers.
controlled
to
exploit
multiple
resonances
by
optimizing
the
multivariables
of
the
system.
These
include
the size
and
1.
Introduction
location
of
each
sphere,
number
of
dielectric
layers
coating
each
sphere
as
well
as
the
thickness
and
relative
dielectric
Many authors have
studied
the
scattering
of
electromagnetic constant
of
each
layer
as
already
done
for conducting
plane
wave
by
a
dielectric sphere
coated
with
a
dielectric
cylinders
[13].
shell.
Aden
and
Kerker
[1]
obtained
analytical
expressions
to
the
scattering
of
electromagnetic plane
wave by
a
2.
Formulation
of the
Problem
dielectric sphere coated
with
a
concentric
spherical
shell
of
different dielectric materials,
while
Scharfman
[2]
presented
Consider
a
linear
array
of
N
dielectric
spheres
each
coated
numerical
results
for
the
special
case
of
a
small
electrical
with
a
dielectric
shell
and
having different radii
and
unequal
radius
(ka<l)
dielectric
coated conducting
sphere.
It
was
spacing
with
centers lying
along
the
z
axis,
as
shown
in
Fig.
found
in
those
early studies
that
the
presence
of
dielectric
1.
Electromagnetic
plane
wave
of
unit
electric
field
coatings
leads
to
substantial
increase
in
the
backscattering
intensity,
whose
propagation
vector k
lies
in
the
x-z
plane
cross
section
for
an
appropriate
choice
of
the
dielectric and makes
an
angle
a
with
the
z-axis,
is
assumed
to be
constant
and
thickness
of
the
coating
relative
to
that
of
incident
on
the
spheres.
Its
incident
electric and magnetic
uncoated
sphere.
Further,
Wait
has
extended
the
solution
to
fields are
the
case
of
scattering
by
a
radially
inhomogeneous
sphere
--k -
[3],
while
a
numerical
solution
using
the
method
of
Ei =ek
y
(1)
moments
obtained
by
Medgyesi-Mitschang
and
Putnam
for
the
case
of
dielectric-coated
concentric
sphere
[4].
More
H
=-
eJkr(cos
a
i-sinoti)
(2)
recently,
an
exact solution
of
electromagnetic plane
wave
?7
scattering
by
an
eccentric
multilayered
sphere
was
with
k
being
the
wave
number,
i,5,
and
2
are the
unit
developed
by
Lim and
Lee
[5].
Numerous
papers
on
the
vectors along
the
x, y
and
z
axes,
respectively,
and q/
is
the
scattering
from
systems
of
spheres
of
various natures
in
surrounding medium
intrinsic
impedance.
The
incident
close
proximity
have been
treated
by
numerous
researchers
electric and
magnetic
fields
may be
expanded
in
terms
of
[6-11].
elect
or ae fios
a
b
e
en ter
of
Up
to
now,
there
has
been
no
analytical
or
numerical
spherical
vector
wave
functions around
the
center
ofthe
pth
solution
to
the
problem
of
scattering
of
electromagnetic
sphere
as
plane
wave
by
an
array
of
conducting
spheres
each coated
1054-4887
©
2003
ACES
92
ACES
JOURNAL,
VOL.
18,
NO.
4,
NOVEMBER
2003
m
= n
-m =(
(r,, I
[P,(m,n)N,(r,,8,p,)
(3)
77H
(r,p,,p,)-j
E
[AE,,(m,n)MWm(rP,p,bp)
(10)
fl
-n=1
m=-n
n=I
m=
+Q,(~n)H,',)(r,0P,0)] n -n
+Amp
(m,
n)N
(,)
(rp,gOp,
op)
]
where
AEp
(m,n),
AMp(m,n)
are
the unknown scattered
field
77Hi(r,,,O,,p)=
ji -[P(mn
'n)M.,)(rp'Op'q5p) (4)
coefficients. To
express
the
scattered
fields
from
the
qth
"
='-n
+
Q,
(m,n)NmI
(rp,O,,
p)
sphere
in
the
coordinate
system
of
the
pth
sphere,
we
apply
the
spherical
vector translation addition
theorem
for
where
M
and
are
the
spherical vector
wave
translation
along
the
z-axis
[15], i.e.,
functions
of
the
first
kind
representing
incoming
waves
W(3)(r,,0 q>=
[A'
(d )M(
1
)(r
0
(1
associated
with the
spherical
Bessel
function, while
V=r
mn
-) m
p
' kp
Pp(m,n)
and
Qp(m,n)
are the
incident
field
expansion
+
my(d
coefficients defined
in
[7-8,14].
