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Abstract—A parallel-plate Luneburg lens (LL) based on
all-metal metamaterial is presented in this paper. To achieve the
required refractive index distribution of the LL, an all-metal unit
cell with a separated cuboid is proposed, whose height is related to
its refractive index. This inserted cuboid is attached to neither the
top plate nor the bottom plate of the parallel plate. Compared
with traditional bed of nail design, the proposed metamaterial
unit cell exhibits a wider bandwidth. The operation principle of
such a unit cell is investigated using the transverse resonance
technique. To construct the all-metal metamaterial LL into one
body, a cruciform cuboid is added to each unit cell such that ad-
jacent unit cells can connect to each other. Based on the designed
metamaterial LL, a multibeam antenna is developed by providing
seven inputs, which can generate seven predefined beams. Several
parts of the prototype are separately fabricated and assembled,
and good agreement is observed between simulation and meas-
urement. The designed LL based multibeam antenna has several
advantages, including wide bandwidth, high aperture efficiency,
and high radiation efficiency.
Index Terms—Parallel plate Luneburg lens (LL), wideband,
all-metal metamaterial, multibeam antenna.
I. INTRODUCTION
ULTIBEAM antennas are becoming increasingly indis-
pensable components in wireless communication sys-
tems [1]. Such antennas enable the generation of several di-
rective beams to cover a predefined angular range. Currently,
dominant technologies to produce multiple beams include
using circuit-type beam-forming networks [2]-[5] or qua-
si-optical multibeam antenna systems [6]-[7]. Particularly, the
Luneburg lens (LL) is a favored candidate for multibeam an-
Manuscript received ** **, 2022. This work was supported in part by the
National Natural Science Foundation of China under Grant 62101259, Grant
62025109 and Grant 61931021, in part by the National Key Laboratory on
Electromagnetic Environment Effects under Grant JCKYS2019 DC4, in part by
the Primary Research & Development Plan of Jiangsu Province under Grant
BE2022070, and in part by the Open Research Program of State Key Labora-
tory of Millimeter Waves under Grant K202229. (Corresponding authors:
Dazhi Ding).
Ji-Wei Lian is with the School of Electronic and Optical Engineering,
Nanjing University of Science and Technology, Nanjing 210094, China, and
also with the State Key Laboratory of Millimeter Waves, Southeast University,
Nanjing 210096, China.
Maral Ansari and Y. Jay Guo are with the Global Big Data Technologies
Centre, University of Technology Sydney, Ultimo, NSW 2007, Australia.
Peng Hu, and Dazhi Ding are with the School of Electronic and Optical
Engineering, Nanjing University of Science and Technology, Nanjing 210094,
China.
tenna applications such as long-range point to multipoint
communications due to its superior behaviors, such as
wide-angle scanning, broad bandwidth, and high gain.
Several techniques have been developed to design LLs
[8]-[20]. Traditional LLs are of spherical shapes, which can
generate narrow beams in two dimensions [8]-[9]. In recent
years, 3-D printing techniques have been widely applied in
electromagnetic applications since they can produce arbitrary
shapes as desired [21]-[30]. There is also renewed interest in
the design of LLs due to advancements in manufacturing
technologies such as 3D printing, where the realization of gra-
dient refractive index is accomplished by gradual changing of
the geometrical parameters [21]-[28]. In [21], a 3-D printed
circularly polarized spherical LL is designed, whose unit cells
are comprised of dielectric slabs and air slabs. Another LL
design is proposed in [22] by changing the size of plastic blocks
to achieve different refraction indexes. In [23], a 3-D printed
LL fed by the magneto-electric dipole is proposed, whose an-
isotropy is later reduced in [24]. In [25], different types of feeds
have been investigated to obtain the optimal radiation pattern of
spherical LL.
For many applications, such as radar, imaging systems, air-
craft landing, 2D light-of-sight alignment of highly directional
beams, and full coverage scanning systems is very difficult.
LLs can be converted from 3D to 2D cases, namely cylindrical
shapes, where they can form a narrow beam in one dimension
while a fan beam in the other [14]-[17]. 3D printing technolo-
gies are also popular in cylindrical LL designs [26]-[28]. A
circularly-polarized parallel-plate LL fabricated using 3-D
printing technology is proposed in [26]. Similar designs can
also be found in [27]-[28]. It should also be noted that spherical
LLs can be converted into flat LLs using transformation optics
methods [19]-[20].
As mentioned above, transformation optics methods can help
shape the LL. Using this method, a 3-D printed ellipsoidal LL is
proposed in [29] with a lower profile. What is more, a flat LL
using 3-D printing is reported in [30]. It is worth mentioning
that the above 3-D printed cases are all based on all-dielectric
structure, the operation principle of which can be analyzed
using effective medium theory. However, 3-D printed
all-dielectric LLs usually suffer from severe dielectric losses
and low radiation efficiencies, which is attributed to the high
loss tangent of the used specific material. For example, the
Photopolymer VeroClear used in [23] has a loss tangent of 0.01.
