Biomedical Engineering Reference
In-Depth Information
Figure 11.2
(a) GA spiral array, (b)
τ
spiral array, (c)
μ
spiral array, (d)
π
spiralarray.(e)GAspiralreciprocal;(f)
τ
spiralreciprocalspace;(g)
μ
spiral
reciprocal space; (h)
π
spiral reciprocal space.
11.2.1
Structural Properties of Vogel Spiral Arrays
Vogel's spiral structures have been investigated by mathemati-
cians, botanists, and theoretical biologists [42] in relation to the
geometrical problems of phyllotaxis [43-45], which concerns the
understanding of the spatial arrangements of leaves, bracts, and
florets on plant stems.
AperiodicVogelspiralarraysofnanoparticlesarerapidlyemerg-
ing as a powerful nanophotonics platform with distinctive optical
properties of interest to a number of engineering applications
[36, 46-48]. This fascinating category of deterministic aperiodic
media features circularly symmetric scattering rings in Fourier
space entirely controlled by simple generation rules that induce a
very rich structural complexity. Trevino et al. [37] have recently
described the structure of Vogel spiral arrays of nanoparticles
using multi-fractal geometry and discovered that such structures
feature a degree of local order in between short-range correlated
amorphous/liquid systems and uncorrelated random systems.
Moreover,ithasbeenrecentlydemonstratedthatVogelspiralarrays
of metallic nanoparticles feature distinctive structural resonances
and produce polarization-insensitive, planar light diffraction across
a broad spectral range, referred to as circular light scattering [34].
