Biomedical Engineering Reference
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believe that this effect indicates a distinctive self-imaging behavior
of Vogel spirals, which is currently under investigation. We recall
that full image reconstruction will happen at a distance
L
from
a coherently illuminated array with discrete spatial frequencies
locatedinreciprocalspaceatringsofradii
ρ
2
2
−
(
m
/
L
)
2
where
=
1
/λ
m
is an integer such that 0
[73]. Self-imaging effects
have been vastly investigated in the context of periodic structures
(e.g., the Talbot effect) as well as in quasi-periodic Penrose arrays,
where it has been recently shown that they can focus light into
sub-wavelength spots in the far-field without contributions from
evanescent fields [74-76]. However, to the best of our knowledge,
self-imaging effects in aperiodic media that lack diffraction peaks
have never been reported.
In summary, the results shown in Fig. 11.10 indicate that the
peculiar diffractive behavior of the
α
1
spiral results from the coher-
ent interplay of two well-separated spatial regions of the structure
with very dissimilar structural order: on one side the disordered
central region of the spiral that diffracts wavelets isotropically in
any direction, and on the other side the surrounding region of the
structure with well-defined chirality defined by the CCW rotation
of the parastichies arms. In this region, the radiated optical power
from each scatterer couples into orthogonal parastichies arms, thus
“inverting” the spatial pattern at intermediate self-imaging planes
of the array. The near-field coupling and propagation behavior of
electromagnetic energy scattered at 1.56
μ
m by arrays of silicon
nitride nanopillars with Vogel spiral geometry has been recently
investigatedexperimentallyinRef.[65].Byusingscanningnear-field
optical microscopy in partnership with full-vector finite difference
time domain numerical simulations, Caselli et al. [65] demonstrate
a characteristic rotation of the scattered field pattern by a Vogel
spiral consistent with net transfer of OAM in the Fresnel zone,
within few micrometres from the plane of the array. We believe that
the unique interplay between aperiodic order and chiral structures
such as the investigated
α
1
spiral can provide novel opportunities
for the manipulation of sub-wavelength optical fields and disclose
richer scenarios for the engineering of focusing and self-imaging
phenomena in nanophotonics.
≤
m
≤
L
/λ
