Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected]. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. paper submitted to IEEE Trans. on Antennas and Propagation 1 Abstract— This paper reports experimental results which demonstrate the possibility to synthesize focused near-fields from a planar printed circuit which is fed with a simple coaxial probe. A prototype operating at 10GHz has been manufactured and tested. As predicted by the theory described in the first part of this paper, high 75% focusing efficiency of circularly polarized fields is obtained as a result of the proper modulation of the dimensions of the Archimedean-shaped printed slot. The designed coaxial feeding provides good matching (below -10dB) in the entire frequency band. Finally, the scanning of the focal length as a function of the frequency is described in this paper, showing measured results and accurate theoretical explanation based on the frequency dispersion of the tapered leaky mode. This phenomenon is general for this type of two dimensional leaky- wave lenses, and might find many applications in imaging, sensing and heating. Index Terms— Microwave lens, electromagnetic focusing, leaky waves, surface waves, holographic antennas, printed circuits. I. INTRODUCTION ICROWAVE lenses were first proposed in 1960’s to focus the electromagnetic energy in the near-field (Fresnel) region [1], and their properties were studied in detail in the 1980’s [2-4]. The first designs were based on dielectric lenses and metallic reflectors, which are externally illuminated by a space plane-wave which is focused at the desired focal point due to the three-dimensional shape of the focusing body (normally parabolic or hyperbolic geometries) by virtue of Geometric Optics [5]. Phased arrays of horns [3, 6], patches [7-10], and printed dipole antennas [11], have Manuscript received June 15, 2012. This work has been supported by Spanish National project TEC2010-21520-C04-04 and AYA2010-10054-E, European FEDER funding, and program "Ramon y Cajal" RYC-2009-04924. D. Blanco and E. Rajo-Iglesias is with the Department of Communications and Signal Theory, Carlos III University, Spain ([email protected]). J.L. Gómez-Tornero is with the Department of Communication and Information Technologies, Universidad Politécnica de Cartagena, Cartagena 30202 Spain (e-mail: [email protected]). N. Llombart is with the Optics Department, Universidad Complutense de Madrid, Spain ([email protected]) also been proposed in order to focus the electromagnetic fields in the near-field zone. In these cases, the array feeding network is responsible to excite each element of the array with the requested quadratic-phase and amplitude illumination to synthesize the desired focusing pattern. Similarly, an externally-fed printed reflectarray has been recently proposed to focus in the near-field [12]. In any case, printed-circuit array configurations [7-12] offer lightweight, compact, low-profile, cheap solutions when compared to bulky three-dimensional shaped bodies used for dielectric and metallic microwave lenses. One step forward in the design of electrically-large printed- circuit near-field microwave lenses is the elimination of the complicated feeding network associated to phased arrays with multiple radiating elements [7-11], and keeping an integrated feeding mechanism (in opposition to reflectarrays which are externally fed [12]). In this sense, leaky-wave antennas (LWAs) offer an integrated and simple mechanism to illuminate large radiating areas by exciting a leaky mode [13]. Ohtera was the first one to propose the use of a curved one- dimensional (1D) LWAs to obtain focused near-fields [14], and Burghignoli et al. theoretically demonstrated in [15] that a leaky wave propagating along a 1D rectilinear structure can be properly modulated (tapered) to focus the radiated fields, avoiding the complicated bending of the radiator. The first practical designs of rectilinear modulated 1D leaky-wave lenses (LWL) were presented in [16] using a dielectric waveguide loaded with a tapered slot. In [17], a parallel-plate waveguide loaded with an inductive sheet formed by microstrip lines was controlled with FETs in order to electronically steer the focal region. Nevertheless, all the aforementioned LWL designs [14-17] are limited to one-dimensional leaky lines, which are able to focus only in their longitudinal plane, thus providing 2D focusing patterns which are sharp in the longitudinal plane and wide in the transverse direction. However, three-dimensional focusing patterns are requested in most practical applications for medicine [6], industry [7], and imaging/sensing [8-12]. Recently, cylindrical leaky waves have been proposed to Holographic Surface Leaky-Wave Lenses with Circularly-Polarized Focused Near-Fields. Part II: Experiments and Description of Frequency Steering of Focal Length Darwin Blanco, José Luis Gómez-Tornero, Member, IEEE, Eva Rajo-Iglesias, Senior Member, IEEE, and Nuria Llombart, Member, IEEE. M
Transcript
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paper submitted to IEEE Trans. on Antennas and Propagation
1
Abstract— This paper reports experimental results which
demonstrate the possibility to synthesize focused near-fields from
a planar printed circuit which is fed with a simple coaxial probe.
