Photonic Structures in the Animal Kingdom: Valuable Inspirations for Biomimetic Applications - Biomimetic Architectures by Plasma Processing - page 17

For these topologically complex photonic structures, analytical
descriptions, as present for the thin films or multilayer structures,
do not exist. Fortunately, in the recent decades computational
approaches have been developed for studying the wave propagation
in complex optical systems. These computational programs calculate
the propagation of the electromagnetic fields in a virtual “simulation
box” that contains the photonic structure by solving the (differential)
Maxwell equations [5,54]. Thus, the photonic bandgap diagrams
(PBD, also called photonic band structures) can be computed.
Figure 1.9d shows a PBD for a diamond-type photonic crystal
and gives the range of allowed frequencies in the crystal. If for a
given crystal orientation, determined by the position within the
irreducible first Brillouin zone of the crystal [5,55], no bands overlap
in k-space, a photonic bandgap is opened. Light with frequencies
within the frequency range of the bandgap cannot propagate inside
the photonic structure and are consequently reflected. Thus, the
photonic bandgap size and its position in space are crucial for the
photonic properties of a photonic crystal. Two parameters are the
central descriptors for the optical behaviour of a photonic crystal,
that is, the (cubic) unit cell size

, determining the length scale of the
reflected wavelength and the material filling fraction

a

[56].
A photonic bandgap is called a complete bandgap when it exists
over all possible orientations of a crystal for any polarisation of
incident light; it is called a partial bandgap or pseudogap when the
range of forbidden wavelengths changes with the orientation of the
crystal. In the biological photonic crystals, the RI contrast is usually
too low to form complete photonic bandgaps, since a complete
bandgap for a diamond-type photonic crystal only opens up for a RI
contrast of minimally 2 [46,57].
Nevertheless and especially due to the too small RI contrast,
biological photonic structures feature remarkable iridescences. The
iridescence of a photonic crystal can be most adequately described
by the concept of the first Brillouin zone, which contains the
underlying local symmetries of the structure and the characteristic
length scales that cause iridescence. By investigating the diamond-
type photonic crystals of the diamond weevil,

f

, with the
ISM, the iridescence created by a partial bandgap material could be
visualised for the first time (see Figs. 1.9b,c and [46]). The ISM thus

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