Biomedical Engineering Reference
In-Depth Information
Figure 7.8
Several types of Vogel's spiral patterns obtained from three
different divergence angles (
α
). The approximate values for the divergence
angles are (a)
α
=
192.92, (b)
α
=
137.51, and (c)
α
=
108.34.
, it becomes possible to obtain various
spiral patterns. Some examples of Vogel's spiral patterns are shown
in Fig. 7.8: The pattern in Fig. 7.8(b) is obtained by adopting the
golden ratio to the divergence angle and is usually referred to as
a golden spi
r
al. The
By changing the value
α
ϕ
values for
al
l the patterns in Fig. 7.8
a
re (a)
1
+
√
3
1
+
√
5
1
+
√
7
ϕ
=
/
2.
Among the patterns shown in Fig. 7.8, the golden spiral pattern
in Fig. 7.8(b) has the most complex chirality. In this pattern, several
winding paths are evident, in which the direction of rotation can
be either CW or CCW. As a consequence, the nature of the response
from the viewpoint of topological charge is very complex. Although
slightly diminished, the pattern in Fig. 7.8(a) exhibits both RH and
LH characteristics in the arrangement of the apertures. Although
the pattern in Fig. 7.8(c) clearly shows an LH arrangement in the
outer region, mixed LH and RH arrangements are observed in the
small region near the center of the pattern. For the structures in
Fig. 7.8(a) and (b), it would be expected that the handedness of
the helicity in the transmitted fields for these patterns cannot be
distinctively identified. However, for the structure in Fig. 7.8(c), a
certain handedness can beobserved.
ForthestructuresinFig.7.8,letusexaminethenumericalresults
obtained from the RCWA simulations. The conditions used for the
simulations are as follows: the incident wavelength, the thickness
of silver metal plate, and diameter of each circular aperture are
assumed to be 750 nm, 200 nm, and 100 nm, respectively. Due
/
2, (b)
ϕ
=
/
2, and(c)
ϕ
=