The
field
in
the
region
II
r -
can be
also
expressed
in
terms
of
the
vector
spherical
wave
N-(q',q,(kq)=
[A,,(dpq)N(v)(r'Opqp)
(12)
functions
of
the first and
third kinds.
Hence
the
electric
and
+B
I
(12)
magnetic fields
may
be
written
as
+ v
(dpq"
Man
p(rOp
1 p0
where
Am,
(dpq)and
Bmv
(dpq)
are the
translation
... .
[AE(mn),
(r
0
0) (5)
coefficients
of
the
spherical
vector
translation
addition
+A
Ep(mnnl)N(rp
,9P,/)
(
theorem. To
determine the unknown scattered
field
+A'mp(mn,n)jW.((r
0pO,)
coefficients,
we
apply
the
boundary
conditions
on
the
+
A"Mp
(m,n)M(m)(rp,Op,
p)] various
interfaces,
i.e.,
[A
~
~ ~ ~
Z
Ep ?)m
FpO)F
E(bp,
Op,
0p)
+ A'
ES(bp,Op,0p)
=
p.×
El(bb,'9p,0p
) (3
--- +
A
Ep(m'?1)MW')
(rp'P
P))
(6) I N--s
+A'Mp(m,n)lM4(r
n( ,,p,,
()
FpX[Hj(bp,Op,)
p)+
p
H
o(bp,P)
7
II(bp,pqpD)
(14)
ZL P=P
+p
x
Eii(ap,Op,
Op)
=
7p
x
Ei(ap,Op,
p)
(15)
where
ApE
(r,
n),
A
pM
(m,n),
A
pE
(m,n),
and
p
xHi(ap,
Op,
Op)=
xH,-(apIOpIp)
(16)
A
pM
(n,n)
are
the field
expansion coefficients,
while
Substituting
the
appropriate
field
expansion expressions in
(3)
j(3)
equations
(13)
to
(16),
and
applying
the
orthogonality
n(3)
and
)Vm
are
the
vector
spherical
wave
functions
of
m
n
n properties
of
spherical
vector
wave
functions
and
the
third kind
representing outgoing
waves
associated
with
eliminating
the
transmission
coefficients
we
obtain
the
spherical Hankel
function. The subscripts
E
and
M
N
denote
transverse
magnetic (TM)
and
transverse
electric
AEp(m,n)=v,(pp)Pp(in,n)+_.
[A.
(dpq)A,,,(m,v)
(17)
waves
(TE),
respectively.
The
field
in
region I
of
the
pth q p )Av( )
sphere
may be
written
in
terms
of
the
vector
wave
functions
+B..(dpq)Ap(m,v)]
of
the
first kind,
i.e.,
N
of
te
fist
knd,
~e.,A~p(m,n)=u,(pp)Qp(m,n)+Yj
[A.,(dpq)A,,P(m
,' v)
(18)
q= =1
ErP0)ZZ
[Ap(nz,n)Nm.1
( p, , qkp
,) (7) q*P
,--
....
0)+
B
";
(dpq)AEp
(m,
v)]
Amn(-,pp
,where
vn ( p
p)
and
u,,
(pp)are
the
electric
and magnetic
H, I
[A,,(nln)A)(rP,0P,,
) (8, ) scattered
field
coefficients
for
a
single
dielectric
sphere coated
n=
m=-l
[M.
(8)
with
a
dielectric
layer
[1,9].
Equations
(17)
and
(18)
may
be
+AMp
(m,n)N.,n)(r,,O,
,)]
written
in
matrix
form
for the
purpose
of
computing
the
scattered
field
coefficients,
i.e.
where
AEP
and AMP
are
the
unknown
transmitted
A
=L
+TA
(19)
coefficients.