As a reference, the loss tangent of Rogers 5880 substrate, a
Wideband and High-Efficiency Parallel-Plate
Luneburg Lens Employing All-Metal Metamaterial
for Multibeam Antenna Applications
Ji-Wei Lian, Maral Ansari, Peng Hu, Y. Jay Guo, and Dazhi Ding
M
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2
popular substrate used in PCB fabrication, is merely 0.0009.
To cope with this loss issue, some researchers devote to fully
metallic LLs with low losses [31]-[38]. An all-metal spherical
LL is proposed in [31]. The lens is firstly sliced into multiple
planar layers, and then equally spaced conducting inclusions
are inserted into each layer to alter the refractive index distri-
butions. Later in [32], the cubic grid with cubic inserts is
replaced by a hexagonal grid with cylindrical inserts to pursue
lower anisotropy and lower cost. Since the inserts are separated,
layers of lightweight foams are required as supporters.
All-metal structures are also popular in cylindrical counter-
parts. A parallel-plate LL is proposed in [33] by continuously
altering the height of the parallel plate. A series of
glide-symmetric holes are introduced in parallel plates to de-
sign LLs in [34]-[35]. The designed LLs in [36]-[37] employ
metallic nails with graded heights to achieve the required re-
fractive index distribution. In [38], off-shifted opposite layers
are constructed to design an ultra-wideband LL. It is noted that
these designs are not comparably flexible in contrast to 3-D
printed LLs since the unit cells are attached to the top or bottom
plates. Under this circumstance, the LL is usually comprised of
a bed of nails or its complement, i.e., a holey surface [36]-[37],
[44]. An alternatively new configuration would be to separate
the unit cell from the parallel plate. By doing so, the parallel
plate only functions as a perfect conductor, and it is not re-
quired to support the inclusion attached. As a result, the parallel
plate can be made thin enough to reduce the total mass of the
LL or alternatively, it can be replaced by a low-cost PCB.
Considering the aforementioned issues, a new parallel-plate
LL based on all-metal metamaterial is proposed in this paper.
Compared with previously published parallel-plate LLs, new
unit cells with independent cuboids are introduced here, and
they help separate the all-metal metamaterial from the parallel
plates. Employing the proposed all-metal metamaterial, the
designed LL has several advantages, including wide bandwidth,
high aperture efficiency, and high radiation efficiency
The structure of t his paper is as follows. Section II int roduces
the operation mechanism of the proposed all-metal unit cell.
Multibeam antenna design is introduced in Section III. Fabri-
cation and measurement are performed in Section IV. Finally, a
brief conclusion is given in Section V.
II. A
LL
-M
ETAL
U
NIT
C
ELL
D
ESIGN
A. Unit Cell Configuration
The model of the proposed unit cell is shown in Fig. 1, in
which an all-metal configuration is utilized. Different from
most parallel-plate unit cells, the inclusion is separated from the
(a) (b)
Fig. 1. (a) Perspective view and (b) Simulated CST model of the proposed uni
t
cell. (l=10.16, h=5.00, p=5.00, w=1.00, t
1
=2.00, t
2
=2.00. Unit: mm)
(a)
(b)
(c)
(d)
Fig. 2. (a) Perspective view, (b) dispersion diagram, (c) refractive index an
d
(d) gain of a LL antenna of the traditional and the proposed unit cell.
8 9 10 11 12
1.0
1.2
1.4
1.6
1.8
2.0 h=3.0 mm
h=4.0 mm
h=5.0 mm
h=6.0 mm
h=7.0 mm
h=8.0 mm
h=2.5 mm
h=3.0 mm
h=3.5 mm
h=4.0 mm
h=4.5 mm
h=5.0 mm
Frequency (GHz)
Refractive index
8 9 10 11 12
15
16
17
18
19
20
21
Proposed design
Traditional design
Frequency (GHz)
Gain (dBi)
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top and bottom plates. The incoming wave propagates along the
z-axis with the E-field along the x direction. Such a unit cell is
constructed within a parallel waveguide with a thickness of l.
The periods are both p along z- and y-directions. The related
simulated model using CST is included in Fig. 1, in which the
top and bottom sides are assigned as Perfect E boundary and the
lateral sides as periodic conditions. The structure of the unit cell
is mainly comprised of an adjustable cuboid and two supporting
cuboids in cruciform. The adjustable cuboid is utilized to
change the refractive index of the unit cell. The supporting
cuboids are capable of connecting adjacent unit cells to make
the whole all-metal metamaterial one body. Without them,
adjacent unit cells are separated and impractical in fabrication.
