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Deliverable 5 – Page
D 5:
1
Report on the properties of basic test structures
During the first year of the project we fabricated and characterized many 1- and 2D test structures. The analytical reports on their fabrication and characterization are
described in WP 2, M 2.1 and WP 1, M 1.2 respectively. Here, we present results on the
most important 1-D structures:
1)
10 GHz 1-D composite metamaterials (CMMs). [FORTH, Bilkent]
The in-plane CMM at ~10 GHz was fabricated and tested at FORTH in order to
understand better the interactions of SRRs and wires that lead to the evolution of the LH
peak (see progress report M 1.2). The lattice parameters of the CMM are αx= 5 mm and
αy= 3.63 mm, while the geometrical parameters of the SRR are w= d= t= 0.33 mm and
l= 3 mm (see Figure 1 of WP 1, M 1.2). The SRRs-only structure shows a dip in the
transmission data at ~8.5-10.5 GHz corresponding to the magnetic resonance of the SRR,
while the wires-only structure shows a cutoff frequency at ~10.5 GHz that corresponds to
the plasma frequency of the “thin wires” structure. The CMM shows a transmission peak
between 8.5 and 10 GHz, at almost the same frequency region where the SRR dip
appears. This was originally interpreted as the signature of the appearance of LH
behavior.
We then varied the separation between the boards in order to study how the “LH
peak” evolves. We firstly observed that the “SRR dip” remains almost unaffected by the
variation of the separation between the boards. However, by decreasing the separation
between the boards the dip broadens and a second drop in the transmission appears at
higher frequencies. This second drop could be attributed (see also WP1, Task 1.1:
Modeling) to the electric response of the SRR structure.
The wires-only structures show large dependence on the board separation.
Increasing the board separation leads to a decrease of the characteristic cutoff frequency
of the wires array. Finally, the in-plane CMMs behave remarkably. By increasing the
board separation, the so-called “LH peak” broadens and shifts to lower frequencies. This
behavior could be explained by the fact that the corresponding decrease of the cutoff
frequency of the wires-only array suggests that εeff remains positive down to lower
frequencies. Since both εeff and μeff are then positive, a transmission peak appears.
However, this peak should then be right-handed and not left-handed, as it was initially
thought. We can conclude that the electric response of the CMM should be treated as the
result of the interactions between the SRRs and the wires. The conclusion that a peak in
the transmission data is due to LH could be misleading if these interactions are not taken
into account. It came out from our theoretical simulations that the best model to really
investigate the electric response of the CMM is to close the gaps of the SRR in the CMM
structure. By this way, we expect the magnetic resonance of the SRRs to be switched off
and thus to really observe the electric response of the CMM. The results of this study
shed light on the appearance of different peaks in the transmission data of the in-plane
CMMs (see also WP1, Task 1.1: Modeling).
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The SRRs contribute to the electric response of the CMM, thus shifting the cutoff
frequency of the wires-only array to lower frequencies. It is remarkable that the new
cutoff frequency that corresponds to the CMM (ωp΄ as annotated in FORTH’s theoretical
model) perfectly coincides with the onset of the “LH peak”. In the case of the “closed
SRRs” CMM there is no dip in the transmission data since the magnetic response of the
SRRs is switched off. We strongly believe that the observed peak in the transmission data
of the in-plane CMM is right-handed since εeff and μeff are both positive between 8.5 and
9.5 GHz. The dip at ~9.5-10.5 GHz is due to the magnetic resonance of the SRRs that
renders μeff negative. As εeff remains positive above ωp΄ no transmission of the
electromagnetic waves (EM) is then allowed between 9.5 and 10.5 GHz. Beyond
10.5 GHz μeff switches again to positive values and this results again in the transmission
of the EM waves.
CMMs with circular shaped SRRs alternating with cut-wire arrays yielded higher
transmission values than the ones with square shaped SRRs (see progress report M 1.2).
