Chemistry Reference
In-Depth Information
characteristic that most conveniently can be observed to change in re
ection
holograms in the presence of an analyte is the wavelength of the diffracted light.
When illuminated with light of a broad spectral range, a re
fl
fl
ection hologram
diffracts selectively, and operates as a wavelength
filter. The maximum diffraction
ef
es Eq. (
2.1
). A change in either of the
effective refractive index or the lattice spacing causes a change in the wavelength of
the diffracted light (Eq.
2.1
). It is assumed that the hologram has a thick volume and
the angle of observation is constant. In order to quantify how different parameters
in
ciency occurs at a wavelength that satis
fl
uence the Bragg peak position, we differentiate Eq. (
1.1
) using the product rule:
DK ¼
2
D
n
0
K
sin
h þ
2n
0
DK
sin
h þ
2n
0
K
cos
h Dh
ð
2
2
Þ
:
where
are the changes in the position of the Bragg peak,
effective index of refraction, grating period and the Bragg angle, respectively. We
divide both sides of Eq. (
2.2
)by2n
0
K
ʔλ
,
ʔ
n
0
,
ʔʛ
and
ʔʸ
sin
h
:
Dk
2n
0
K
2
D
n
0
K
sin
h
2n
0
DK
sin
h
2n
0
K
cos
hDh
h
¼
h
þ
h
þ
ð
2
3
Þ
:
sin
2n
0
K
sin
2n
0
K
sin
2n
0
K
sin
h
which can be simplified as:
Dk
k
¼
D
n
0
n
0
þ
DK
cos
hDh
sin
K
þ
ð
2
4
Þ
:
h
Dk
k
¼
D
n
0
þ
DK
n
0
K
þ
cot
hDh
ð
2
5
Þ
:
uence of the changes of optical properties on the Bragg
peak can be modelled. Any dimensional change of the polymer matrix in which the
hologram is recorded, such as swelling or shrinking produces a change in the lattice
spacing, and thus alters the spectral response of the hologram (Fig.
2.6
a). A typical
Bragg peak shift of a holographic sensor is shown in Fig.
2.6
b, and the shift as a
function of analyte concentration (Fig.
2.6
c). A simulation assuming that the effective
refractive index and probe angle remain constant reveals that practically achievable
changes in the volume of the polymer matrix could produce large changes in the
wavelength of the Bragg peak (Fig.
2.6
d). A dimensional change of 30 %, which is
normally achieved in an acrylamide-based photopolymer hologram, would produce
over a 100 nm shift depending on the initial Bragg peak wavelength [
80
].
The effective refractive index of the polymer matrix in which the hologram is
recorded can change due to the absorption of the target analyte. Assuming that the
only property that changes the effective refractive index, the resulting change in the
Bragg peak wavelength can be calculated using Eq. (
2.5
) (Fig.
2.6
e). The initial
effective refractive index was 1.5. A signi
Using Eq. (
2.5
), the in
fl
cant change in the effective refractive
index is required in order to obtain a visually observable change in the peak
wavelength (Fig.
2.6
e). For example, an effective refractive index change of