A prototype operating at 10GHz has been manufactured and
tested. As predicted by the theory described in the first part of
this paper, high 75% focusing efficiency of circularly polarized
fields is obtained as a result of the proper modulation of the
dimensions of the Archimedean-shaped printed slot. The designed
coaxial feeding provides good matching (below -10dB) in the
entire frequency band. Finally, the scanning of the focal length as
a function of the frequency is described in this paper, showing
measured results and accurate theoretical explanation based on
the frequency dispersion of the tapered leaky mode. This
phenomenon is general for this type of two dimensional leaky-
wave lenses, and might find many applications in imaging, sensing
and heating.
Index Terms— Microwave lens, electromagnetic focusing,
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paper submitted to IEEE Trans. on Antennas and Propagation
2
generate 3D focused Bessel beams [19],[20]. However, those
results did not make use of tapered leaky modes because the
emphasis was not on near-field focusing efficiency. In the first
part of this paper [18], we presented the design of a two-
dimensional leaky lens which provides the interesting features
of efficient three-dimensional focusing, printed-circuit
technology, low-profile, and integrated simple feeding. The
lens is based on an Archimedean-spiral-shaped double-slot
printed on a double grounded substrate, which resembles an
annular slot antenna [21] with two continuous slots placed at a
distance of SW/4 from each other to minimize multiple
reflections.
This paper reports experiments performed on a fabricated
prototype, and it is distributed as follows. Section II describes
the feeding circuit and presents measured focusing pattern at
the design frequency of 10GHz. Section III is devoted to
describe the important ability of this type of device to steer the
focal distance as frequency is shifted. This phenomenon is
inherent to any LWL [16], and this paper demonstrates that a
similar phenomenon occurs for 3D focusing patterns.
Moreover, an accurate frequency dispersion theory allows to
efficiently predict this interesting result which might have
potential application in imaging, sensing and heating.
Fig. 1. Photograph of fabricated holographic leaky-wave lens (LWL) in
printed-slot technology.
II. EXPERIMENTAL RESULTS AT THE DESIGN FREQUENCY
Figure 1 shows a picture of the fabricated prototype. The
modulated dimensions (position P and width W) of the printed
slots were designed in the first part of this paper [18]. Rogers
Duroid 5880 substrate with thickness h=3.175mm, r=2.2, and
tan=0.002, and with a total size of 20cm x 20cm (6.670 x
6.670 at 10GHz) has been used.
A. Design of Integrated Coaxial Feeding
A key feature of the novel planar lens is that it affords a
simple single-source integrated in the supporting substrate, in
opposition to more complicated feeding networks used in
phased-array printed lenses [7-11], or external spherical-wave
feeders needed in reflectarrays [12]. The scheme of the vertical
coaxial feeding, depicted in the inset of Fig.2 together with its
main dimensions, is typical of radial-line slot antennas (RLSA)
[22-23], commonly used to create low-cost large directive
antennas. This circuit is located at the lens center, and a SMA
connector at the bottom ground plane provides the interface to
RF cables as shown in the pictures of Fig.2. The probe
penetration A has been tuned to optimize the input matching,
obtaining S11<-10dB in 9GHz-11GHz bandwidth as shown by
CST simulations and measurements in Fig.3. The
discrepancies are due to tolerances and errors in the
adjustment of the aforementioned probe depth A.
Fig. 2. Feeding coaxial probe, illustrating the main dimensions.
9 9.5 10 10.5 11-25
-20
-15
-10
-5
0
f(GHz)
CST
ExperimentsS
11(dB)
Fig. 3. Comparison between simulated and experimental input matching of
the fabricated holographic leaky-wave lens.
B. Measured Near Fields
A near-field measurement set-up has been prepared using
foam substrate to support a field probe as shown in Fig.4. The
orientation of this probe is varied to measure the different
components of the electric field along the main axes of the
lens. Several probe dimensions have been studied in order to
minimize its impact on the measured field. It has been found
out that the most critical parameter is the length of the probe
which has to be minimized. The optimized probe length is
6mm and the coaxial diameter 5mm, both small in terms of the
wavelength. Therefore a small perturbation of the antenna
near-field is expected. The scanning range is around
7=21cm in both axial and transverse planes. The scanning
step, 5mm, is chosen to be similar to the probe length.