In contrary to the continuous wire structures that exhibit a stop band with no lower edge,
the cut-wire configuration exhibits a stop band with a well-defined lower edge due to the
discontinuous nature of the wires. The stop band of the discontinuous thin wire structure
extends from 6 GHz to 18 GHz. The reflection measurements indicate that all of the
incident EM waves are reflected back from the structures within the stop band. So, the
structure behaves like a good mirror throughout the stop-band. For the pass-band region,
the measured reflection is near –15 dB. As the transmitted power is also low at these
frequencies, we can conclude that the EM waves cannot efficiently couple into
propagating modes and strongly scatter within the structure. The CMM structure is
constructed by stacking the SRR and wire mediums periodically. There appears a broad
pass band extending from 9.6 to 14.3 GHz. The average transmission within the pass
band is around -4.5 dB, corresponding to a transmission -0.3 dB for each unit cell. This
transmission is significantly higher than the previously reported composite metamaterial
transmission properties. In this frequency range, both effective permeability and
permittivity are negative. Since if only one of the constitutive parameters is negative and
the other is positive we would have evanescent waves rather than propagating waves in
the medium. So, the structure can be named as a double negative metamaterial. However,
we are still working on getting more understanding on the effect of the cut-wires array on
the CMM transmission properties.
2)
10 GHz 2-D composite metamaterials (CMMs). [Bilkent]
For an efficient 2D CMM design, the split-ring resonators and wires are printed
on the same board with off-plane configuration, i.e. SRRs are on one plane of the board
and wires are on the other plane of the board. Spacing between similar elements (SRRSRR or wire-wire) is 9.3 mm. The distance between overlapping SRR and wire is
~1.2 mm (thickness of the board). The boards are then assembled in interlocking slits to
form the 2-D CMM structure. The constructed structure has 15 layers along the
horizontal directions. Transmission analysis presented here is based on the normal
propagation, where one side of the 2-D structure is parallel to the propagation direction.
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We first verify that each of the 1-D CMMs building up the 2-D CMM structure has
indeed a transmission band observed in previous 1-D CMM structures. Each side of the
2-D CMM (denoted here as side “A” and side “B”) has a similar 1-D CMM transmission
spectrum with a definite transmission band between 10.5-12.5 GHz.
From the 2-D CMM transmission spectrum it can be seen that the transmission
level is reduced by about 10 dB in amplitude, and the bandwidth is reduced to ~1 GHz
when compared with the 1-D CMM. We note that in the normal propagation through the
2D CMM structure, one of the 1-D CMMs is facing perpendicular to the propagation
direction. Therefore the propagating field is incident on a large metallic surface, which
might decrease the transmission amplitude considerably. We are currently working on
structures to maximize the transmission amplitude. The next step will be to construct a
2D structure with sufficiently large aspect ratio to perform refraction experiments for
various incident angles of the incoming electromagnetic field.
3)
35 GHz GaAs-based composite metamaterials. [Forth, Bilkent]
Originally, CMMs at 35 GHz were fabricated consisting of 600 μm-thick GaAs
substrates patterned with square SRRs and thin wires on the same plane. Figure 1 shows a
single SRR of the type used for these experiments. The thickness of the deposited metal
(silver or copper) is 1 μm. The parameters of the SRR are t= 20 μm, w= 30 μm, d= 40 μm
and l= 260 μm. After constructing the SRRs and the wires on each GaAs substrate
following conventional fabrication sequence steps applied in lithographic processes, the
substrates were aligned and stacked in a periodical arrangement.
From the transmission spectra of the GaAs-based CMMs it can be seen that the
CMM allows propagation of EM waves in the frequency range 31.8-33.8 GHz. The peak
transmission amplitude of the passband is ~-10 dB. We tried to exploit the speculation
that this transmission peak is due to LH behavior of the GaAs-based CMMs. Therefore,
numerical calculations were performed for the constructed CMMs. The GaAs-based
CMM exhibits a passband between 29-34 GHz, which is in good agreement with the
experimental results. The SRRs-only structure shows a forbidden band between 3134 GHz, which points to negative values of the effective magnetic permeability, μeff, of
the SRR structure. It is, however, still necessary to study the electric response of both the
wires-only structure and the “closed SRR plus wires” structure in order to determine
both ωp and ωp΄ (see also the theoretical model developed at FORTH for the behavior of
the “LH” CMMs, Task 1.1: Modeling). In this way, we shall conclude if the effective
permittivity, εeff, of the CMM is negative in the frequency range < 34 GHz where a peak
in the transmission data for the CMM and a dip in the transmission data for the SRR-only
structure appears. Consequently, it will be clarified if real LH behavior is observed for
the GaAs-based CMM.