Finally,
the
scattered
electric
and
magnetic
where
-
and
E
are
column matrices
for
the
unknown
fields from
the
pth
sphere
are
expanded
as
scattered
and
incident
field
coefficients, respectively,
and
--
m=n
ES(rp'O9p'bp)=Z
I
[AE(mn)N'(rP,9P,,)
T
is
a
square
matrix
which
contains
the
translation
addition
= .... [ ( M" ,
(9)
coefficients.
+AMp(in,n)M
(rp,0p,p,,)]
Once
the
scattered
field
is
computed
from
equation
(19),
the
normalized bistatic
cross
section
can
be
obtained
as
in
[16].
Hamid,
et
al.:
Scattering
by
a
System
of
Dielectric
Spheres
Coated with
a
Dielectric
Shell
93
for the
outer layer
is
3
and
the
electrical
separation
between
3.
Numerical
Results
the
centers
of
the
spheres
is
3.0
(touching).
In
order
to
check
the
validity
of
our computer program,
4.
CONCLUSIONS
several
numerical tests
were
conducted
and the
results
compared
favorably
with
previously published
results
[7-
We
have
obtained
an
analytic
solution
of
the
problem
of
8,11].
These
tests
included
the
limiting
cases
of
(i)
an
array
scattering
by
an
array
of
dielectric
spheres each coated
with
of
dielectric spheres
obtained
by
setting
kb
=ka,
E
=I
or
a
dielectric
shell.
The
boundary
conditions
are
satisfied
at
various interfaces
with
the
help
of
the
vector
translation
61ir
=
Eir
(ii)
an
array
of
conducting
spheres
each
coated
addition theorem. The system
of
equations
was
written
in
with
a
single
dielectric
layer
obtained
by
setting
EIr
=
oo
and matrix form
while
the
scattered
field
coefficients
were
obtained
by
matrix inversion.
Numerical
results
were
(iii)
an
array
of
conducting
spheres
obtained by setting
presented
for
different numbers
of
spheres,
angles
of
E£r
=
0o
and
kb
=ka
or
Ellr
=1.
incidence, electrical
separation,
and
relative
dielectric
In
this
paper,
we
presented
numerical results
for
different
constant.
For
the general
case
of
spheres orientation,
the
sphere arrays
to
show
the
dependence
of
the
radar
cross
reader
may
find
more details
in
[8].
section
on
various
parameters characterizing
the
geometry,
material
properties,
and incidence
angles.
Fig.
2
shows the
ACKNOWLEDGMENT
normalized bistatic
cross
section
versus the
scattering angle
0
for
a
system
of
three identical
spheres
in
the
E and
H-
The
first
author
wishes
to
acknowledge
the
support provided
planes. The electrical
radii
of
the
outer
and
inner
spheres
are
by
University
of
Sharjah. The second
author
wishes
to
ka=2.0
and
kb=2.5,
respectively,
while
the
electrical
acknowledge
the
support
of
the
United
Arab Emirates
separation between successive
spheres
is
kd=7.0,
and the
University,
while the
third
author
wishes
to
acknowledge
relative dielectric
permittivity
of
the
inner dielectric layer
is
the financial
support
of
the
University
of
South
Alabama
3.0
and
the
outer
is
air.
The
purpose
of
this
comparison
is
to and the
National
Science
Foundation.
check
the
accuracy
of
the
computer
code
for
the
dielectric
sphere
case
[8]
as
a
special
case
of
the dielectric
spheres
except
the
relative
dielectric
permittivity
of
the
dielectric
layer
is
set
equal to
unity.
The parameters
of
Fig.
3 are
similar
to
Fig.
2
except
that
the
dielectric
layer
has
a
value
Z
of
2.
We
can see
that
the
number
of
resonances
in E
plane
is
increased. Figs.
4
and
5
have the same
parameters
as
in
Fig.
3
except
that
the
number
of
spheres
is
increased
to five
and eight,
respectively.
We can
see
that the
number
of
P
resonances
also
increases
with
the
number
of
spheres.
xP
Fig.
6
shows
the
normalized backscattering
cross
section
versus
the
electrical
distance
(kd), which ranges from
8
(touching)
to
15.5
for
end
fire
incidence
and
the
number
of
dpq
spheres
is
five.
The
electrical
radii
of
outer
and
inner
spheres
are
ka=4.0
and
kb=3.0,
repectively,
while
the
xq
-
relative dielectric
permittivity
of
the
inner dielectric layer
is
3.0
and for the
outer
layer
is
2.
Fig.
7
is
similar
to
Fig.
6
except
the
number
of
spheres
is
increased
to
8.
We can see
"c
1
that the location
of
the
maximum peaks
did
not
change
by
increasing
the
number
of
spheres
for
both
cases.
x
Furthermore,
the
magnitude
of
the
normalized
backscattering
cross
section
at the
maximum
peaks K
increased
with
increasing
number
of
spheres.
In
Figs.
8
and
9
we
have
plotted
the
normalized
backscattering
cross
as
a
function
of
the angle
of
incidence
a,
which
ranges from
0
to 90
degrees for
a
system
of
three
Fig.
1:
Geometry
of
the
scattering
problem.
and
eight
spheres.
The
electrical radii
of
the
outer
and
inner
spheres
are
ka=l.5
and
kb=l.0,
repectively,
while the
relative
permittivity
of
the
inner
dielectric layer
is
4
while
94
ACES
JOURNAL,
VOL.
18,
NO.
4,
NOVEMBER
2003
10' 10'
102
HP
102H-Plane
1'--E -Plane 10'
10' 10'
.1
10
10
10*
1
10
10. 10 2
-3
10.
10" 0 20 40 60 00 100 120 140 100 10
0 20 40 60 80 100 120 140 160 180 Scattering angle (0)
Scattering angle (0)
Fig.
2:
Normalized bistatic
cross
section
patterns
for
Fig.
4:
Normalized
bistatic
cross
section patterns
for
five
three
identical dielectric
spheres
each
covered
with
identical
dielectric
spheres
each
covered
with
a
dielectric
dielectric layer
with
ka=2.0,
kb=2.5, kd=7.0,
layer
with
ka=2.0,
kb=2.5,
kd=7.0,
a
=0,gr
=3.0,
and
a
=0,
gir
=3.0, and
Elir
=1.0.
In
the
E-plane
(
=r/2)
Er=2.
and
H-plane
(=
0).
10'
103
E-P
lane
F_
-Pla
2
.- H-Plane
10'
-. HPae10'
10, 10
10- 1 "
10-' 10
-, 10
10 0 10100 20 40 60 80 100 120 140 160 180
0 20 40 60 80 100 120 140 160 10
Scattering angle (0) Scattering angle (0)
Fig.
3:
Normalized
bistatic
cross
section
patterns
for
Fig.
5:
Normalized
bistatic
cross-section patterns
for
eight
three
identical
dielectric
spheres
each
covered
with
identical
dielectric
spheres
each
covered
with
a
dielectric
dielectric
layer
with
ka=2.0,
kb=2.5,
kd=7.0,
layer
with
ka=2.0,
kb=2.5,
kd=7.0,
a
=0,c1r
=3.0,
and
a
'
=0,
Ir
=3.0,
and
E8ir
=2.0.
Ei1
=2.0.
Hamid,
et
al.:
Scattering
by
a
System
of
Dielectric
Spheres Coated
with
a
Dielectric
Shell
95
1.8
1.69
1.4
1.2 7
1 6
0 .8 - 6
0.6
-4
0.4 3
0.2
2
9 10 11 12 13
14
15
kd
Fig.
6:
Normalized
backscattering
cross section
versus
0 10 20 30 40 50 60 70 80 90
electrical separation (kd)
for
end-fire incidence
and
a
linear
array
of
five
identical dielectric
spheres each
Fig.
8:
Normalized
backscattering
cross section versus
covered
with
a
dielectric layer
with:
ka=4.0,
kb=3.0,
aspect
angle
a
for
a
linear
array
of
three identical
a
=
0.0,
Eir
=3.0,
and
Elir
=2.0.
dielectric
spheres
each
covered
with
a
dielectric
layer
with
ka=l.5,
kb=1.0,
kd=3.0,
Elr
=4.0,
and
E11r
=3.0.