In order to investigate the bandwidth performance of the
proposed unit cell, the simulated models of the traditional bed
of nail design and the proposed design are depicted in Fig. 2 (a).
The biggest difference between them is that the adjustable nail
is extracted and placed in the middle of the unit cell. The dis-
persion diagrams of the traditional design and the proposed
design are plotted in Fig. 2 (b) for comparison. The change of
the proposed design is mainly attributed to the supporting cu-
boid, which is used to connect adjacent unit cells. In Fig. 2 (c),
the refractive indexes of these two cases versus frequency is
shown. It can be seen that the refractive index of the proposed
unit cell is more stable with the frequency changing. In this
situation, the proposed unit cell is expected to achieve a wider
bandwidth compared with traditional bed of nail design.
Straightforwardly, the gain of a LL antenna constructed by the
traditional unit cell or the proposed unit cell is included in Fig.
2 (d). The details of such a LL antenna design would be dis-
cussed in Section III. When using the proposed unit cell, it is
seen that the gain is gradually increased with a higher fre-
quency, indicating a more stable aperture efficiency from 8
GHz to 12 GHz.
Table I summarizes the main characteristics of the proposed
unit cell compared with other similar unit cells in LL designs.
Those designs using PCB or 3-D printing technologies usually
suffer from dielectric loss, as reported in [10], [12], [26], and
[28]. Several all-metal unit cells are presented in [33]-[36],
which may be manufactured by CNC machining technology. It
is noted that the biggest difference between the proposed unit
cell and other designs is that the inclusion of the proposed unit
cell is separated from the parallel-plate waveguide.
B. Theoretical analysis
The proposed unit cell can be analyzed using the transverse
resonance technique [39]. The supporting cuboid is removed
for simplication, since the adjustable cuboid is the dominant
component in changing the refractive index of the unit cell. The
side view of the proposed unit cell with its transverse resonance
equivalent circuit is shown in Fig. 3. As discussed previously, a
thin conductor plate can be added to the center of the unit cell
without disturbing the E-field distribution. Here, a PEC is in-
troduced to cut the unit cell in half. The unit cell is comprised of
two parts, i.e., the parallel plate area (h/2≤z≤l/2) and the me-
tallic grating area (0≤z≤h/2). The interface between these two
areas is set as the reference plane. Accordingly, we have
uppz
ZZ
(1a)
dmgz
ZZ
(1b)
where u
Z
and
d
Z
are the input impedances looking to the up
and down, ppz
Z
and mgz
Z
are the transverse characteristic
impedance of the parallel plate area and metallic grating area,
respectively. Looking from the top view, the metallic grating
area is a bed of metal posts on a ground plane, whose refractive
index is written as [40]
2
1tan
2
mgz
kh
nW
(2)
where
0
1.05k
is the propagation constant along the z-axis,
and W is the weighting factor. For the square post in this design,
pw
Wp
(3)
mgz
Z
is equal to the surface impedance of the corrugated sur-
face, which is derived as [41]-[44]:
tan 2
mgz
mgz mgz
mgz
h
Zj k
n
(4)
where mgz
is the wave impedance, mgz
k
is the transverse
propagation constant of the metallic grating region. Consider-
ing the air-filled design, we have
TABLE
I
C
OMPARISONS
B
ETWEEN THE
P
ROPOSED
U
NIT
C
ELL WITH
S
IMILAR
D
ESIGNS
Ref. Period
(λ)
Height
(λ)
Dielectric
loss
Fabrication
technology
Separated
from PPW
[10] 0.04 0.04 Yes PCB No
[12] 0.2 0.13 Yes PCB No
[26] 0.21 0.7 Yes 3-D printed No
[28] 0.08 0.08 Yes 3-D printed No
[33] N.A. N.A. No CNC machining No
[34] 0.3 N.A. No CNC machining No
[35] 0.28 0.18 No CNC machining No
[36] 0.13 1.55 No CNC machining No
This 0.17 0.34 No CNC machining Yes
Fig. 3. Side view of the proposed unit cell and its transverse resonance
equivalent circuit.
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00mgz
(5a)
2
mgz
k
(5b)
Similarly, the transverse characteristic impedance of the
parallel plate
p
pz
Z
is obtained using transmission line theory:
0
tan ( )
2
ppz
ppz ppz
klh
Zj k
(6)
where
p
pz
k is the transverse propagation constant of the paral-
lel-plate region. The longitudinal propagation constant must be
the same in both regions to achieve phase matching of the
tangential fields at the interface between these two regions [39].
Therefore, the longitudinal propagation constant ucy
k of the
proposed unit cell shown in Fig. 1 is equal to that in the paral-
lel-plate region
p
py
k and that in the metallic grating region mgy
k.
Here, effe
and effe
n are the effective dielectric constant and
effective refractive index of the proposed unit cell, respectively.
