Optical Waveguide-Based Biosensors Using Noble Metal Nanoparticles - From Bioimaging to Biosensors: Noble Metal Nanoparticles in Biodetection - page 85

function of the surrounding medium is assumed to be frequency
independent, the dielectric function of metal is complex and
depends on the frequency. If ε 2 is small or weakly dependent on ω ,
the resonance condition is fulilled roughly when ε 1 ( ω ) = −2 ε S , or
λ = ~500 nm for gold in air and λ = ~350 nm for silver in air. 47
Previous study demonstrated that, within a limited RI range, the
absorbance of a NMNP layer is linearly dependent on the RI of the
surrounding medium. 19 Examination of Eq. 5.5 indicates that the
value of the second term is also affected by the medium RI but in a
non-linear fashion and, hence, a plot of absorbance versus medium
RI is expected to be non-linear. However, the linear sensor response
(intensity, transmittance, or absorbance) of the FO-PPR sensor
over a range of medium RI indicates that the change of the sensor
response due to the change of numerical aperture and V-number at
different medium RI is negligible. 23 In other words, the second term
in Eq. 5.5 is negligible when the evanescent absorption coeficient
of the NMNP layer is large enough. As a result, Eq. 5.5 describes
the attenuation caused by the absorption of light in the cladding
and shows a pseudo-Beer's dependence of the absorbance on the
evanescent absorption coeficient of the NMNP layer, which depends
on the length of the iber core modiied with NMNPs, the surface
concentration of NMNPs on the iber core, and the mean extinction
cross-section of the NMNPs. Empirically, we found that the plot of I S
(or I S / I R ) versus n S has a better linear relationship than the plot of
−log( I S / I R ) versus n S , 23 and thus the following expression is used in
subsequent sections:
RS

. .

= = Δ (5.15)
where k ′ and k ″ are constants depending on the optical setup and the
structure of the NMNP layer and Δ n = n S − n R .
It is evidence that afinity-based biosensor technology has
changed the way we view bio-molecular interactions. The ability
to probe complex formation in real time provides detailed insights
into the binding process. In the simplest model for the interaction
of an immobilized species B (a receptor) and a mobile species X
(an analyte), both reactants reversibly form a 1:1 complex BX . The
general equilibrium reaction is
B + X = BX (5.16)
Considering a Langmuir adsorption model and assuming that
the deviation of the equilibrium solution concentration of X from

′ ′′ ′ ′′

I --( -)+ I knn k k nk +

RS