2.5
180
160
2
140
1.5 120
100
1 0
60-
0.5 40
OL ~20
5 10 11 12 13 14 15 0
kd 0 10
20 30 40
50
60
70 80 90
Fig.
7:
Normalized
backscattering
cross section
versus
electrical
separation
(kd)
for
end-fire incidence
and
a
Fig.
9:
Normalized
backscattering
cross section
versus
linear
array
of
eight
identical
dielectric
spheres
each
aspect
angle
afor
a
linear
array
of
eight
identical
covered
with
a
dielectric layer
with:
ka=4.0, kb=3.0, dielectric
spheres
each
covered
with
a
dielectric
layer
with
a=
0.0,
eI,
=3.0,
and
EjIr
=2.0.
ka=l.5,
kb=1.0, kd=3.0,
Ei,
=4.0,
and
Elir
=3.0.
REFERENCES
4.
Medgyesi-Mitschang,
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Putnam,
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he
was
with the
faculty
of
electrical engineering
at
1971.
King
Fahd
University
of
Petroleum
and
Minerals,
7.
Hamid,
A-K.,
Ciric
I.R.,
and
Hamid, Dhahran,
Saudi
Arabia.
Since
Sept.
2000
he
has
been
an
M.,"Multiple scattering
by
a
linear array
of
associate
Prof.
in
the
electrical\electronics
and
computer
conducting
spheres",
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Phys.,
vol.
68,
pp.
engineering
department
at
the
University
of
Sharjah,
1157-1165,
1990.
Sharjah,
United
Arab
Emirates.
His
research
interest
8.
Hamid,
A-K.,
Ciric
I.R.,
and
Hamid,
M.,
includes
EM wave
scattering
from
two and
three
"Iterative Solution
of
The Scattering
by
an
dimensional
bodies,
propagation
along waveguides
with
Arbitrary
Configuration
of
Conducting
or
discontinuities,
FDTD
simulation
of
cellular phones,
and
Dielectric
Spheres",
IEE
Proc.,
Part
H,
vol.
148,
inverse
scattering
using
pp.
565-572,
1991.
Neural
Networks.
9.
Hamid,
A-K.,
Ciric
I.R.,
and
Hamid,
M.,
"Analytic
Solutions
of
The
Scattering
by
Two
Mousa
I.
Hussein
received
the
B.Sc.
degree
in
electrical
Multilayered Dielectric Spheres",
Can.
J.
Phys.,
engineering
from
West
Virginia
Tech,
USA,
1985,
M.Sc.
vol. 70,
pp.
696-705,
1992.
and
Ph.D.
degrees from
University
of
Manitoba,
10.
Comberg,
U.,
and
Wriedt,
T."
Comparison
of
Winnipeg,
MB,
Canada,
in
1992
and
1995,
respectively,
scattering
calculations for aggregated
particles both
in
electrical
engineering.
From
1995
to 1997,
he
was
based
on
different models,"
J.
of
Quantitative
with
research and
development group
at
Integrated
Spectroscopy
and
Radiative
Transfer,
vol.
63,
pp.
Engineering
Software
Inc.,
Winnipeg,
Canada,
working
149-162,
1999. on
developing
EM
specialized
software
based
on the
11.
A-K. Hamid,
M.I.
Hussein,
and
M.
Hamid,
Boundary Element
method.
In 1997
he
joined
the
faculty
"Radar Cross
Section
of
a
System
of
Conducting
of
engineering
at
Amman
University,
Amman,
Jordan,
as
Spheres Each
Coated
with
a
Dielectric
Layer,"
J.
an
Assistant
Professor.
Currently
Dr.
Hussein
is
an
of
Electromagnetic
Waves
and
Applications,
vol.
Associate
Professor
with the
Electrical Engineering Dept.
17,
pp.
431-445,
2003.
at
the
United
Arab
Emirates
University. Dr.
Hussein
12.
