Biomedical Engineering Reference
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in Fig. 7.7(b). Therefore, although the handedness of the geometry
can still be regarded to be an LH pattern, the dependence of the
'gathering'natureofthefieldtothecenterregiononthepolarization
is inverted compared with the case ofan obtuse angle.
This tendency of bent angle dependent concentration or distrib-
utionofthefieldintensitycanbeextendedtopatternsthataremore
complex. For example, if the wings of gammadion are not composed
of segments of straight lines but in smooth curves, the curvature
dependence of the 'focusing' nature of a gammadion-like plasmonic
apertures can be analyzedin a similarmanner.
7.4 Plasmonic Chirality in Complex Chiral Patterns:
Vogel's Spiral Apertures
Let us consider more complex chiral patterns. For this objective,
we choose quasiperiodic aperture patterns following the so-called
Vogel'sspiral[30].TheVogel'sspiraliswellknownasthephyllotaxis
type geometry in nature—the pattern commonly found in the
sunflower head, daisy, pinecone, and pineapple [30]. This pattern is
the optimized arrangement for the seeds or leaves to be exposed to
sunlight or rain. To construct such a pattern, Vogel [30] proposed
placingtheseedsonaFermat'sspiralwithdistancesincreasingwith
aratioofconsecutiveFibonaccinumbers(withagoldenratio).Some
studies on diffracted or scattered light by metallic particles or (non-
metallic)aperturesarrangedbyVogel'sspiralpatternhaveappeared
recently [31-34].
Usually, the position of the
n
-th seed of a Vogel's spiral in polar
coordinates (
r
n
,
θ
n
) can be represented as,
a
√
n
,
r
n
=
(7.5)
θ
n
=
n
α
,
(7.6)
where
a
is a constant scaling factor and
is the divergence angle
usually give
n
with an irrational number related with a golden ratio
ϕ
=
α
1
+
√
5
/
2:
2
.
α
=
2
π/ϕ
(7.7)