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Negative refraction and subwavelength resolution in a two-dimensional
photonic crystal. [Bilkent]
One important application of left-handed materials is their possible use for
constructing a perfect lens. In this part of the report, we explain our experimental and
theoretical work on the negative refraction and subwavelength focusing of
electromagnetic waves in a 2-D PC. Our structure consists of a square array of alumina
rods in air. The frequency range that gives negative refraction extends from 13.10 GHz to
15.44 GHz.
Transmission measurements were performed to verify the predicted negative
refraction behaviour in our structure. The centre of the outgoing Gaussian beam is shifted
towards the left hand side of the center of the incident Gaussian beam, which clearly
corresponds to negative refraction. Negative index of refraction determined from the
experiment is -1.94, which is very close to the theoretical value of -2.06 calculated by the
FDTD method. For comparison purposes, the measurements and the simulations are
repeated with a slab that contains only polystyrene pellets, which has a refractive index of
1.46. The refracted beam is now on the right hand side of the incident beam
corresponding to a positive index of 1.52.
Since we know the optimum frequency for a broad angle negative refraction, we
can use our crystal to test the superlensing effect that was predicted for negative
refractive materials. For this purpose, a PC having 15 layers in the propagation direction
and 21 layers in the lateral direction is used. To show the focusing on the image plane in
the vicinity of the PC, the time averaged intensity distributions along the image plane
with and without the PC are calculated. The full width half maximum (FWHM) of the
measured focused beam is found to be 0.21  , which is in good agreement with the
calculated FWHM. The calculated FWHM of the beam at this plane without the PC is
found to be 5.94  . So, our structure exhibits 25 focusing at this plane with respect to
free space.
Subwavelength resolution using negative refractive materials has been
theoretically suggested by other researchers. We performed the experiments and
simulations with two incoherent point sources 0.7 mm away from the PC, which are
separated by a distance of 6.78 mm and having frequencies 13.698 GHz and 13.608 GHz
respectively. The peaks corresponding to each point source are clearly resolved in both
measurement and simulation. To our knowledge, this is the first experimental observation
of subwavelength resolution of two incoherent sources in negative refractive materials.
The negative refraction effect we have observed depends only on the refractive
index of the dielectric material and the geometrical parameters used in 2D PCs. So, this
effect can also be observed at optical wavelengths where it is possible to obtain similar
refractive indices using transparent semiconductors. This is in contrast to the previously
reported metal-based LHMs. In such structures, increased absorption in metals prohibits
the scaling of these structures to the optical wavelengths. In terms of fabrication, a slab
shaped lens structure is easier to fabricate than a conventional curved shaped lens
structure. So, our slab shaped lens structure can also be used for nanophotonics and
nanooptics applications.
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Photonic crystal based high-gain antenna. [Bilkent]
We have experimentally and theoretically studied the angular distribution of
power emitted from a radiation source embedded inside a photonic crystal. In our
experiments and FDTD calculations we have calculated and measured the angular
distribution of power emitted from a monopole source embedded inside a 2D square
array of cylindrical alumina rods whose radius is 1.55 mm and dielectric constant is 9.61.
The separation between the centers of the rods along the lattice vectors is 1.1 cm. The
monopole source used in the experiments is obtained by removing 0.5 cm of the cladding
from a coaxial cable and leaving the metal part. An HP-8510C network analyzer is used
to excite the monopole source and to measure the power emitted from the monopole
source. We have measured the angular distribution of power at the upper band edge
frequency for various crystal lengths. There is an optimum crystal length, which is found
to be 24 layers in our case. The minimum half power beam width is obtained at 24 layers
and it is found to be 6 degrees. We observed that as the number of layers is increased
from the optimum layer number the change in the far field radiation pattern is not as
strong as the change observed when the layer number is decreased from the optimum
layer number. This can be explained by fact that as we move away from the center
radiator the amplitude of the radiators decrease very rapidly. Hence, as we increase the
number of layers from the optimum layer number the effect of the increasing the number
of radiators will be small compared to the effect of the decreasing the number of
radiators. To our knowledge this is the minimum half power beam width value obtained
by using PCs.