Figure 5 compares the measured and simulated x- and y-
near-fields at the design frequency of 10GHz. The axial cut is
represented in Fig.5-a, showing that the measured focal depth
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3
and position of the focus perfectly match the theoretical
results, and that both components are well balanced. The
transverse cut in the x-axis (=0º) at the focal height
z=139mm (4.630) is plotted in Fig.5-b. Very good agreement
between measured and theoretical near fields is shown for the
focal widths and sidelobe levels. Thus, these results
experimentally confirm the high focusing efficiency of the
designed prototype. Note that it is not possible to measure the
relative phase difference between different field components
necessary to plot the fields in circular polarization, due to the
fact that we need to manually rotate the probe.
Fig.4. Scheme of the near-field measurement set-up.
2 3 4 5 6 7 8 9 10-15
-10
-6
-3
0
z/0
Ex CST
Ey CST
Ex Experiments
Ey Experiments
a)
dB
-3 -2 -1 0 1 2 3-25
-20
-15
-10
-6
-3
0
x/0
Ex CST
Ey CST
Ex Experiments
Ey Experiments
b)
dB
Fig. 5. Comparison between simulated and measured near-field focusing
patterns of the fabricated holographic leaky-wave lens at 10GHz a) Axial cut
along z-axis (x=y=0) b) Transverse cut along x-axis (z=139mm).
III. DESCRIPTION OF FREQUENCY STEERING OF THE FOCUS
Leaky-wave antennas are known to be strongly frequency
dispersive: this behavior has been classically used in 1D leaky
lines to scan a fan beam in the far field [24]. Recently, it was
theoretically demonstrated in [16] that a 1D leaky lens has the
equivalent property in the near-field, resulting in the shifting of
the position of the focus as the frequency is varied. However,
the case of 1D leaky-line sources is quite different to the
scenario studied here of 2D leaky apertures. 2D leaky-wave
antennas are normally operated at the frequency which
satisfies the splitting-condition to radiate a pencil beam at
broadside [24-27]. For lower frequencies the gain at broadside
drops as a consequence of the cutoff regime of the leaky wave,
while for higher frequencies the pencil beam transforms into a
conical beam [24,25]. In this paper we study for the first time
the behavior with frequency for a focused 2D leaky aperture,
showing that the focal length can be steered up to a limit as the
frequency of the signal is shifted. Theoretical results based on
the dispersion of the modulated cylindrical leaky-wave
accurately predict the performance of the holographic lens
with frequency, which is validated with experiments.
A. Frequency Response of Focused Cylindrical Leaky Wave
In [18], it was demonstrated that a single modulated leaky
wave can be used to represent the field radiated by the
holographic lens antenna. Therefore, by studying the variation
of the cylindrical leaky-wave complex wavenumber along the
lens radial distance versus frequency, we can characterize the
frequency steering of the focal length. The designed modulated
dimensions of the printed-slot dimensions W(), P() are used
as fixed parameters in a modal solver [28], which provides the
phase and attenuation terms of the leaky wave as a function of
frequency, and for each radial position of the slot unit-cell:
),(),(),( fjffk
(1)
Particularly, the modulated leakage angle RAD, has a
strong dependence with the modulated distance between slots
P() and with frequency, which can be expressed as:
)(
/),(),(),(sin
0
00
P
fc
k
f
k
ff
SW
RAD (2)
The term c0/fP in (2) (where c0 is the speed of light in
vacuum) describes a variation in the resulting scanning angle
from backward-endfire to broadside as frequency is increased,
as it customarily happens in frequency-scanning antennas [24].
This can be seen in Fig.6, where the dispersion of the
modulated cylindrical leaky wave as a function of the radial
distance of the designed lens is represented for five different
frequencies in the 9-11GHz band. At the design frequency of
10GHz, it is shown in Fig.6a that RAD() follows the specified
variation from RAD=-5º at =R0=7.5mm to RAD=-30º at the
lens edge position =97.5mm. For lower frequencies, the
modulated RAD() is shifted to more negative values, reaching
a variation from -15º to -50º at 9GHz. On the contrary, higher
frequencies tilt the local scanning angles towards broadside, as
can be seen at 11GHz with a variation of RAD from 0º to -15º.
