Biomedical Engineering Reference
In-Depth Information
in maintaining proper voltages across the power system. Reactive
powerflow is manifested in measurable dissipative losses due to
periodic energy recycling through the grid and sudden disruptions
inthereactivepowerflowpatterncancauseavoltagedropalongthe
line [49]. Likewise, the reactive powerflow away from the metal-
dielectric interface associated with the SPP propagation along the
interface does not contribute to the net energy transfer. The power
is temporarily stored in the form of magnetic and electric fields.
As the SPP mode is an eigensolution of the Maxwell equations
rather than a wave generated by either a localized source or a plane
wave, an insight into its energy storage mechanism can be gained
by plotting the instantaneous Poynting vector distribution [50]. The
instantaneous optical powerflow at any given moment in time can
becalculated as follows:
2
Re
E
×
He
i
ω
t
.
1
1
2
Re(
E
×
H
∗
)
+
S
=
(8.7)
Itcanbeseenthatthetime-averagedpowerflowexpression(8.4)
is represented by the first term in (8.7), and the second term drops
out due to its sinusoidal behavior when performing the averaging
procedure. The instantaneous Poynting vector of the SPP wave is
plottedinFig.8.3eandfeaturesrepeatingareasofcirculatingoptical
powerflow centered on the metal-dielectric interface. These data
lead us to the conclusion that electromagnetic energy recycling
through local optical vortices on the interface is behind tight field
localization, high energy density, and reduced group velocity of the
SPP waves. The new look at the old problem provided by revealing
the circulating powerflow also offers a new take on the meaning of
thelargein-plane
k
-vectorphotonstatesthatonlyexistverycloseto
the interface supporting SPP waves. The circulating instantaneous
SPP optical powerflow is characterized by the photon angular
momentum, which has a conserved value at every point in space
[51]. In turn, the value of the linear momentum that is tangential
to the circulating powerflow scales inversely with the distance to
the powerflow center (i.e., with the distance to the metal-dielectric
interface).Thetangentialmomentuminthedirectionperpendicular
to the interface is canceled out by the time averaging, leaving only
the in-plane tangential momentum, which, in turn, drops off away
from the interface.
