Biomedical Engineering Reference
In-Depth Information
radius
a
, the geometrical cross-section is
σ
geom
=
π
a
2
. In particular,
the scattering, absorption and extinction cross-sections (
σ
s), and
e
ciencies (
Q
s) are given by the expressions:
σ
scat
=
P
scat
/
I
inc
=
Q
scat
P
0
σ
abs
=
P
abs
/
I
inc
=
Q
abs
P
0
σ
ext
=
P
ext
/
I
inc
=
Q
ext
P
0
(14.3)
The scattering, extinction, and absorption cross-sections for
a spherical CNP are obtained with Mie theory multipole-based
series expansions [17, 45]. The scattering (absorption) e
ciency of
the particle relates the amount of power scattered (absorbed) by
the scatterer to the amount of power incident upon its surface. The
extinctioncross-sectionindicateshowmuchpowerisremovedfrom
the incident field. The corresponding e
ciencies are dimensionless
quantities relating the effective cross-sections to the geometrical
cross-section of the scatterer. Clearly, the extinction e
ciency can
be written as the sum of the absorption and scattering e
ciencies:
Q
ext
=
Q
abs
. Note that for active scatterers, that is, scatterers
containing a gain medium, it is possible for the absorbed power,
P
abs
, to become negative leading to a negative value for
Q
abs
. This
behaviorindicatesthatfieldsarebeingamplifiedinsidetheparticle.
If the negative absorption becomes greater than the scattering
losses, the extinction cross-section becomes negative, that is,
Q
ext
<
0. This means the scattering losses have been overcome, and the
incident field will then be amplified. To maximize the extinction
e
ciency, it is necessary to design a particle that strongly interacts
electromagnetically with the incident field, that is, to design a
particle with a large effectivescattering cross-section.
A size and wavelength-dependent permittivity model has been
used to determine the material properties of gold, Au, and silver,
Ag [11], for all examples presented later. These Au and Ag models
recoverthemeasuredresultsgiven,forexample,in[46].Theoriginal
gainstudies[11]consideredathree-levelrareearthandacanonical
gain model. The Mie theory model that underlies our analysis
starts conceptually with the assumption that the gain medium
is describable at least by a three-level system. A pump signal is
assumed that drives the gain medium into its excited state. The
desired excitation frequency for either a plane wave or an EHD
Q
scat
+
