Sensing of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 96

field

time

absorbance

LSP
resonance

electron clouds

l

nanoparticle

Fig. 2.36 The generation mechanism of LSP resonance and a typical absorption spectrum

The LSP resonances of an isolated metallic sphere occur at the frequencies

! l D ! p Œl=.2l C 1/ 1=2 ;

(2.88)

where l D 1;2;3;::: and ! p D .N el e 2 =m" 0 / 1=2 is the plasma frequency correspond-
ing to a concentration N el of free electrons per unit volume with mass m. Because no
particle size enters the above equation, a dielectric permittivity dependence on the
size of various nanomaterials such as spheres, cylinders, etc., is imposed. Although,
strictly speaking, the Mie theory holds for noninteracting spherical nanoparticles
only, it can be generalized to nanomaterials with other shapes (needle-like, elliptical,
cylindrical, etc.), which display a strong dependence of the LSP resonance on size
and show multiple resonances.
As in the case of SPP, an LSP sensor could be a simple glass plate, in which
multiple light reflections occur, covered with gold nanoparticles Hamamoto et al.
2006 . A photodetector which measures the LSP resonance and a CDD camera to
monitor the reflection are other two components necessary for this LSP sensor, as
illustrated in Fig. 2.37 .
Besides single nanoparticles or arrays of nanoparticles organized in various
shapes, metallic nanowires support also LSP. The electromagnetic response of the
nanowire is caused mainly by dipole moments. Assuming that the metallic nanowire
has a length L Š exc , diameter D; and radius R exc , such that R is comparable
to the skin depth in the metal, the polarization around the first LSP resonance
L D LSP =2 induced by the electric field E parallel to the nanowire is

d E D .1=3/ŒLR 2 f./E" m Œ1 C f./" m L 2 ln.1 C L=D/ cos=D 2 ; (2.89)