Hamid,
A-K.,"
Modeling
the
Scattering
from
a
research
interests include
computational
electromagnetics,
Dielectric
Spheroid
by
System
of
Dielectric
electromagnetic scattering,
antenna
analysis
and
design,
Spheres",
J.
of
Electromagnetic
Waves
and
EMI
and signal
integrity. microstrip
antennas, phased
Applications,
vol.
10,
no.5,
pp.
723-729,
1996.
arrays,
slot
and
open
ended
waveguide
antennas.
13.
Hamid,
M.,
and
Rao,
T.C.K,"
Scattering
by
a
multilayered
dielectric-coated conducting
Michael Hamid
Graduated
from McGill
University in
cylinder",
International
J.
of
Electronics,
vol.
38,
Montreal
with
a
B.Eng.
degree
in
1960,
a
M.Eng.
degree
pp.
667-673,
1975.
in
1962
and
from
the
University
of
Toronto
with
a
Ph.D.
14.
Stratton,
J.A.,
"Electromagnetic
Theory",
degree
in
1966,
all in
Electrical Engineering.
He
joined
(McGraw
Hill,
New
York),
1941.
the
University
of
Manitoba
in 1965
where he
became a
15.
Cruzan,
OR.,
"Translational
addition
theorems
Professor
of
Electrical
Engineering
and
head
of
the
for
spherical
wave
functions",
Quart.
Appl.
Antenna
Laboratory.
He was
a
visiting
Professor
at
the
Math.
,
20, pp.
33-40.
1962.
Naval
Postgraduate
School
as
well
as
the
universities
of
16.
Hamid,
A-K.,
Hussein,
M.I.,and
Hamid,
M.,
California
Davis
and Central
Florida
and
is
presently a
"Bistatic Cross Section
of
an
Array
of
Dielectric
Professor
of
Electrical
Engineering
at
the
University
of
Spheres
Each
Covered
with
a
Dielectric
Shell,"
South
Alabama.
He
is
a
past president
of
the
International
the
19
th
Annual
Review
of
Progress
in
Applied Microwave
Power
Institute,
a
Fellow
of
IEE
and IEEE
Computational
Electromagnetics,
Naval and
published
307
referred
articles and
25
patents.
Postgraduate
School,
Monterey, California,
U.S.A.,
pp.
77-81,
March 2003.
A.-K.
Hamid
was
born
in
Tulkarm, West
Bank,
on
Sept.
9,
1963.
He
received the
B.Sc.
degree
in
Electrical
Engineering
from
West
Virginia
Tech,
West Virginia,
U.S.A.
in
1985.
He
received
the
M.Sc.
and
Ph.D.
degrees
from
the
university
of
Manitoba, Winnipeg, Manitoba,
Canada
in
1988
and
1991,
respectively, both
in
Electrical
Engineering.
From 1991-1993,
he
was
with Quantic
Laboratories
Inc.,
Winnipeg, Manitoba,
Canada,
developing
two
and
three
dimensional electromagnetic
field
solvers
using
boundary
integral
method. From
1994-
Article
Full-text available
Many scientific fields--including astronomy, climatology, and biology, among others--require the calculation of the scattered optical fields from multiparticle distributions. In the present study, we combine the established results for the scattering from clusters of homogeneous spheres and from single core-shell particles into a computationally tractable solution that is valid for irregular configurations of nonidentical, coated particles. The presented multiparticle scattering (MPS) model is based on a generalized Lorenz-Mie theory framework and the vector translation theorems for the vector spherical harmonics. We provide the MPS model in both the near and far fields, and for plane-wave and Gaussian beam illumination. A message-passing-interface protocol is used for the computational implementation of the model in a parallel computer program. The computer model is validated by verifying the accuracy of the vector translation theorems utilized in our theoretical methods and by qualitative comparison to existing multiparticle scattering data. We conclude by presenting the scattering profiles from several examples of particle distributions. This MPS model is a practicable method of calculating the optical fields arising in the scattering from particle aggregates and is straightforwardly extensible to arbitrary illumination and to more complex internal-particle structures, such as stratified spheres. Vital applications of this model include the exact computation of forces exerted on irregular objects in optical traps and the simulation of light propagation through biological tissues.
Article
Full-text available
The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.
