Biomedical Engineering Reference
In-Depth Information
10
2
10
1
10
0
10
−2
10
−1
a/
λ
0
Figure 12.1
The dependence of the square of the normalized propagation
constant squared (i.e., the effective index squared) on the wire radius. For
gold at free-space wavelength of 800 nm, the value
24 was used
(ignoring the imaginary part, which is around 1.6), and for water, the value
d
m
=−
=
1.7689 was used. The two limiting cases are for a flat surface (thin
line) and for an infinitessimal wire (dashed line) are shown.
group velocity decrease with wire radius, the emission rate into the
plasmonicwirescalesas
a
−
3
.Asthedampingratescalesasthethird
poweroftheinversedistancebetweentheemitterandthewire,itis
possible to have greatly enhanced emission into the plasmon mode
without quenching out the emitter (Chang et al., 2006).
12.2.2
Localized Surface Plasmons
We now consider a cylindrical wire of finite extent. The surface
waves on such a wire will reflect at the ends, due to impedance
andmode-shapemismatch.ThisallowsforFabry-Perotresonances,
or standing waves, to be set up along the wire. The Fabry-Perot
condition forthe resonance along the wire is givenby:
β
l
+
φ
=
m
π
(12.4)