For guiding mode solution, the following condition is satisfied
[45].
uc ucy
kk (7)
Then we have
22 22
00
22 2 2
000
2
01
ppz ppy ucy
uc effe
effe
kkkkk
kk k k
kn
(8)
Using the transverse resonance condition ud
Z
Z
, the rela-
tionship between the effective refractive index effe
n and the
height of the metallic grating l can be obtained as:
2
02
0
0
00
2
0
1tan 1 ( )
2
tan 0
1.05
1tan
2
effe
effe
kn lh
kn
h
h
pw
p
(9)
With a given value of l, the corresponding effective refractive
index effe
n can be calculated by solving equation (9). Alterna-
tively, the property of the periodic unit cells can be efficiently
computed by resorting to commercial simulators [46]. A pop-
ular simulation-assisted method to calculate the refractive in-
dex n of the inhomogeneous metamaterial is given as [47]-[48]:
122
11 21
21
11
cos (1 )
2
nSS
kd S
(10)
where S21 and S
11 are the transmission and reflection coeffi-
cients of the unit cell.
When forming the LL using the proposed unit cell, some
periodic holes would appear in the bottom layer. To investigate
the impact brought by these holes, it is beneficial to study the
height t1 and thickness t2 of the supporting cuboids, which
would directly decide the dimension of these holes. Here, we
set h=t1 and calculate the reflective indexes with different t1 in
Fig. 4 (a), which indicates the minimum refractive index
achieved by the proposed unit cell. The rest of the design pa-
rameters are the same with those in Fig. 1. When reducing the
parameter t1, the minimum refractive index reaches closer to 1.
Similarly the refractive indexes related to different t2 are plotted
in Fig. 4 (b). It is seen that the thickness t2 of the supporting
cuboid can barely affect the refractive index. In fabrication, a
higher and thicker supporting cuboid is preferable to provide
better mechanical strength; otherwise, the whole metamaterial
would suffer from the risk of deformation. A bigger t1, however,
would increase the minimum refractive index that the proposed
unit cell can achieve. In conclusion, t1=2 mm and t2=2 mm are
selected for the final design. In other words, the minimum
refractive index of the proposed unit cell is about 1.06. The
calculated refractive indexes of the proposed unit cell at dif-
ferent frequencies are shown in Fig. 4 (c). It is noted that with
the frequency increasing, the refractive index suffers from a
higher error.
The mass of the unit cell is another critical factor in practical
applications. As previously discussed, it is predicted that the
unit cell can function well without the drilled holes, but at the
expense of an increasing mass. Since the adjustable cuboid is
(a)
(b)
(c)
Fig. 4. Refractive index of the unit cell with different (a) t1 (b), t2, and (c) h.
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
6 GHz 7 GHz 8 GHz
9 GHz 10 GHz 11 GHz
12 GHz 13 GHz 14 GHz
t
1
(mm)
Refractive index
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
6 GHz 7 GHz 8 GHz
9 GHz 10 GHz 11 GHz
12 GHz 13 GHz 14 GHz
t
2
(mm)
Refractive index
23456789
1.0
1.2
1.4
1.6
1.8
2.0 6 GHz
7 GHz
8 GHz
9 GHz
10 GHz
11 GHz
12 GHz
13 GHz
14 GHz
h (mm)
Refractive index
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necessary to manipulate the refractive index, we only take the
mass of the supporting cuboid into consideration. Assuming the
used material in fabrication is aluminum alloy with a density of
2.7mg/mm
3
. When t
1
=1 mm and t
2
=1 mm are selected, the mass
of the supporting cuboid is 9 mg. This case is also producible
but more complicated processes are required during the fabri-
cation. When t
1
=2 mm and t
2
=2 mm are selected and used as the
final design parameters, the mass of the supporting cuboid is 32
mg. When t
1
=2 mm and t
2
=5 mm are selected, in which no
drilled holes would appear, the mass of the supporting cuboid is
50 mg. It means that the drilled holes can reduce the mass of the
supporting cuboid by 36%.
III. M
ULTIBEAM
A
NTENNA
D
ESIGN
A. All-Metal LL Design
The refractive index at a specific point in a LL is described
by the following equation [36]:
2
() 2 ( )nr r R (11)
where
r is the distance from the specific point to the lens center,
and R is the radius of the LL. Given by equation (1), the re-
fractive index range is from 1 to
2
. The spherical wave
emitting from the focal point is gradually converted to a plane
wave through the LL.
