Nanotechnology-Enabled Sensors

6.6 Nanotechnology Enabled Optical Sensors 353
cal nanoparticles, real-world problems can be much more complicated as
nanoparticles can take a large variety of different morphologies. Also the
presence of the supporting substrate, solvent, spacing of particles and aggregations
which dictates the electromagnetic coupling coefficient can
make such calculations more cumbersome.
6.6.3 Sensors based on Plasmon Resonance in Nanoparticles
When a metallic nanoparticle is irradiated with light, the alternating
electric field causes the conduction band electrons to oscillate coherently
as shown in Fig. 6.47. 104 After irradiation, a restoring force is generated
between the electrons and nuclei due to the displacement of the electron
cloud. This results in an oscillation of electron clouds relative to the nucleus.
The oscillation frequency depends on density of electrons, the shape
and distribution of the charge, as well as effective mass of the electron.
Fig. 6.47 The schematic of plasmon oscillation for a sphere, showing the displacement
of the conduction electron charge cloud relative to the nuclei.
The resultant collective oscillation of the electron is referred to as dipole
plasmon resonance of the particle. Higher mode such as quardopole may
also occur when the electron cloud moves in parallel to the electric field.
For calculation of the resonant frequency, it is assumed that the size of
the nanoparticles are less than the wavelength of the impinging light (λ >>
2R, for gold 2R < 25 nm). In this case, the quasi-static electrostatic approximation
can be used.
Let’s assume the electric field vector, E 0 , is:
E = E xˆ
, (6.71)
0
0
where xˆ is the unit vector and E0 is the electric field magnitude in the x direction.
The Laplace equation is: