Biomedical Engineering Reference
In-Depth Information
To explore the origin of coloration in the feather barbules, the photonic band
structure of an infinite 2D photonic crystal was calculated by a PWE method, shown
in Fig.
8.30
c. The structural parameters for this photonic crystal were taken from the
measurements, i.e.,
r
rod
=a D 0:4
and
r
air
=a D 0:25
,where
r
rod
and
r
air
are the radii
of the melanin rods and air holes, respectively, and
a
is the lattice constant. The
refractive indices of keratin and melanin were taken to be 1.54 and 2.0, respectively.
This 2D photonic crystal does not exhibit a complete photonic bandgap. However,
a partial photonic bandgap for both polarizations exists along the
X
direction.
It is noted that the photonic band structure for the two polarizations shows a small
difference at low frequencies (corresponding to the visible wavelengths), and it
differs at high frequencies (corresponding to the UV wavelengths or below). The
difference between the midgap frequencies for the two polarizations is rather small.
This indicates that the peacock feather barbules exhibit small polarization effects
in coloration. Strong reflections are expected for frequencies within the partial
photonic bandgap along the
X
direction, responsible for barbule coloration. It
should be mentioned that the partial photonic bandgap shifts to a higher frequency
range with the increasing angle of incidence, leading to iridescence.
For blue, green, and yellow barbules, their colors stem from the partial photonic
bandgap of the 2D photonic crystal in the cortex. This can be confirmed by the
calculated reflection spectra of generic 2D photonic crystals with a finite number of
periods by a TMM, shown in Fig.
8.30
d. The calculated reflection spectra correctly
reproduce the main features of the experiments.
Note that brown is a mixed color. The partial photonic bandgap can only cause
a reflection peak covering green, yellow, orange to red wavelengths. Simulations
[
124
,
125
] revealed that the Fabry-Perot interference plays an important role in
the color production of brown barbules. For any finite photonic crystal, Fabry-
Perot interference should exist owing to the interference from their two surfaces,
leading to oscillating side peaks on the two sides of the reflection peak produced by
the partial photonic bandgap. For a finite photonic crystal with a large number of
periods, the reflection peak produced by the partial photonic bandgap is dominant,
while the contribution of the side peaks to coloration by Fabry-Perot interference is
negligible. However, with the decreasing number of periods, side peaks also play a
role in coloration, giving rise to an additional color. For brown barbules, the number
of periods is the least. As a result, the Fabry-Perot interference leads to an additional
blue reflection peak which is comparable to the main peak from the partial photonic
bandgap, eventually giving rise to a structural brown color by color mixing. It was
found [
125
] that other factors such as the interdistance and missing air holes between
the two melanin layers nearest to the cortex surface are important in the production
of the structural brown color.
Peacock feathers take advantage of a 2D photonic crystal in the barbule cortex
for coloration. The strategies for diversified color production are very ingenious
and rather simple, i.e., by means of the variation of the lattice constant and the
number of periods. Varying the lattice constant will shift the midgap frequency
of the partial photonic bandgap, leading to different colors. The reduction in the
number of periods may cause an additional color, resulting in mixed coloration. By
the two strategies, diversified structural colors can be produced.
