Biomedical Engineering Reference
In-Depth Information
can beidentified by its axial ratio
ar
=
E
y
/
iE
z
as
(
i
α/β
+
tan
θ
)
e
−
i
k
·
L
+
(
i
β/α
−
tan
θ
)
−
(
i
+
β/α
tan
θ
)
e
−
i
k
·
L
ar
=
+
(
i
−
α/β
tan
θ
)
,
(5.19)
where
L
is the slab thickness. The transmitted waves will be
transformed to RH or LH circularly polarized (RCP or LCP) at
θ
=
0
or
θ
=
π/
2providedthattheaxialratiosofREPandLEPeigen
st
ates
and the thickness of helix slab satisfy the conditions
α/β
=
√
2
+
1
and
k
·
L
=
π
. The sample shown in the inset of Fig. 5.5(a), which
has seven periods along
x
direction, can realize such a wave plate
with appropriately geometric parameters. Such a helix slab can also
rotate linear polarization in a wide frequency range. If
k
·
L
=
π
and
θ
=±
π/
4, the transmitted wave is still linearly polarized but
with rotated polarization direction along
∓
π/
4. This property is
independent of the axial ratio of elliptical eigenstates. In contrast,
a conventional wave plate cannot implement two different kinds of
polarization transformation simultaneously.
Figure 5.7(b) presents measured and simulated transmission
spectra.AccordingtothecalculatedbandstructureinFig.5.5(a),the
thinnest wave plate for linear-to-circular polarization transforma-
tion(orviceversa)onlyrequiressevenperiodsalongthe
x
direction.
Both the calculations and measurements demonstrate that the
transmitted waves are transformed to RCP or LCP, respectively,
under
y
-polarized or
z
-polarized incidence as shown by the solid
lines and dashed lines in Fig. 1.7(a,b). The calculated/measured
transmittance is above 95%/85% in the range of 3.9
∼
9.6 GHz.
Measured results show that the signal-to-noise ratios (
T
Y,RCP
/
T
Y,LCP
or
T
Z,LCP
/
T
Z,RCP
) are larger than 20dB in the frequency range of
4.1-8.8GHz. We also fabricated the 14-period and21-period sample
slabs with the same geometric parameters in Fig. 5.5(a). Following
the analysis stated above, these two samples shall bring 2
π
and
3
π
phase difference between the LEP and REP states, respectively.
The sample with 14 periods shall not change the polarization of
incident waves, and the 21-period sample behaves like the seven-
period sample. Calculated and measured transmission spectra,
shown in Fig. 1.7(c)-(f), agree with our predictions. Figure 1.7(g,h)
show that the seven-layered sample can rotate the polarization
direction of a linear polarized wave. The polarization angle of linear