Substituting (11) into (9), the theoretical distribution of the
parameter h can be expressed as:
2
02
0
0
00
2
0
()1
tan ( ) 1( )
2
tan 0
1.05
1tan
2
krR lh
krR
h
h
pw
p
(12)
A simpler and more efficient way is resorting to the rela-
tionship shown in Fig. 4 (b). Discretizing the refractive index
distribution characterized by (11) with the square unit cell, we
have Fig. 5 (a). With a resort to the relationship between the
refractive index distribution and the parameter h, the refractive
index distribution is transformed into Fig. 5 (b), i.e., the di-
mension distribution of the parameter h. The maximum and
minimum values of the parameter h are 7.5 mm and 1.4 mm,
respectively.
The constructed LL employing all-metal metamaterial is
shown in Fig. 6, in which a lattice of the unit cell is formed to
make the LL one body and the cuboid at every node chooses
different heights to manipulate the refractive index distribution.
The R is set at 90 mm, namely 3 λ
0
, where λ
0
is the free-space
wavelength at 10 GHz.
B. Multibeam Antenna Design
Based on the designed LL, a fully-metallic multibeam an-
tenna is developed in this paper, as shown in Fig. 7. Such a
design is divided into three parts for fabrication, as shown in
Fig. 7 (a), in which the middle layer is denoted in blue color
for more precise viewing. There are many location holes
drilled in these three parts, and they can be assembled by
putting some metallic screws through the location holes. The
assembled model is shown in Fig. 7 (b), including the per-
spective view, the top view and the side view. To generate
multiple beams, seven feeds surrounding the LL are inserted.
The feed used here is WR90, whose cross-sectional size is
22.86 mm*10.16 mm. The radiation aperture is formed by a
flared parallel waveguide to achieve better impedance
matching. It is noted that the designed LL in Fig. 6 is separated
from the parallel waveguide and needs a supporter in fabrica-
tion. To this end, a connection with a thickness of 2 mm is
used to connect the LL and the outer waveguide. To investi-
gate the impact of the introduced connection, the radiation
aperture is simulated with an inserted plate, as shown in Fig. 8
(a). The lateral sides are assigned as perfect H boundaries to
simulate the infinity of the parallel plate. It can be seen from
Fig. 8 (b) and Fig. 8 (c) that the reflection coefficient and the
radiation pattern are barely influenced by the added connec-
tion.
The fabricated prototype is shown in Fig. 9, in which Fig. 9
(a)-(c) are the separated parts. Since the designed LL is not
attached to the top and bottom plates, it can be manufactured
independently. These three parts are fabricated independently
using the CNC Machining technology and then assembled
using some metallic screws. It is also possible to use all-metal
3-D printing technology in fabrication if a higher fabrication
tolerance and lower mechanical strength are allowed. The
assembled prototype is shown in Fig. 9 (d)-(e). The install
setup for pattern measurement is shown in Fig. 9 (f). The
E-field distributions at 10 GHz related to different inputs are
shown in Fig. 10 (a). It is noted that the incoming wave is
gradually transformed from a cylindrical wave to a plane wave
through the LL. And the energy is barely coupled to other
(a) (b)
Fig. 5. (a) Refractive index distribution, and (b) Dimension distribution of the
designed LL.
Fig. 6. Simulated model of the designed LL, where r
1
=90 mm.
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ports, which predicts satisfactory isolation between different
inputs. Similarly, the E-field distributions at 8 GHz, 9 GHz, 11
GHz, and 12 GHz are provided in Fig. 10 (b). It is seen that the
wave coming out of the LL performs as a plane wave at all
these frequencies, which verifies the wideband property of
this design.
The S-parameters in simulation and measurement are
plotted in Fig. 11. The simulated reflection coefficients and
the measured counterparts are plotted in Fig. 11 (a). The in-
vestigated bandwidth here is from 8 GHz to 12 GHz. It can be
(a) (b)
Fig. 7. (a) Separated parts and (b) Assembled model of the designed multibeam antenna based on LL. (r
2
=114.00, h
2
=28.16, h
3
=2.00, h
4
=21.00. Unit: mm)
(a) (b) (c)
Fig. 8. (a) Perspective view of the flared horn, (b) the impact of parameter d
4
on S11, and (c) the impact of parameter d
4
on radiation pattern. (d
1
=28.16, d
2
=21.00,
d
3
=2.00, d
4
=12.00, d
5
=10.16, d
6
=40.00. Unit: mm)
Fig. 9. Fabricated prototype and its measurement setup. (a)-(c) Top view of the separated parts; (b) perspective view of the assembled prototype; (c) patter
n
measurement setup.
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7
seen that the reflection coefficients are below ‒15 dB from 8.2
GHz to 11.7 GHz, including in simulation and measurement.
From 8 GHz to 12 GHz, the simulated and measured isolation
coefficients are well below ‒20 dB. The simulated and
measured patterns at the H-plane (yoz plane) from 8 GHz to 12
GHz with a step of 1GHz are plotted in Fig. 12 (a)-(e), which
show good agreement between simulation and measurement.
