Biomedical Engineering Reference
In-Depth Information
scattering, there are no simple mathematic formulae for Tyndall scattering. But for
spherical particles, light scattering can be mathematically treated by Mie theory
[
26
]. Light scattering by spherical particles is commonly called Mie scattering.
Whether light scattering is coherence or incoherence depends on the coherent
length of illumination light and the scatter arrangement as well. For natural light
such as sunlight, its coherent length is about a few microns. When the separations
of scatters are larger than the coherent length, it can be considered as incoherent
scattering. In contrast, if the separations of scatters are smaller than the coherent
length, light scattering is coherent since scattered light may interfere with each other.
8.3.4
The Combination
For thin films, multilayers, and diffraction gratings, their coloration can be under-
stood simply by interference or diffraction. In the biological world, there exist many
nontrivial photonic structures, e.g., 2D and 3D periodic photonic structures [
1
-
9
].
Their structural coloration cannot be simply interpreted by interference, diffraction,
or scattering alone. Instead, it results from the combination of interference, diffrac-
tion, and scattering.
Periodic photonic structures, those with a spatially periodical variation of
refractive index, are also called photonic crystals [
27
-
29
]. For light interactions with
photonic crystals, there may exist scattering by constituent units, diffraction due to
the periodic arrangement, and interference among scattered or diffracted light, lead-
ing to complicated photonic band structures [
29
], analogous to those for electrons
propagating in crystalline solids. Between photonic bands, there may exist a partial
(along a certain direction) or complete (along all directions) photonic bandgap.
2
For complicated or composite photonic structures, their color production can be
generally interpreted by the combination of interference, diffraction, and scattering.
The understandings are usually conceptual. This is because the interplay among
interference, diffraction, and scattering may considerably complicate our quanti-
tative analyses. It may even result in new optical phenomena. To understand in a
quantitative way, numerical simulations by solving Maxwell's equations are needed.
8.4
Methodology for Studying Natural Photonic Structures
Optical, spectral, and structural information are vital for our understandings of
structural coloration. Consequently, both macroscopic and microscopic observa-
tions on structural colors are essential. To establish the relations between structural
2
In natural photonic structures, there exist only partial photonic band gaps because refractive-index
contrasts among constituent materials are not big enough to open up complete photonic band gaps.
