Nanotechnology-Enabled Sensors

3.3 Optical Waveguide based Transducers 69
As the propagating waves are evanescent in z direction, their amplitude
decays exponentially when entering the sample media. The decay is described
by the penetration depth, Δz, into the sample media which can be
defined as 3 :
=
2
z
λ
π
1
2 2 −
2
( − ) n N
Δ C
, (3.8)
where nC is the refractive index of sample media (Fig. 3.5). For a guiding
mode to exist, the refractive index of the waveguide must be larger than
those of the substrate and the sample medium. In such a case, the effective
refractive index, N, is larger than the refractive indices of the substrate and
sample media, yet smaller than that of the waveguide. From the penetration
depth, the field distribution in the z direction may be defined with:
u
v
m
m
m
−z
Δz
( z)
= u ( 0)
e , (3.9)
m
−z
Δz
( z)
= v ( 0)
e . (3.10)
If the refractive index of the sample media changes, then the penetration
depth will also change. This in turn results in a measurable change in the
field distribution, and is the basis of affinity sensing with optical
waveguides.
When fabricating nanotechnology enabled sensors based on optical
waveguide transducers, materials are chosen such that the penetration
depth generally lies between a few to several hundred nanometers. These
penetration depths are utilized for detecting analyte molecules whose dimensions
are in the order of nanometers. Such analyte materials include
proteins and DNA strands.
3.3.2 Sensitivity of Optical Waveguides
The sensitivity of an optical waveguide based sensor strongly depends
on the interaction between the measurand and the surface confined guided
mode in the sample media. Analyte molecules may diffuse into or out of
the evanescent region, they may become immobilize onto the boundary, or
they may move along the surface by convection. Each of these interactions
can change the effective refractive index, and as a result, produce a response.
The change in effective refractive index can be calculated using
perturbation theory. For TM modes, the result is expressed as 3 :