Chemistry Reference
In-Depth Information
1.3.2 Multilayers
More common 1D photonic structures are multilayer arrangements,
that is, an alternating stacking of thin films with different RI
materials, like the air-chitin multilayers in the wing scales of the
Sunset Moth and many lycaenids (Fig. 1.3b). In fact, multilayered
structures are also used in many technical applications as, for
instance, interference filters and anti-reflection coatings [23]. As
an example, the sparkling, metallic reflections of the elytra of many
jewelled beetles are produced by multilayered stacks of chitin
and melanin. In the Japanese Jewel Beetle,
, a wood-
boring beetle native to Japan (Fig. 1.3c), the sparkling colours are
created by multilayers with varying layer thicknesses [26-28].
The polarisation-dependent and angle-dependent reflectance of
these photonic structures can be well modelled with a gradient RI
approach that accounts for differences in local order [27].
Common multilayers, that is, flat, one-dimensionally stacked
layers of different materials can be treated analytically [23,27]. To
get intuitive insight into the dominant reflected wavelength from a
multilayer stack of layers with alternating thickness
C. fulgidissima
d
and
d
and
1
2
refractive indices
, it is useful to specify the conditions
for constructive interference of the light beams that are reflected
from the individual interfaces of the multilayer stack. Light beams
constructively interfere if the optical path length differences are
equal to an integer multiple of the wavelength, that is
n
and
n
1
2
m
l
,
with
m
integer and positive. Destructive interference occurs when the
optical path length difference is (
m
−
½)
l
. Generally, constructive
l
interference occurs for a wavelength
given by the interference
condition
l
= 2(
n
d
cos
q
+
n
d
cos
q
)/
m
(1.2)
1
1
1
2
2
2
with
are the beam angles with
respect to the normal in media 1 and 2, which follow from Snell's
law [29]. The reflectance and transmittance of a multilayer can be
effectively calculated with a matrix formalism [23,27].
From a material standpoint, an interesting characteristic of
a reflector is the
m
being a positive integer;
q
and
q
1
2
Q
-factor, which is usually defined by the ratio of
peak wavelength
l
of a reflectance spectrum and the peak width
p
(FWHM):
Q
=
l
/
D
l
(1.3)
p
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