Biomedical Engineering Reference
In-Depth Information
The electric and magnetic fields inside the
s
-th chiral spherical
particle have the form [
s
=
1, 2; cf. (4.35)]:
∞
n
s
A
mn
s
N
ψ
mn
s
E
=
(
L
)
s
M
ψ
(
L
)
mn
+
=−
n
=
1
m
n
iZ
s
B
mn
s
N
mn
,
(
R
)
mn
s
M
(
R
)
−
ψ
−
ψ
(4.51)
1
iZ
∞
n
s
A
mn
s
N
ψ
mn
s
H
=
(
L
)
mn
s
M
ψ
(
L
)
+
=−
n
=
1
m
n
s
B
mn
s
N
ψ
mn
,
(
R
)
mn
s
M
ψ
(
R
)
+
−
where the vector spherical harmonics
s
N
ψ
(
J
)
mn
and
s
M
ψ
(
J
)
mn
(where
J
=
L
,
R
) in local coordinates
s
r
of the
s
-th spherical particle are
defined inAppendix 4.B.
Z
again stands for impedance ofparticles.
The electric and magnetic fields of a chiral molecule with the
electric and magnetic dipole moments
d
0
and
i
m
0
, placed at the
point
s
r
0
ofthe
s
-thlocalsystemofcoordinates,canbepresentedas
an expansion over the vector spherical harmonics in the following
form [
s
r
0
>
−
s
r
;
s
=
1, 2; cf. (4.36)]:
∞
n
s
A
(0)
mn
mn
,
s
E
0
=
s
N
ψ
(0)
mn
s
B
(0)
mn
s
M
ψ
(0)
+
=
m
=−
n
(4.52)
n
1
s
H
0
=−
i
∞
n
s
B
(0)
mn
,
s
N
ψ
(0)
mn
s
A
(0)
s
M
ψ
(0)
+
mn
mn
=
m
=−
n
n
1
(0)
(0)
mn
,andthe
where the vector spherical harmonics
s
N
ψ
mn
and
s
M
ψ
coe
cients
s
A
(0)
mn
and
s
B
(0)
mn
can befound in Appendix 4.B.
The electric and magnetic field of the reflected wave can be
expressed as the sum of the partial fields from each of the particles
[22]:
E
sc
1
E
sc
2
E
sc
,
H
sc
1
H
sc
2
H
sc
,
=
+
=
+
(4.53)
where [
s
=
1, 2; cf. (4.37)]
∞
n
s
E
sc
(
s
C
mn
s
N
ζ
mn
+
s
D
mn
s
M
ζ
mn
),
=
=
m
=−
n
(4.54)
n
1
i
∞
n
s
H
sc
(
s
D
mn
s
N
s
C
mn
s
M
=−
ζ
mn
+
ζ
mn
),
n
=
1
m
=−
n
