Biomedical Engineering Reference
In-Depth Information
spherical particle take the form:
∞
n
A
mn
N
mn
−
iZB
mn
N
mn
,
(
L
)
mn
(
L
)
(
R
)
mn
(
R
)
E
=
ψ
+
M
ψ
ψ
−
M
ψ
=
m
=−
n
n
1
∞
n
−
iZ
−
1
A
mn
N
ψ
mn
+
B
mn
N
ψ
mn
.
(
L
)
mn
(
L
)
(
R
)
mn
(
R
)
H
=
+
ψ
−
ψ
M
M
n
=
1
m
=−
n
(4.35)
Electric and magnetic fields of the chiral molecule with the electric
and magnetic dipole moments
d
0
and
−
i
m
0
, respectively, which is
located in the point
r
0
in vacuum, can be presented as an expansion
over the vector spherical harmonics in the followingform (
r
0
>
r
):
∞
n
A
(0)
mn
,
(0)
mn
+
B
(0)
(0)
E
0
=
mn
N
ψ
mn
M
ψ
=
m
=−
n
n
1
H
0
=−
i
∞
n
B
(0)
mn
,
(0)
mn
+
A
(0)
(0)
mn
N
ψ
mn
M
ψ
(4.36)
=
m
=−
n
n
1
ψ
(0)
ψ
(0)
mn
,and
A
(0)
mn
and
B
(0)
where
N
mn
and
M
mn
are defined in Appendix
4.B.
Electric and magnetic fields of the reflected wave can be written
as:
∞
n
E
sc
=
(
C
mn
N
ζ
mn
+
D
mn
M
ζ
mn
),
=−
n
=
1
m
n
=−
i
∞
n
H
sc
(
D
mn
N
ζ
mn
+
C
mn
M
ζ
mn
),
(4.37)
=
m
=−
n
n
1
where
N
ζ
mn
and
M
ζ
mn
are defined in Appendix 4.B.
To find the coe
cients in expansions (4.35) and (4.37), one can
use the continuity of the tangential components of the electric and
magnetic fields on the surface of the sphere [69].
Forthecoe
cients
C
mn
and
D
mn
thatdefinethereflectedfieldsin
(4.28), onecan obtainthe following expressions:
C
mn
=−
α
n
A
(0)
δ
n
B
(0)
mn
,
D
mn
=−
β
n
B
(0)
δ
n
A
(0)
+
+
i
i
mn
,
(4.38)
mn
mn
α
n
,
β
n
,and
δ
n
have the form
where functions
A
(
L
n
W
(
R
)
+
A
(
R
n
W
(
L
)
V
(
L
n
B
(
R
)
+
V
(
R
n
B
(
L
)
n
n
n
n
α
n
=
,
β
n
=
,
V
(
L
n
W
(
R
)
+
V
(
R
n
W
(
L
)
V
(
L
n
W
(
R
)
+
V
(
R
n
W
(
L
)
n
n
n
n
i
B
(
L
n
W
(
R
)
−
B
(
R
n
W
(
L
)
n
n
δ
n
=
.
(4.39)
V
(
L
n
W
(
R
)
V
(
R
n
W
(
L
)
+
n
n
