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Research ArticleA Study of a Wide-Angle Scanning Phased Array
Based on aHigh-Impedance Surface Ground Plane
Tian Lan , Qiu-Cui Li, Yu-Shen Dou, and Xun-Ya Jiang
Department of Light Source & Illuminating Engineering, Fudan
University, Shanghai 200344, China
Correspondence should be addressed to Xun-Ya Jiang;
[email protected]
Received 9 September 2018; Accepted 24 October 2018; Published
20 January 2019
Academic Editor: N. Nasimuddin
Copyright © 2019 Tian Lan et al. This is an open access article
distributed under the Creative Commons Attribution License,
whichpermits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
This paper presents a two-dimensional infinite dipole array
system with a mushroom-like high-impedance surface (HIS)
groundplane with wide-angle scanning capability in the E-plane. The
unit cell of the proposed antenna array consists of a dipoleantenna
and a four-by-four HIS ground. The simulation results show that the
proposed antenna array can achieve a widescanning angle of up to
65° in the E-plane with an excellent impedance match and a small
S11. Floquet mode analysis is utilizedto analyze the active
impedance and the reflection coefficient. Good agreement is
obtained between the theoretical results andthe simulations. Using
numerical and theoretical analyses, we reveal the mechanism of such
excellent wide scanning properties.For the range of small scanning
angles, these excellent properties result mainly from the special
reflection phase of the HISground, which can cause the mutual
coupling between the elements of the real array to be compensated
by the mutual couplingeffect between the real array and the mirror
array. For the range of large scanning angles, since the surface
wave (SW) modecould be resonantly excited by a high-order Floquet
mode TM−1,0 from the array and since the SW mode could be
convertedinto a leaky wave (LW) mode by the scattering of the
array, the radiation field from the LW mode is nearly in phase with
thedirect radiating field from the array. Therefore, with help from
the special reflection phase of the HIS and the designed LWmode of
the HIS ground, the antenna array with an HIS ground can achieve a
wide-angle scanning performance.
1. Introduction
Generally, the main beam of a planar phased array
cannoteffectively scan to large angles due to the mutual
couplingamong the antenna elements and the excited surface
waves(SWs), which can cause the reflection coefficient S11
toincrease rapidly [1]. Several different approaches have
beenapplied to improve the radiation performance of planarphased
arrays, such as a subarray technique for suppress-ing SWs [2],
inhomogeneous substrates [3], reducedsurface wave (RSW) antenna
elements [4], and defectedground structures [5].
In the recent years, there has been an increasing inter-est in
utilizing high-impedance surface (HIS) [6] structuresin array
design. Because of their unique reflection phaseand bandgap
characteristics, HISs provide a new degreeof freedom in antenna
design; for example, HISs arewidely used as the ground planes of
arrays to suppressSW generation using the HIS gap [7–9].
They can also be placed between array elements [10,11] to reduce
the mutual coupling between those elementsto extend the scanning
range of the beam.
Recently, researchers have explored whether the SWmodes
supported by HISs can help to improve certainaspects of the
radiation performance of antennas or antennaarrays. In [12], it is
shown that the TE SW is resonantlyexcited and the edge radiation is
favorable for broadeningthe bandwidth and maintaining the radiating
pattern in thebandwidth. Li et al. [13] proposed that one dipole
antennaand two parasitic elements should be placed in close
proxim-ity to a finite HIS ground. Using the advantage of TE
SWpropagation on an HIS and the HIS edge radiation, a widebeam
tilting toward the endfire direction is achieved. Then,Li et al.
[14] designed an HIS-based linear array with eightdipoles whereby
the HIS edge radiation of the SW supportedby the HIS is also
utilized to achieve wide-angle scanning inthe H-plane. Thus, these
works demonstrate that an HIS SWthat causes HIS edge radiation can
improve the radiation
HindawiInternational Journal of Antennas and PropagationVolume
2019, Article ID 8143104, 10
pageshttps://doi.org/10.1155/2019/8143104
http://orcid.org/0000-0001-6071-0184http://orcid.org/0000-0003-0632-3524https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2019/8143104
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performance for single elements or small arrays on an
HIS.However, this method cannot be applied to a large arrayon an
HIS since the importance of edge radiation will be sig-nificantly
reduced with an increasing number of array ele-ments, and scan
blindness may occur because the SW canabsorb large amounts of
radiating energy. For large antennaarrays and infinite arrays, is
it possible to find a designwhereby the SW mode supported by the
HIS ground canimprove the wide-angle scanning performance? To the
bestof our knowledge, there is no relevant research on this
topic.
