“9.61x6.69” b2815 Tissue Engineering and Nanotheranostics
Plasmonic Nanoparticles Application in Biosensor and Bioimaging 155() ()
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42 2^22
12
sca 4 22
1232
,
2
m m
mpεV εεε
σ
λ εεε
−+
=
++
(8)
where V is the particle volume, and εmm=n^2 is the medium’s dielectric
function. Also nR and nI are the real part and imaginary part of metal
dielectric index, respectively.
Else, the particles’ size increase beyond the Rayleigh size limit
(particle diameter >1/20 of incident wavelength), many important
changes will occur in the scattering and absorption properties. These
include new resonance bands that appear in the absorption and scat
tering spectra profile and shift toward longer wavelength, angular
distribution of scattered light intensity behavior maxima and minima,
the scattering crosssection increases slower than r 6 and degree of
polarization decreases, and the scattered light intensity becomes con
centrated in the forward direction. These changes may arise from the
increasing contributions from electric and magnetic multipoles in
addition to the usual electric dipole contribution.
2.2. Gan Theory
Limitations of Mie theory is it that is applicable only to spherical par
ticles. Richard Gans extended Mie’s result to spheroidal particles of
any aspect ratio in the small particle approximation in 1912.^4 He
conclude that the absorption crosssection for a prolate spheroid is
very similar to a sphere, which is shown in Equation (7). This is as
follows:
{
3 2 2(^22)
2
12
1
(^31)
j
abs m
j j
m
j