Take port #4 as an example, the simulated gains are 16.4 dBi,
17.5 dBi, 18.4 dBi, 19.4 dBi, and 20.0 dBi, respectively. The
corresponding radiation angles related to ports #1-#7 are 0º,
±17º, ±34º, ±51º. Especially a stable gain can be observed
with switching different inputs. Operating at 10 GHz, for
instance, the simulated gains related to ports #1-#7 are 17.9
dBi, 18.2 dBi, 18.4 dBi, 18.4 dBi, 18.4 dBi, 18.2 dBi, and 18.0
dBi, which indicate a gain difference of only 0.5 dBi. The
maximum gain difference within the investigated bandwidth
is 0.7 dBi. According to Fig. 7, the core and cross polariza-
tions here are x and y polarizations, respectively. The nor-
malized cross-polarization level can be obtained by normal-
izing to the core polarization, which is plotted in Fig. 12 (f).
The cross-polarization levels in simulation and measurement
are less than ‒40 dB and ‒29 dB, respectively. It is seen that
the measured cross-polarizations are higher than the simulated
counterparts, especially at the angle where co-polarization is
high. This phenomenon also happens at other frequencies, e.g.,
8 GHz, 9 GHz, 11 GHz, and 12 GHz. This is attributed to the
reflection brought by the cables, rotator, connectors and other
necessary facilities in measurement. From 8 GHz to 12 GHz,
the maximum cross-polarization level in measurement is less
than ‒28 dB.
The simulated and measured patterns at the E-plane (xoz
plane) are provided in Fig. 13. Satisfactory agreement be-
tween simulation and measurement is observed. Fig. 14 in-
cludes the simulated and measured gains from 8 GHz to 12
GHz. It is meaningful to investigate the radiation efficiency
and aperture efficiency of this design. The radiation efficiency
(a) (b) (c) (d)
(e) (f) (g) (h)
Fig. 10. (a)-(d) E-field distribution with different inputs at 10 GHz; (e)-(f) E-field distribution at different frequencies.
(a) (b) (c)
Fig. 11. (a) Simulated and measured reflection coefficients, (b) simulated isolation coefficients, and (c) measured isolation coefficients.
8 9 10 11 12
-35
-30
-25
-20
-15
-10
-5
0
S11, Simu. S11, Meas.
S22, Simu. S22, Meas.
S33, Simu. S33, Meas.
S44, Simu. S44, Meas.
Frequency (GHz)
S-parameter (dB)
8 9 10 11 12
-40
-35
-30
-25
-20
-15
-10
-5
0
S21 S31 S41
S51 S61 S71
S32 S42 S52
S62 S72 S43
S53 S63 S73
Frequency (GHz)
S-parameter (dB)
8 9 10 11 12
-40
-30
-20
-10
0
S21 S 31 S41
S51 S 61 S71
S32 S 42 S52
S62 S 72 S43
S53 S 63 S73
Frequency (GHz)
S-parameter (dB)
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8
can be obtained by comparing the gain value and the di-
rectivity value. Here, the measured radiation efficiency is
calculated using the measured gain and simulated directivity.
The minimum radiation efficiencies in simulation and meas-
urement are 96% and 82%, respectively. In many other de-
signs, the degradation of the radiation efficiency results from
reflection loss, coupling loss, and dielectric loss. In this work,
however, low reflection loss and coupling loss are achieved,
as indicated in Fig. 11. Attributing to the fully metallic
structure, this design omits the dielectric loss. These factors
together contribute to high radiation efficiency. To explore the
aperture efficiency, the ideal directivity is added to Fig. 14,
which is calculated by 4πA/λ2. Here, A is the cross-sectional
area of the lens [31]. The aperture efficiency can be obtained
by comparing the gain value and the ideal directivity value.
The aperture efficiency is within the range of 65%-82% from
8 GHz to 12 GHz.
Table II summarizes the performance of this design com-
pared with other similar designs. It is noted that the radiation
efficiency of a design is mainly decided by the dielectric loss,
the reflection loss and the coupling loss. In this work, the LL is
constructed employing a new all-metal unit cell, which is
separated from the top and bottom plates. One salient ad-
vantage of such a proposed unit cell is the wideband property.
As indicated by the S-parameter results and Table I, the
multibeam antenna using the proposed unit cell has achieved
(a) (b) (c)
(d) (e) (f)
Fig. 12. Simulated and measured co-polarization at (a) 8 GHz, (b) 9 GHz, (c) 10 GHz, (d) 11 GHz, (e) 12 GHz, and cross-polarization at (f) 10 GHz.
TABLE II
COMPARISONS BETWEEN THE DESIGNED MULTIBEAM ANTENNA AND SIMILAR DESIGNS
Ref. Realization Frequency (GHz) BW (%) DL (λ) RL (dB) SR (º) Gain (dBi) RE (%) AE (%)
[10] Meandering microstrip lines in
PCB 13 35 12.4 12 ±45 15.9-18.3 >51 N.G.