Actually, the central region of the lens is in the stopband
regime at this frequency of 11GHz, and therefore this central
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4
zone does not contribute to radiation. This stopband regime is
characterized by null values of RAD and a sudden rise in /k0
[24,26], as it can be observed in Fig.6 at 11GHz in the section
contained between =0mm and =40mm.
Nevertheless, the dispersion with frequency suffered by the
locally-modulated radiating angle shown in Fig.6a, translates
in a displacement of the focal length as qualitatively illustrated
in Fig.7. For higher frequencies the emerging rays tend to
broadside, thus converging at a higher distance. Besides, it is
expected that the focal depth noticeably increases for higher
frequencies as a result of the increased focal height [1-4], as
also illustrated in Fig.7.
0 20 40 60 80 100
0
-10º
-20º
-30º
-40º
-50º
(mm)
RAD
()
a)
10.0 GHz
9.5 GHz
9.0 GHz
10.5 GHz
11.0 GHz
0 20 40 60 80 1000
0.02
0.04
0.06
0.08
0.1
(mm)b)
10.0 GHz
/k0()
11.0 GHz
10.5 GHz
9.5 GHz
9.0 GHz
Fig. 6. Dispersion with frequency of the tapered cylindrical leaky wave along
the radial distance of the designed holographic lens.
200 100 0 100 200
0
75
150
225
300
375
z (
mm
)
(mm)
f=90GHz
f=10 GHz
f=11 GHz
f=9 GHz
Fig. 7. Scheme illustrating the dispersion of the focal region with frequency.
To accurately compute the near-fields created by the
designed lens at any frequency, one can modify the analysis
theory presented in [18], obtaining the following complex
aperture fields as a function of frequency:
ˆ),,(),,(),(),,(
fjfjAP
LW eefAfE (3)
)(1
),(),(),,(
df
ef
fA (4)
)(1
),(),,( dff (5)
)(
)(
)(2)()(),(
00
1f
f
f
Rff
SW
SW
SW
SW (6)
Where the term A describes the amplitude modulation of the
aperture (due to the tapering of the leaky-phase constant),
stands for the phase modulation due to the tapering of the
leakage rate, and the term describes the azimuthal phase-
shift variation created by the spiral shape. As an example,
Fig.8 shows the variation with frequency of the amplitude and
phase terms A and for =0º (x-axis), when introducing in (4)
and (5) the tapered leaky-mode dispersion behavior shown in
Fig.6 for the five studied frequencies.
Already by looking to the frequency variation of these
terms, one can study the impact of the frequency on the near-
fields. This theory is particularly suited to analyze large
antennas as a function of the frequencies, where direct full-
wave simulations become prohibitive. As shown in Fig.8a, the
aperture phase has a quadratic-type parabolic response
which eccentricity decreases for higher frequencies (which will
result in a higher focal point). The amplitude of the aperture
fields in Fig,8b also changes as frequency is varied, observing
at higher frequencies the non-illuminated central region due to
the aforementioned stopband.
0 20 40 60 80 1000
2
4
6
8
10
(mm)a)
11.0 GHz
9.0 GHz
9.5 GHz
10.0 GHz
10.5 GHz
()
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
(mm)b)
10.5 GHz
10.0 GHz
9.0 GHz
9.5 GHz
11.0 GHz
A()
Fig. 8. Dispersion with frequency of the aperture fields along the radial
distance for =0º, in the designed holographic lens.
The theoretical near fields created by the focused aperture at
any frequency can be computed using a Green’s function
formalism. Figure 9 shows the intensity of the fields at the zy
plane, and for four different frequencies. The focused region
shifts to higher heights as frequency moves from 9GHz to
11GHz, and it is also observed an evident enlargement of the
3dB focal depth in the z-axis. On the other hand, the 3dB focal
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5
width along the y-axis does not change so intensely as
frequency is varied. For 12GHz, the focusing pattern strongly
varies, and the focal region is no more located at the lens
vertical z-axis. The single focus located at y=0 splits into
several hot spots. This phenomenon is similar to the splitting
condition in 2D leaky-wave antennas focused at the far-field
regime, whose single-beam focused at broadside splits into a
scanned conical beam for higher frequencies [24-26].
Similarly, for the case of 2D leaky-wave lenses focused in the
near-field zone, it is obtained a splitting from a single focus to
a conical (toroidal) focus.
Fig. 9. Theoretical near-field intensity at zy-plane as a function of frequency.
