Biomedical Engineering Reference
In-Depth Information
Figure 11.8
Statistical distribution first neighbor distances in irrational-
angle spiral structures and corresponding spatial Delaunay triangulation
maps for (a,e) GA spiral array, (b,f)
τ
spiral array, (c,g)
μ
spiral array, and
(d,h)
spiral array. Values represent the distance between neighboring
particles
d
normalized to the most probable value
d
o
, obtained by
(increasing numerical values from blue to red colors). The vertical axis
displays the fraction of
d
in the total distribution.
π
In the next section, we will focus on the application of aperiodic
spiral plasmonic arrays for the generation of structured light that
encodes numerical sequences in the OAM azimuthal spectrum.
11.3 Engineering Orbital Angular Momentum of Light
It was recently discovered that Vogel spiral arrays of metallic
nanoparticles, when illuminated by optical beams, give rise to
diffracted radiation carrying very complex OAM patterns [34, 51,
52]. Recently, Dal Negro et al. [51] developed an analytical model
that captured the Fourier-Hankel spectral properties of arbitrary
Vogel spiral arrays in closed form solution, thus providing the
toolsets necessary to engineer complex OAM states in the far-field
diffraction regions. Within the framework of scalar Fourier optics,
it was shown that the Fourier spectrum (i.e., Fraunhofer diffraction
pattern) ofVogel spirals is described by the complex sum [51]:
N
e
j
2
π
√
na
0
ν
r
cos(
ν
θ
−
n
α
)
E
∞
(
ν
r
,
ν
θ
)
=
E
0
(11.4)
=
n
1
