Chemistry Reference
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2
2
R
rr rr
rr rr
=
++
+
2
cos
cos
2
f
f
12
23
12 23
(1.1)
2
2
1
+
2
2
12
23
12 23
Where the indices 1, 2 and 3 refer to the incident light medium, the
thin film, and the exiting light medium, respectively, the reflectance
amplitudes at each interface
r
are given by Fresnel coefficients, the
ij
f
p
l
q
l
constant
= (2
/
)
n
d
cos
and the light wavelength is
[22,23].
1
1
Figure 1.3
Exemplary cases of 1D photonic structures. (a,d) On the
wings of the papilionid butterfly
glass
scales exist that are formed by two apposed layers of chitin
[22]. (b,e) The lycaenid
Graphium sarpedon
has wing scales
that carry perforated chitin-air multilayers [19]. Reprinted
from Ref. [25], by permission of the Royal Society. (c,f,g) The
metallic colours of the Japanese Jewel beetle,
Polyommatus icarus
Chrysochroa
fulgidissima
, are due to melanin-chitin multilayers with
different dimensions [26,27]. Bars: (a-c) 1 cm and (d-g)
500 nm.
Interestingly, by measuring the reflectance spectrum of a thin
film under normal light incidence (
q
°
), the thickness of the layer
can be conveniently deduced by plotting the wavenumber (that is
1/
= 0
1
l
) against the extremum number, which can be deduced with the
assumption that the inverse wavelengths have to fit a linear function,
1/
l
=
su
. The slope of the linear function,
s
= 1/(4
nd
) then yields the
u
thickness,
d
[24].
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