6)
Swiss-Roll structures. [ICSTM2]
The emphasis of the first year’s effort in this workpackage has been to develop,
characterize and use magnetic metamaterials (MM) in MRI. In particular, we have built
an RF “lens” (or, more accurately, a “faceplate”). This has been fully characterized, and
its impact on the RF field distribution determined for the full range of permeability
available from the material. We have used the “lens” to demonstrate geometry preserving
flux ducting in a 0.5 Tesla MRI machine operating at 21.3 MHz. To complement the
work on bulk MMs, we have also started the development of RF components based on
individual MM elements. For example, we are developing a flux compressor based on
loop resonators, the RF equivalent of the SRR used at microwave frequency. This will be
a key element in the development of a MM yoke, which will assist in the delivery or
detection of RF signals.
Transmission measurements
The behaviour of the prism was characterized by measuring the transmitted field
distribution from a dipole source as a function of frequency. A small (3 mm diameter)
loop was used as the source, and was placed at the back of the box containing the prism,
some 5 mm away from the end of the rolls, oriented so that its axis was parallel to the
axis of the Swiss Rolls. Similar loops, oriented to receive the three orthogonal
components of the transmitted field were scanned in the XY and XZ planes of the output
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space. The loops were connected to a network analyser that recorded the signal as a
function of frequency in the range 15 – 35 MHz, thus spanning the magnetically active
frequency range. The data were processed to provide maps of field intensity in the output
planes at each frequency, and hence as a function of the permeability. At both low and
high frequency, where μ ~ 1, a dipole field distribution is observed. On resonance, at 21.3
MHz, an intense central peak is found. Above the resonant frequency, where μ < 0, a
complicated variety of field patterns is observed, that cover the entire surface of the
prism, constrained only by the boundary conditions on its edges. For example, at 24.75
MHz, where μ ~ -1, there is a central peak, surrounded by a ring of intensity of radius ~
80 mm. At 29.7 MHz, where μ ~ 0, the field distribution is quite uniform.
It is clear that a wide variety of field behaviour is obtained, and detailed analysis
is being performed. Meanwhile, a simple examination of the propagation of radiation
through an anisotropic effective medium has been undertaken to understand certain of the
features of these data, and predict aspects of the MM performance so they can be
demonstrated in the MR environment.
Preliminary measurements of flux ducting
Preliminary characterization was carried out using 3 mm diameter loops as both
source and receiver. The source was placed centrally on the outside of the base of the
box, about 5 mm from the base of the Swiss Roll array. The receiver loop was scanned
across the surface of the array, 68 mm above the source, and the signal was measured
using a network analyzer.
The intensities at 15 and 21.3 MHz are shown as the red lines in Fig. 30, as a
function of distance from the center of the slab measured along a diagonal. The material
was then removed, and the scan repeated (at a height of 68 mm. Finally, the receiver was
set at a height of 8 mm, the equivalent height had the 60 mm long Swiss Rolls not been
present, and the scan repeated.
At low frequency (15 MHz), the permeability is slightly elevated (μ = 1.4). The
signal through the material slab lies between the two background scans, and the peak
intensity is 20 dB below the 8 mm reference level. At 21.3 MHz, however, the signal
matches the reference level closely, across the whole extent of the scan, except at the
nearest neighbor positions, where the reference signal passes through a minimum.
Scanning Measurements
To test the two-dimensional imaging performance of the material, we constructed
an antenna from a pair of anti-parallel wires, bent into the shape of the letter M. This
generated a line of magnetic flux, so providing a characteristic field pattern for imaging.
It was placed horizontally, and the material was positioned on top of it.
The transmitted field was measured by scanning a 3 mm diameter loop probe in a
horizontal plane, about 2 mm above the surface of the material. Measurements were
made on a grid, 2 mm square, using a network analyzer. The pattern thus observed at 21.3
MHz is shown in Fig. 33 of the progress report of WP 1-M 1.2, in which the Swiss Roll
structure is overlaid on the field pattern.
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It is clearly shown that the material does indeed act as an image transfer device
for the magnetic field. The shape of the antenna is faithfully reproduced in the output
plane, both in the distribution of the peak intensity, and in the “valleys” that bound the M.
These mimic the minima in the input field pattern either side of the central line of flux.
The upper right arm of the M itself was twisted, so that the flux pattern was launched
with a reduced vertical component. This is reproduced in the weaker intensity observed in
this region.