This behavior with frequency is also evident in Fig.10,
which represents the field cuts in the transverse xy plane for
each studied frequency, and for the resultant focal height
(z=84mm at 9GHz, z=139mm at 10GHz, and z=240mm at
11GHz). A single focal region with maximum energy
concentrated above the lens center (x=y=0) is obtained for the
scanning band comprised between 9 and 11GHz. At 12GHz,
however, it is clearly observed the splitting of the focus into
two focused zones approximately located at x=0 y=50mm.
This splitting condition above 11GHz limits the upper
operation frequency of the scanning lens. On the other hand,
the lower frequency band is determined by the radiation cutoff
of the TM0 leaky-wave, which in our case is below 9GHz.
The results shown in Figs.9 and 10 correspond to the RHCP
component. The response of the crosspol LHCP component as
frequency is varied in the steering bandwidth (9-11GHz) is
also shown in Fig.11a for the transverse x-cut, and for the
corresponding focal heights (results are similar for the y-cut).
Fig. 10. Theoretical near-field intensity at xy plane as a function of frequency
and for the corresponding focal heights.
-100 -50 0 50 100-20
-15
-10
-5
0
x (mm)
dB RHCPLHCP
9GHz z=84mm10GHz z=139mm11GHz z=240mm
a)
-50 0 50-100º
-50º
0º
+50º
+100º
x (mm)
9GHz z=84mm
10GHz z=139mm
11GHz z=240mm
b)
Fig. 11. Theoretical near-field intensity along x-axis for the corresponding
focal heights as a function of frequency a) Amplitude and b) phase patterns.
As it can be seen, pure RHCP focused near fields are
obtained at the lens axis (x=y=0) in the entire scanning
bandwidth, with increased RHCP and LHCP sidelobes as the
focal height is frequency steered. Also, it is shown an increase
of the focal width as the focal length is enlarged. The level of
the LHCP is relatively high due to the limited control of the
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6
polarization in the presented lens antenna. A design based on
resonant perpendicular slots such as the ones used in RSLA
antennas [22-23] would have led to a better control of this
polarization. This increase in the LHCP can be attributed to
the spatial distortion suffered by the phase pattern, which is
shown in Fig.11b.
B. Experimental Validation of Frequency Dispersion
The near fields were measured along the z-axis from
z=5mm to z=213mm for five frequencies in the 9.2-11GHz
band. The measured Ex component is compared with the field
obtained from the theoretical dispersion of the leaky wave
(LW), showing very good agreement as it can be seen in
Fig.12. As predicted by theory, the focal length and the focal
depth augment as frequency is increased. The amplitude of Ey
component presents similar response with frequency, and it is
not shown for brevity. As expected, balanced amplitude of the
transverse fields and negligible Ez component was obtained
for all this scanning frequency range.
0 50 100 150 200 250 300 350 400-20
-15
-10
-5
0
z (mm)
dB10.5 GHz
Dispersion LW Measured
11.0 GHz
9.5 GHz
10.0 GHz
9.2 GHz
Fig. 12. Frequency dispersion of Ex field intensity at the axial cut.
The Ex and Ey fields in the transverse x-axis (=0º) at a
fixed height, z=139mm, are shown in Fig.13a and Fig.13b at
9.5GHz and 10.5GHz, respectively. The agreement with the
measurements is in within the possible inaccuracies introduced
by the measurement setup when displacing manually the
probe. The experiments are consistent with theory, thus
validating the approach to obtain the frequency dispersion of
the fields also in the transverse directions. Fig.13c compares
the theoretical distortion of the transverse focusing pattern at a
fixed height as frequency is varied, observing that the highest
focusing effect (minimum focal width for Ey) is obtained at
10GHz, which corresponds to the frequency for which the
focal distance is located at the observation height z=139mm.
Similar validation for the fields in the transverse y-axis
(=90º) was obtained, but it is not shown due to space
restriction.
Fig.14 shows the variation of the focal length, width and
depth, as frequency is shifted between 9GHz and 11GHz. CST
results are compared with leaky theory, and also experimental
data are plotted with circles, observing good agreement. This
figure summarizes the performance of the novel holographic
lens as a frequency-steering device with 20% bandwidth.
