Biomedical Engineering Reference
In-Depth Information
Onthecontrary,increatinganano-amplifier,thegoalistomaximize
the amplification of the scattered field and thus to maximize
Q
scat
.
Consequently,thedesignofsuchanamplifiershouldresultinalarge
localization of the incident field, which could then affect a large
effective cross-section. In Fig. 14.2a and 14.2b, it is clear that the
incident field interacts with the active CNP from distances much
further than its physical extent. This behavior is emphasized in the
localizationofthe incidentpower inthose figures and theenhanced
cross-section results shown in Fig. 14.1a.
Asnotedpreviously,theactiveCNPhasascatteringcross-section
that is effectively much larger than its geometrical size. This also
means that the gain region is effectively larger as well. Since the
excitation field interacts with an effectively larger particle, the total
gain enhancement of the incident fields therefore will be effectively
greater. To account for this behavior, the concept of an effective gain
constant was introduced [17]
, t
hat is, the active CNP acts as though
its gain coe
cient is
κ
=
√
Q
scat
κ
bulk
, which means the required
theoreticalgaincoe
cientisrelatedtotheactualphysicalbulkvalue
as
Q
scat
.
g
bulk
=
g
eff
/
(14.4)
Consideragainthesuper-resonantstateoftheactiveCNPandits
cross-section results shown in Fig. 14.1. The effective and bulk gain
coe
cients versus the theoretical value
κ
are plotted in Fig. 14.4
[17].Recallthatthemaximumofthescatter
in
gcross-sectionoccurs
at 501.9 nm when
κ
=−
0.25 and gives
√
Q
scat
≈
630. To achieve
thisvalueof
κ
,thecorrespondinggainbulkconstantwouldbe
g
eff
=
6.0
×
10
4
cm
−
1
. Although such high gain values have been obtained
with quantum dots, they are not available with more common gain
media such as dyes. This would imply that the realization of these
active CNP designs could be quite di
cult. Nevertheless, as shown
in Fig. 14.4a, the reduction in the bulk values associated with the
effects of the enlarged cross-section are significant. This means
that the required physical bulk gain values are much smaller than
their theoretical values, in agreement with the successful dye-based
experiments [37, 39].
The first experimental NP spaser [39] employed a dye-doped
silica shell surrounding a gold core. This IO configuration is
