Biomedical Engineering Reference
In-Depth Information
Figure 1.9
Models of NPs and core-shell NCs used in the calculations.
Reprinted with permission from Ref. [34]. Copyright c
2012 Wiley-VCH
Verlag GmbH & Co. KGaA, Weinheim.
conveniently identified using Eqs. (1.32) and (1.33). The total
electric and magnetic fields are givenas:
E
i
e
,1
n
+
N
o
/
e
,1
n
(3)
/
(1)
(
k
+
)
A
(3)
/
(1)
o
M
o
/
e
,1
n
(3)
/
(1)
(
k
+
)
=
/
n
=
1,2,3,...
e
,1
n
M
o
/
e
,1
n
(3)
/
(1)
(
k
−
)
−
N
o
/
e
,1
n
(3)
/
(1)
(
k
−
)
,
+
B
(3)
/
(1)
o
/
A
(3)
/
(1)
o
e
,1
n
M
o
/
e
,1
n
(3)
/
(1)
(
k
+
)
+
N
o
/
e
,1
n
(3)
/
(1)
(
k
+
)
ε
0
+
μξ
2
H
i
=−
i
/
μ
=
n
1,2,3,...
e
,1
n
M
o
/
e
,1
n
(3)
/
(1)
(
k
−
)
−
N
o
/
e
,1
n
(3)
/
(1)
(
k
−
)
.
B
(3)
/
(1)
o
−
(1.34)
/
where the sub-index
i
represents the
i
-th layer, (3) and (1) indicate
that the function
z
n
(
ρ
) in Eq. (1.32) is the spherical Hankel function
ofthefirsttype[
h
(1
n
(
ρ
)]orthesphericalBesselfunction[
j
n
(
ρ
)].On
theboundaryofeachlayer,thetransversecomponentofelectricand
magnetic fields is continuous. The coe
cients
A
(3)
/
(1)
o
/
e
,1
n
and
B
(3)
/
(1)
o
/
e
,1
n
of
those modes can be found by solving the matrix equations given in