-100 -50 0 50 100-20
-15
-10
-5
0
x (mm)
dB Ex Ey
9.5GHz
a)
Dispersion LW Measured
-100 -50 0 50 100-20
-15
-10
-5
0
x (mm)
dB
10.5GHz
b)
Ex Ey
Dispersion LWMeasured
-100 -50 0 50 100-20
-15
-10
-5
0
x (mm)
dB
c)
Ex Ey
9.5 GHz10.0 GHz10.5 GHz
Fig. 13. Frequency dispersion of field intensity along x-axis for z=139mm.
9 9.5 10 10.5 110
50
100
150
200
250
300
frequency (GHz)
mm
Dispersion LWCST Measured
Focal Length zf
Focal Depth z
Focal Width x
Fig. 14. Variation of focal length, depth and width with frequency.
The focal length can be scanned from z=84mm at 9GHz to
z=240mm at 11GHz, observing increased steering sensitivity
(mm/GHz) for higher frequencies. The focal depth has a
corresponding growth from z=85mm at 9GHz to z=300mm
at 11GHz, while the focal width x changes from x=22mm at
9GHz to x=41mm at 11GHz. Above 11GHz, the focus splits
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into two lateral focused regions, as it was described before,
and the lens loses the capacity to generate a single focused
zone at the vertical axis.
9 9.5 10 10.5 110
20
40
60
80
100
frequency (GHz)
Eff
icie
ncy
(%
)
Radiation Eff.Focusing Eff. XFocusing Eff. Y
Dispersion LW CST Measured
Fig. 15. Variation of focusing and radiation efficiencies with frequency
Finally, Fig.15 shows the variation with frequency of the
focusing efficiency and the radiation efficiency. The focusing
efficiency has been computed from the focal width for each
principal transverse plane (FOCX
, FOCY) as described in [18].
The theoretical radiation efficiency RAD has been calculated
directly from the leaky-wave leakage distribution (neglecting
ohmic losses) as:
R
df
RADef
0
),(2
1)( (7)
Full-wave CST simulations are compared with leaky theory,
providing very good matching in the entire bandwidth. Also,
the focusing efficiency measured at the central frequency is
plotted with a circle. At the design frequency of 10GHz, the
specified 70% focusing efficiency for both principal planes
and 80% radiation efficiency are obtained. As frequency is
increased, the radiation efficiency decreases as a result of the
generation of the non-radiative central region of the lens,
which was illustrated in Fig.8, resulting in RAD=60% at
11GHz. On the contrary, the focusing efficiency tends to
increase to 100% as frequency is augmented, as a result of the
stronger growth in the focal length than in the focal width
(which results in higher F/x ratios and therefore in higher
values of FOC [18]), as it was summarized in Fig.14. The
opposite behavior is observed as frequency is decreased,
showing higher radiation efficiency around 85% and lower
focusing efficiency around 60% at 9GHz. Nevertheless, all
estimated efficiencies present values over 50% in the whole
bandwidth. As a consequence, it is demonstrated that the novel
holographic near-field lens provides very efficient focusing
performance in the entire steering region of the focal length.
IV. CONCLUSION
Experimental results in the 10GHz band confirm the
working mechanism of a novel type of microwave lens based
on modulated leaky-wave concepts and simple integrated
feeding mechanisms. As it has been demonstrated in this
paper, matching below -10dB over the whole 9-11GHz
frequency band is obtained by using a single vertical coaxial
probe located at the center of the lens area. Also, it is
important to mention that the proposed holographic lens uses a
continuous spiral-modulated printed slot-circuit with radial
separation in the order of half wavelength, and therefore only
five unit cells are needed to cover an aperture radius of 30.
This is a much simpler structure that previously proposed
holographic antennas based on subwavelength unit-cells,
[29,30)] or RLSA designs based on discrete resonant slots [21-
23], which need hundreds of radiating elements to generate the
holographic pattern (thus resulting in tighter fabrication
tolerances and advanced design and optimization procedures
[31]). Therefore the holographic antenna presented in this
contribution has the potential to be used at higher frequencies
than previous solutions. Its main drawback, however, resides
in its poorer circular polarization performance due to the use
of a continuous slit.
Moreover, it has been explained and demonstrated the
interesting effect of frequency steering of the focal length,
which allows electronically adjustment of the focus position in
a region by simply changing the frequency of the input signal.