Article
Full-text available
An analytic solution to the problem of the scattering of a plane electromagnetic wave by an arbitrary configuration of dielectric spheres is presented using an iterative procedure to account for the multiple scattered fields between the spheres. To compute the higher order terms of the scattered fields, the translation addition theorem for the vector spherical wave functions is used to express the field scattered by one sphere in terms of the spherical co-ordinates of the other spheres to impose the boundary conditions. Coefficients of the various order scattered fields are obtained in matrix form. Numerical results for the normalised backscattering and bistatic cross-section patterns are presented for one- and two-dimensional arrays, and these show that scattered fields up to the fourth order are needed in the special case of contacting conducting linear arrays of spheres to achieve results in excellent agreement with the available data published in the literature
Article
An analytical solution to the problem of scattering of a plane electromagnetic wave by an array of dielectric spheres each covered with a dielectric shell is derived using the multipole expansion method. The boundary conditions are enforced at the outer dielectric surface of each sphere by using the vector spherical translation addition theorem. Numerical results are computed and presented graphically for the bistatic cross section of an array of spheres.
Article
Analytical solution to the problem of scattering of a plane electromagnetic wave by an array of conducting spheres each coated with a dielectric layer is derived. The incident, scattered and transmitted electric and magnetic fields are expressed in terms of the vector spherical wave functions. The vector spherical translation addition theorem is applied to impose the boundary conditions on the surface of each dielectric‐coated sphere. Numerical results are computed and presented graphically for the radar cross of several configurations of dielectric‐coated spheres.
Article
The solution to the problem of electromagnetic waves scattering by an array of spheres is used to simulate the scattering by a spheroid. The scattering by an array of spheres is formulated by expressing the incident, transmitted, and scattered fields in terms of the vector spherical wave functions, and the boundary conditions are satisfied by applying the translation addition theorem for the vector spherical wave functions. The advantage of using the proposed technique is the simplicity and efficiency in computation. The modeling of a conducting or dielectric spheroid is outlined and numerical results are presented graphically and compared with those based on other available methods to show the validity of the analysis.
Article
The scattering cross section of a conducting cylinder coated with a multilayer of homogeneous dielectric due to a plane electromagnetic wave incident at any arbitrary angle is derived by the boundary-value method. The analytical results are treated by Rosenbrock's method to generate optimum radial dielectric profiles corresponding to minimum and maximum backscattering cross sections.
Article
Various theoretical methods and corresponding computer programs exist which can be used to compute electromagnetic scattering by a cluster of several arbitrarily shaped particles. The aim of this paper is to compare results of various theories to "nd the range of applicability of the di!erent methods. At "rst some comments will be made on the programs employed: the order-of-scattering Mie program (OS-Mie), the discrete dipole approximation (DDSCAT) and the multiple multipole program (MMP). As examples, results for four spheres within varying distance will be compared. In addition computations of the scattering of one bigger transparent sphere with two smaller absorbing &satellite' spheres and of the scattering of two small oblates will be presented. A table includes data to give a hint on the computational demands.
Article
The generalization of the Lorenz-Mie theory for scattering from a homogeneous sphere to a radially inhomogeneous sphere is given. In this case, the scatterer consists of a spherical body with any number of concentric homogeneous regions. The treatment makes use of the analogy with non-uniform transmission line theory.
Article
Formulas for the backscattering and total scattering cross sections for dielectric coating spheres of arbitrary size were developed following the methods of Hansen and of Aden and Kerker. Calculations based on the resultant formulas were made in the region of the first resonance (outside dimension of the concentric spheres is approximately 0.4 wavelength). It was found that certain choices of coating thickness and dielectric constant can lead to increases in the scattering cross sections of more than 100 percent relative to a solid metal sphere of the same outside diameter. A number of calculated and measured curves are presented, and they show the variation of the backscattering and total scattering cross sections as functions of coating thickness, coating permittivity, and outside diameter of the coating. Where both calculations and measurements were made for the same conditions, the values agree to ±2 percent.
Article
A solution is given for the problem of the scattering of plane electromagnetic waves from a sphere with a concentric spherical shell. The solution is general, and under appropriate conditions is reduced to the well‐known solution for scattering from a single sphere.