Biomedical Engineering Reference
In-Depth Information
labeledas(0)inFig.5.2,hasastronglongitudinalcomponent
E
z
and
this mode picks up a circular polarized character as
k
z
increases. It
goes to a quasi-longitudinal mode with a finite frequency at
k
z
=
0
with both the electric fields and magnetic fields essentially parallel
to the helical axis. The inter-helix coupling pushes the longitudinal
mode to higher frequencies. In general, a mode couples to incident
waveof the same handedness as the helix if
n
·
k
z
>
0.
5.2.4
Robustness of the MST Approach for Band Structure
We test our semi-analytic MST approach by comparing with brute
force numerical simulations. For comparison, the total length
L
=
(
p
2
+
(2
π
a
)
2
)
1
/
2
of a unit is fixed. Figure 5.3 shows that the band
structure calculated by our analytical method [colored dots in Fig.
1.3(a), (c), and (e)] is basically the same as those computed by
the commercial package CST Microwave Studio [colored dots in Fig.
1.3(b), (d), and(f)].
5.2.5
Wide Polarization Gap and Negative Refraction at
Low Frequencies
An important feature of the band structure is a wide polarization
gap [shaded in grey in Fig. 5.2(c)] that only allows the passage
of incident waves of the opposite handedness. For example, a RH
helix array has an RCP gap. The gap becomes wider for a higher
helixfillingratio(smaller
d
).Anotherinterestingfeatureoftheband
structure is the emergence of negative group velocity bands at both
sides of the polarization gap, which is different from the previous
theoretical prediction that the negative refraction only happens
above the resonant gap [32]. Both the high frequency (
+
1,F) and
thelowerfrequency(
+
1,S)branchexhibitnegativegroupvelocities.
The (
+
1,S) branch exhibits negative group velocity after reaching a
maximumfrequencythatpinstheloweredgeofthepolarizationgap.
Concomitant with the negative refraction bands in the slow mode,
one can see from Figs. 5.2 and 5.3 that there are band crossings at
the BZ boundary (
k
=
π/
p
) and the degenerate modes are pinned
atfrequencies
f
0,1
and
f
1,2
thatarenearlyindependentofthelattice
constant
p
.Acomparativestudyshowsthatthegenuinelongitudinal