Maximum focal length is limited by the splitting of the single
focus above a certain frequency. This is a general behavior for
any holographic near-field lens, due to the dispersive nature of
the modulated leaky wave. In the designed lens, the focal
length has been steered from 10cm to 25cm as frequency was
increased from 9GHz to 11GHz (20% bandwidth), showing a
significant increase in the focal depth from 10cm to 30cm,
while the focal width varies from 2cm to 4cm. This interesting
frequency response has been accurately and efficiently
predicted by the proposed theory for modulated leaky modes,
and it might be useful for microwave imaging, sensing and
heating applications. Compared to electronically scanned
focused antennas [11,17], frequency scanning provides a much
simpler mechanism to steer the focus, avoiding the use of
expensive active circuits such as phase shifters [11] or FET
transistors [17].
Therefore, the novel printed-circuit leaky-wave lens opens
to a new variety of microwave focusing devices which are
highly efficient, extremely simple, and low-cost (if compared
to current state-of-the-art technologies), and which provide the
interesting capability of frequency adjustment of the focal
length. For the authors’ knowledge, it is the first time that
these features are proposed and experimentally demonstrated.
REFERENCES
[1] J. W. Sherman, “Properties of focused apertures in the Fresnel region,”
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[2] Y. Li and E. Wolf, ”Focal shifts in diffracted converging spherical
waves,”, Optics Comm., vol.39, no.4, pp.211-215, October 1981.
[3] W. J. Graham, “Analysis and synthesis of axial field patterns of focused
apertures,” IEEE Trans. Antennas Propagat., vol. 31, pp. 665-668, July
1983.
[4] R. C. Hansen, “Focal region characteristics of focused array antennas,”
IEEE Trans. Antennas Propagat., vol. 33, pp. 1328-1337, Dec. 1985.
Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
paper submitted to IEEE Trans. on Antennas and Propagation
8
[5] C.A. Balanis, Antenna Theory, Singapore: John Wiley and Sons, 1982,
pp.453-454.
[6] W. Gee, S. W. Lee, C. A. Cain, R. Mittra, and R. L. Magin, “Focused
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[8] K. D. Stephan, J. B. Mead, D. M. pozar, L. Wang, and J. A. Pearce, “A
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[30] G. Minatti, F. Caminita, M. Casaletti, S. Maci, “Spiral leaky-wave
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Antennas," IEEE Trans. Antennas Propag., in press.
Darwin Blanco received the Electrical
Engineering degree from the University of
Antioquia, Colombia, in 2009 and the Master
degrees in Multimedia and Communications
from the University Carlos III de Madrid,
Madrid, Spain, in 2011.
Currently he is doing his Ph.D. Degree in
Multimedia and Communications at the University Carlos III
de Madrid, Madrid, Spain. His current research interests
include leaky wave antennas, frequency selective surfaces and
phase array antennas.
José Luis Gómez Tornero (M'06) was born
in Murcia, Spain, in 1977. He received the
Telecommunications Engineer degree from
the Polytechnic University of Valencia
(UPV), Valencia, Spain, in 2001, and the
"laurea cum laude" Ph.D degree in
Telecommunication Engineering from the
Technical University of Cartagena (UPCT), Cartagena, Spain,
in 2005.
In 1999 he joined the Radio Communications Department,
UPV, as a research student, where he was involved in the
development of analytical and numerical tools for the
automated design of microwave filters in waveguide
technology for space applications. In 2000, he joined the
Radio Frequency Division, Industry Alcatel Espacio, Madrid,
Spain, where he was involved with the development of
microwave active circuits for telemetry, tracking and control
(TTC) transponders for space applications. In 2001, he joined
the Technical University of Cartagena (UPCT), Spain, as an
Assistant Professor. From October 2005 to February 2009, he
held de position of Vice Dean for Students and Lectures affairs
in the Telecommunication Engineering Faculty at the UPCT.
Since 2008, he has been an Associate Professor at the
Department of Communication and Information Technologies,
UPCT. His current research interests include: 1- The
development of numerical methods for the analysis and design
of leaky-wave devices in planar and waveguide technologies,
2- Their application for telecoms, RFID, microwave
heating/sensing, wireless power transmission/harvesting,
hyperthermia, and analog signal processing. 3- The innovation
Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
paper submitted to IEEE Trans. on Antennas and Propagation
9
in the area of higher-education teaching/learning. He has
authored or co-authored over 50 peer-reviewed journal papers.
He has been visiting researcher/professor at University of
Loughborough (UK, England), Heriot-Watt University (UK,
Scotland), Queen’s University of Belfast (UK, Northern
Ireland), and CSIRO-ICT Centre (Sydney, Australia).