[12] Air hole in PCB 77 2 6.5 10 ±41 About 18.7 >54 N.G.
[16] Stacked PCB 31.5 35 13.7 10 ±72 About 10-17 >76 42
[17] Tapered dielectric disk 15 13 6.3 10 ±60 About 19-21 N.G. N.G.
[18] Medium using hole drilling 26 N.G. 7.7 N.G. N.G. 17.4 >75 N.G.
[26] 3-D printed dielectric posts 26.75 43 4.0 10 N.G. 10-12 >50 26-57
[28] 3-D printed air hole 15 6 9.3 10 ±60 13-17 >80 N.G.
[33] Tapered parallel plate 31 9 10.3 10 ±90 About 15-17 N.G. 50-70
[34] Glide-symmetric holes 28 29 N.G. 15 ±50 About 18 88 N.G.
[36] Metallic nails loaded 30 26 4.9 10 ±60 10-13 N.G. 57-75
This Inserted all-metal cuboid 10 40 6 13 ±51 15.8-21.0 >96 65-82
*BW: bandwidth; DL: diameter of the lens; RL: return loss; SR: scanning range; RE: radiation efficiency; AE: aperture efficiency; N.G.: not given.
-90 -60 -30 0 30 60 90
-20
-10
0
10
20
30
S1 S2 S3 S4 S5 S6 S7
M1 M2 M3 M4 M5 M6 M7
Theta (deg)
Gain (dBi)
-90 -60 -30 0 30 60 90
-20
-10
0
10
20
30
S1 S2 S3 S4 S5 S6 S7
M1 M2 M3 M4 M5 M6 M7
Theta (deg)
Gain (dBi)
-90 -60 -30 0 30 60 90
-20
-10
0
10
20
30
S1 S2 S3 S4 S5 S6 S7
M1 M2 M3 M4 M5 M6 M7
Theta (deg)
Gain (dBi)
-90 -60 -30 0 30 60 90
-20
-10
0
10
20
30 S1 S2 S3 S4 S5 S6 S7
M1 M2 M3 M4 M5 M6 M7
Theta (deg)
Gain (dBi)
-90 -60 -30 0 30 60 90
-20
-10
0
10
20
30 S1 S2 S3 S4 S5 S6 S7
M1 M2 M3 M4 M5 M6 M7
Theta (deg)
Gain (dBi)
-90 -60 -30 0 30 60 90
-60
-50
-40
-30
-20 S1 S2 S3 S4 S5 S6 S7
M1 M2 M3 M4 M5 M6 M7
Theta (deg)
Normalized cross-polarization (dBi)
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9
low re flecti on loss, low coupling between diffe rent inputs, and
no dielectric loss from 8 GHz to 12 GHz. These factors
together contribute to the high radiation efficiency from 8
GHz to 12 GHz, namely 96% of this design.
IV. CONCLUSION
In this paper, a wideband multibeam antenna based on a par-
allel-plate LL is designed. The LL is constructed using a sep-
arated all-metal metamaterial, which can adjust the refractive
index of the unit cell. Seven inputs are inserted around the LL
to achieve multibeam function. The diameter of the designed
LL is 6 λ . The working ban dwidth is from 8 GHz to 1 2 GHz, i.e.,
40%. The simulated radiation efficiency is higher than 96% and
the simulated aperture efficiency is higher than 65%. The gain
difference between multiple beams is less than 0.7 dB within
the interested bandwidth.
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-90 - 60 -30 0 30 60 9 0
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-15
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25
Simu. 8 GHz Meas. 8 GHz
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Ji-Wei Lian (Member, IEEE) was born in Guang-
dong, China. He received the B.S. degree in elec-
tronic science and technology from Hunan Univer-
sity, Changsha, China, in 2015, and the Ph.D. degree
in electromagnetic field and microwave technology
from the University of Electronic Science and
Technology of China (UESTC), Chengdu, China, in
2020.
From 2018 to 2020, he was a Visiting Student with
the Global Big Data Technologies Centre, University
of Technology Sydney, Ultimo, NSW, Australia. He
is currently an Associate Professor with the School of Electronic and Optical
Engineering, Nanjing University of Science and Technology, Nanjing, China.
He has authored or coauthored over 20 papers in peer-reviewed international
journals and conference proceedings. His current research interests include
beam-forming networks, multibeam antennas, and metasurface technologies.
Dr. Lian is serving a s a reviewer for several international journals, including
the IEEE Transactions on Antennas and Propagation, IEEE Transactions on
Microwave Theory and Techniques, IEEE Transactions on Circuits and Sys-
tems I: Regular Papers, IEEE Antennas and Wireless Propagation Letters.
