
121Biosensing Based on Surface-Enhanced Raman Spectroscopy
magnetic eld vector components in the same spatial volume are solved at the next instant
in time; and the process is repeated over and over again until the steady-state EM eld is
fully evolved. The Maxwell curl equations in Cartesian coordinates can be rewritten as
∂
∂
=
∂
-
∂
∂
Ë
Á
¯
˜
∂
∂
=
∂
∂
-
∂
-
Ë
Á
¯
˜
∂
H
x
t
E
y
z
E
z
y
E
x
t
H
z
y
H
y
z
E
x
H
y
s,
∂∂
=
∂
∂
-
∂
∂
Ê
Ë
Á
ˆ
¯
˜
∂
∂
=
∂
∂
-
∂
∂
-
Ê
Ë
Á
ˆ
¯
˜
∂
∂
t
E
z
x
E
z
z
E
y
t
H
x
z
H
z
x
E
y
H
z
s
tt
E
x
y
E
y
x
E
z
t
H
y
x
H
x
y
E
z
=
∂
∂
-
∂
∂
Ê
Á
ˆ
˜
∂
∂
=
∂
∂
-
∂
∂
-
Ê
Á
ˆ
˜
s,
If we dene the discrete mesh grid (i, j, k) in Cartesian coordinates, these partial
differential equations can be transformed to the following nite dif