Biomedical Engineering Reference
In-Depth Information
(
I
0
), where the refractive index of a sample,
n
S
, differs from that of a
blank,
n
R
. At a nonabsorbing wavelength, a change in critical angle,
φ
c
, for internal relection will cause a change in numerical aperture
(
NA
),
40
where
NA
is related to the core RI,
n
1
, and cladding RI,
n
2
, by
the following equation:
2
2 1/2
(5.1)
NA
= −
(
n
n
)
1
2
and the resulting transmittance signal,
T
=
I
S
/
I
0
, is given by
2
I
A
S
S
2
T
==
(5.2)
I
NA
0
0
2 2 1/2
(5.3)
NA
=
(-)
n
n
0
1
0
NA
=
(-)
n
2 2 1/2
n
(5.4)
S
1
S
Refractive index sensing based on Eq. 5.2 has been demons-
trated.
41
However, because of the long penetration depth of the
evanescent wave which leads to lower biosensing sensitivity
42
and
the need for thin monomode waveguides with a large difference
of RI between the waveguide and substrate materials to have high
sensitivity,
43
biosensing applications based on this concept are not
much explored.
At an absorbing wavelength, the resulting absorbance signal,
A
, can be described by a relationship given by Degrandpre and
Burgess:
40
⎛⎞
⎜⎟
2
I
NA
.
S
S
2
A
= γ
-log
L
-log
⎝⎠
(5.5)
I
NA
0
0
where
γ
is the evanescent absorption coeficient and
L
is the sensor
length. For a weakly guiding iber, the evanescent absorption
coeficient is related to the bulk absorption coeficient by the
expression
γ
=
η
.
α
(5.6)
where the power distribution,
η
, is the fraction of total light intensity
in the evanescent ield and
α
is the bulk absorption coeficient of the
NMNP layer.
44
The power distribution can be calculated from
22
k
V
η=
(5.7)
.
2
NA
πρ
(5.8)
V
=
λ
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