Maral Ansari (S’17) received the M.S. degree (Hons.)
in Electrical and Communication Engineering from
Tabriz University, Tabriz, Iran, in 2015. She is cur-
rently a Post-Doctoral Researcher with the Global Big
Data Technologies Center, School of Electrical and
Data Engineering, Faculty of Engineering and IT
(FEIT), University of Technology Sydney (UTS),
Ultimo, NSW, Australia. Her current research inter-
ests include multi-beam antennas, lens antennas,
mm-wave antenna arrays, and beamforming net-
works.
Dr Ansari was the recipient of Best Student P ape r Awards at Australian
Symposium on Antennas in 2021, TICRA-EurAAP Travel Grant for
Eucap2021, First Place Award for the Best Research Showcase at UTS,
FEIT in 2020, NAWA Scholarship (Polish National Agency for Academic
Exchange) in 2019, and UTS International Research Scholarship (IRS)
and UTS President’s Scholarship (UTSP) in 2017.
Peng Hu was born in Henan, China. He received the
B.S. and M.S. degrees from Xinyang Normal Uni-
versity, Xinyang, in 2015 and 2018, respectively. He
is currently pursuing the Ph.D. degree with the School
of Electronic and Optical Engineering, University of
Science and Technology of Nanjing (NJUST), Nan-
jing, China.
His current research interests include Luneburg
lens antennas, and multibeam antennas.
Y. Jay Guo (Fellow’2014) received a Bachelor’s
Degree and a Master’s Degree from Xidian Univer-
sity in 1982 and 1984, respectively, and a Ph.D
Degree from Xian Jiaotong University in 1987. His
research interests include antennas, mm-wave and
THz communications and sensing systems as well as
big data technologies. He has published six books
and over 600 research papers including over 320
IEEE Transactions papers, and he holds 26 interna-
tional patents. He is a Fellow of the Australian
Academy of Engineering and Technology and a Fellow of IEEE, and was a
member of the College of Experts of Australian Research Council (ARC,
2016-2018). He has won a number of the most prestigious Australian national
awards including the Australian Engineering Excellence Awards (2007, 2012)
and CSIRO Chairman’s Medal (2007, 2012). He was named one of the most
influential engineers in Australia in 2014 and 2015, and one of the top re-
searchers across all fields in Australia in 2020, 2021 and 2022, respectively.
Together with his students and postdocs, he has won numerous best paper
awards.
He is a Distinguished Professor and the funding Director of Global Big Data
Technologies Centre (GBDTC) at the University of Technology Sydney (UTS),
Australia. He is the founding Technical Director of the New South Wales
(NSW) Connectivity Innovation Network (CIN). Prior to joining UTS in 2014,
> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <
11
Prof Guo served as a Director in CSIRO for over nine years. Before joining
CSIRO, he held various senior technology leadership positions in Fujitsu,
Siemens and NEC in the U.K.
Prof Guo has chaired numerous international conferences and served as a
guest editor for a number of IEEE publications. He was the Chair of Interna-
tional Steering Committee, International Symposium on Antennas and Propa-
gation (2019-2021). He has been the International Advisory Committee Chair
of IEEE VTC2017, General Chair of ISAP2022, ISAP2015, iWAT2014 and
WPMC'2014, and TPC Chair of 2010 IEEE WCNC, and 2012 and 2007 IEEE
ISCIT. He served as Guest Editor of special issues on “Low-Cost Wide-Angle
Beam Scanning Antennas”, “Antennas for Satellite Communications”
and “Antennas and Propagation Aspects of 60-90GHz Wireless Communica-
tions,” all in IEEE Transactions on Antennas and Propagation, Special Issue on
“Communications Challenges and Dynamics for Unmanned Autonomous
Vehicles,” IEEE Journal on Selected Areas in Communications (JSAC), and
Special Issue on “5G for Mission Critical Machine Communications”, IEEE
Network Magazine.
Dazhi Ding (Senior Member, IEEE)
received the
B.Sc. and Ph.D degrees in electromagnetic field and
microwave technique from Nanjing University of
Science and Technology (NJUST), Nanjing, China,
in 2002 and 2007, respectively.
During 2005, he was with the Center of wireless
Communication in the City University of Hong
Kong, Kowloon, as a Research Assistant. He joined
the Department of Electrical Engineering, Nanjing
University of Science and Technology (NJUST),
Nanjing, China, where he became a Lecturer in
2007. In 2014, he was promoted to Full Professor in
NJUST. He was appointed Head of the Department of Communication Engi-
neering, NJUST in September 2014. He was appointed Director of Academic
Affairs Office in 2021. His current research interests include computational
electromagnetics, electromagnetic scattering and radiation. He has authored or
coauthored more than 80 papers. He is the recipient of the Foundation for China
Excellent Young Investigators presented by the National Science Foundation
(NSF) of China in 2015.