José Luis Gómez Tornero received in July 2004 the national
award from the foundation EPSON-Ibérica to the best Ph.D
project in the field of Technology of Information and
Communications (TIC). In June 2006, Dr. Gómez-Tornero
received the Vodafone foundation-COIT/AEIT (Colegio
Oficial de Ingenieros de Telecomunicación) award to the best
Spanish Ph.D. thesis in the area of Advanced Mobile
Communications Technologies. This thesis was also awarded
in December 2006 as the best thesis in the area of Electrical
Engineering, by the Technical University of Cartagena. In
February 2010, Dr. Gómez Tornero was appointed CSIRO
Distinguished Visiting Scientist by the CSIRO ICT Centre,
Sydney. He is the recipient or co-recipient of the 2010 IEEE
Engineering Education conference award, the 2011 EuCAP
best student paper prize, the 2012 EuCAP best antenna theory
paper prize, and the 2012 Spanish URSI second prize to the
best student paper.
Eva Rajo-Iglesias (SM’08) was born in
Monforte de Lemos, Spain, in 1972. She
received the M.Sc. degree in
telecommunication engineering from the
University of Vigo, Spain, in 1996, and the
Ph.D. degree in telecommunication from the
University Carlos III of Madrid, Spain, in
2002.
She was a Teacher Assistant with the University Carlos III of
Madrid from 1997 to 2001. She joined the Polytechnic
University of Cartagena, Cartagena, Spain, as a Teacher
Assistant, in 2001. She joined University Carlos III of Madrid
as a Visiting Lecturer in 2002, where she has been an
Associate Professor with the Department of Signal Theory and
Communications since 2004. She visited the Chalmers
University of Technology, Göteborg, Sweden, as a Guest
Researcher, in 2004, 2005, 2006, 2007, and 2008, and has
been an Affiliate Professor with the Antenna Group, Signals
and Systems Department, since 2009. She has co-authored
more than 50 papers in international journals and more than
100 papers in international conferences. Her current research
interests include microstrip patch antennas and arrays,
metamaterials, artificial surfaces and periodic structures,
MIMO systems and optimization methods applied to
electromagnetism.
Dr. Rajo-Iglesias was the recipient of the Loughborough
Antennas and Propagation Conference Best Paper Award in
2007 and the Best Poster Award in the field of Metamaterial
Applications in Antennas sponsored by the IET Antennas and
Propagation Network, at the conference Metamaterials 2009:
3rd International Congress on Advanced Electromagnetic
Materials in Microwaves and Optics. She is currently an
Associate Editor of the IEEE ANTENNAS AND
PROPAGATION MAGAZINE and of the IEEE ANTENNAS
AND WIRELESS PROPAGATION LETTERS.
Nuria Llombart (S’06–M’07) received the
Electrical Engineering degree and Ph.D. from
the Polytechnic University of Valencia,
Spain, in 2002 and 2006 respectively. During
her Master’s degree studies she spent one
year at the Friedrich-Alexander University of
Erlangen-Nuremberg, Germany, and worked
at the Fraunhofer Institute for Integrated
Circuits, Erlangen, Germany. From 2002 until 2007, she was
with the Antenna Group at the TNO Defence, Security and
Safety Institute, The Hague, The Netherlands. From 2007 until
2010, she was a Postdoctoral Fellow at the California Institute
of Technology, working for the Sub millimeter Wave Advance
Technology group of the Jet Propulsion Laboratory, Pasadena,
USA. She was a “Ramón y Cajal” fellowship at the Optics
Department of the Complutense University of Madrid, Spain,
from 2010 to 2012. Since September 2012, she is an Assistant
Professor at the Technical University of Delft in The
Netherlands.
Dr. Llombart has co-authored over 20 journal contributions, 4
patents and over 70 contributions in international conferences.
Dr. Llombart was co-recipient of several NASA awards and of
the H.A. Wheeler Award for the Best Applications Paper of
the year 2008 in the IEEE TRANSACTIONS ON
ANTENNAS AND PROPAGATION. She serves as Topical
Editor for the IEEE TRANSACTIONS ON THz SCIENCE
AND TECHNOLOGY, IEEE ANTENNAS AND
PROPAGATION WIRELESS LETTERS, and for the Antenna
Applications Corner of the IEEE MAGAZINE ON
ANTENNAS AND PROPAGATION. She is also a board
member of the IRMMW-THz International Society. Her
research interests include the analysis and design of planar
