Biomedical Engineering Reference
In-Depth Information
Evenifdissipativelossesarepresent,thenumberofallowedphoton
momenta at the interface is dramatically increased, resulting in the
high LDOS and thus in the high electromagnetic energy density of
the SPP mode. However, a high LDOS and a high intensity of both
electric and magnetic fields (Fig. 8.3c,d) are only observed in close
vicinity to the material interface. Away from the interface, the LDOS
and intensity drop off exponentially.
To get deeper insight into the mechanisms that squeeze
the optical energy of the SPP wave to the region just around
the interface, we study the optical powerflow at the SPP frequency.
The direction and intensity of the time-averaged optical powerflow
at each point of space can be characterized by the Poynting vector,
which is calculated as follows:
1
2
Re(
E
×
H
∗
).
S
=
(8.4)
In the simple geometry of Fig. 8.3a, we can derive an analytical
form of the time-averaged Poynting vector for each medium.
Substitution of (8.2) and (8.3) into (8.4) yields the following
expressions for the time-averaged powerflow above and below the
interface:
x
A
2
2
β
ωε
0
ε
2
e
−
2
k
2
z
>
0:
S
=
z
(8.5)
z
<
0:
S
=
x
A
2
2
β
ωε
0
ε
1
e
2
k
1
z
(8.6)
Comparison of (8.5) and (8.6) immediately shows that the power
flow parallel to the interface reverses direction abruptly when
crossing from one medium to the other. The plot of the time-
averaged powerflow shown in Fig. 8.3e visualizes the above
observation. The time-averaged Poynting vector component in the
vertical direction has a purely imaginary value, which is a signature
of a reactive powerflow. In electromagnetic circuits, reactive power
is the portion of power associated with the stored energy that
returnstothesourceineachcycleandtransfersnonetenergytothe
load [48]. Reactive power is always a factor in alternating current
circuits such as electrical grids, in which energy recycling through
storage elements (i.e., inductors and capacitors) causes periodic
reversals in the direction of energy flow. Although the reactive
powerflow does not deliver any useful energy to the load, it assists
