Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
Figure 5.5
A slab of helices as a wave plate for transversely propagating
waves.(a)Thebandstructure
ω
(
k
x
,
k
y
=
k
z
=
0)fortransversepropagation
throughhelicesarrangedinasquarearray;(Thephotointheinsetpresents
a photo of the seven-layered sample.) The geometric parameters are the
pitch
p
=
4mm,helixradius
a
=
3mm,wirediameter
δ
=
0.6mm,thelattice
constant
d
=
11mm;Bandstructuresby(b)varyingpitchonlyto
p
=
1mm,
=
and(c)varyinghelixradiusonlyto
a
1mm,allotherparametersarefixed.
handedness. On the contrary, the branch
B
L
has a locally resonant
character with a cut-off frequency at
k
x
=
0, but becomes linear
quicklyatasmallvalueof
k
x
,andjoinsthethirdlowestbranchofthe
same handedness at the BZ boundary without opening a noticeable
gap. The dispersions of the
B
L
and
B
R
branches can be engineered
so that they run parallel to each other in a wide frequency range.
This is because they are controlled by the EM coupling along the
helix (z) axis and the Bragg scattering (in the
xy
plane) among
the helices, respectively, and the two different mechanisms can be