In this paper, we will design a two-dimensional infinitedipole
array system with a mushroom-like HIS groundplane. With the unique
reflection phase characteristics ofthe HIS ground plane, this array
can achieve a wide scanningangle of up to 65° in the E-plane with a
small S11. Then, wewill analyze the relationship between the
reflection phase ofthe HIS and the active impedance of the array by
Floquetmode analysis, which demonstrates that the reflection
phaseof HIS is a parameter that is critical to the antenna’s
radia-tion performance, and reveal the mechanisms behind ourdesign.
We find that there are two mechanisms supportingthe wide-angle
performance in such infinite arrays. (i) Thecoupling effect between
real antenna elements and the mir-ror antenna elements with an HIS
as the ground can cancelthe mutual coupling between the real
antenna elements. Thiscanceling ensures the very good radiation
performance for asmall scanning angle range 0°-20°. (ii) For large
scanningangles of 20°-65°, the downward high-order Floquet
radiat-ing field from the antenna array can excite the SW modeof
the HIS, and with periodic scattering of the antenna array,such an
SW mode can be transformed into a leaky wave(LW) mode [15]. Due to
the specially designed reflectionphase of the HIS, the radiation
from the LW mode can becoherently added to the direct upward
radiating field fromthe antenna array in a wide-angle range. The
imaginary partof the active impedance is thereby maintained at a
smallvalue, while the real part remains almost constant over awide
scanning angle range.
This paper is structured as follows. An infinitetwo-dimensional
dipole array with a mushroom-like HISground plane is proposed, and
the simulation results ofthe active impedance and reflection
coefficient S11 of ourdesign are presented in Section 2. Then, we
use Floquetmode analysis to calculate the active impedance and
thereflection coefficient S11 of the system and show the
rela-tionship between the reflection phase of the HIS and theactive
impedance of the array in Section 3.1. The mecha-nisms of the
excellent performance of our design are ana-lyzed in detail in
Section 3.2 and Section 3.3. Finally, weconclude our paper in
Section 4.
2. Dipole Array Design Based on HIS GroundPlane and HFSS
Simulations
In general, to ensure an excellent radiation performance,we hope
that the field reflected by the ground plane willbe in phase with
the direct radiation field of the antennaarray. However, for
traditional design with the PEC asground, we can only guarantee the
“in phase” property
for one angle (e.g., the zero scanning angle) since
thereflection phase is a constant. The phase differencebetween the
reflected field and the direct radiating fieldincreases when the
scanning angle becomes larger. Becausethe reflection phase of HIS
varies with the incident angle,it is possible to achieve the “in
phase” property within acertain range of scanning angle if we
design a specialHIS as ground. In addition, because of its complex
andunique reflection phase, the SW mode of HIS groundcan be very
different from the traditional SW mode ofPEC which will weaken the
radiation performance ofarrays in general. We will show that the SW
mode ofthe HIS can greatly improve the radiation performanceof
antenna arrays under a certain design.
After optimization of the parameters of dipole antenna,the HIS
ground and the dielectric substrate between them,we design a
two-dimensional infinite dipole array, and thesimulation model of
the unit cell of our design is shown inFigure 1. This unit cell
consists of a dipole antenna printedon substrate back by the
four-by-four HIS ground plane.The lattice constant is a = b = λ/2 =
30mm, where λ denotesthe wavelength in free space at the operation
frequency10GHz. The length and width of the infinitely thin
dipoleare l = 10 32mm and t = 0 06mm, respectively. The
regionbetween dipole and HIS is filled with dielectric substrate
withthe thickness d = 5 7mm and the permittivity ε1 = 2 55. ForHIS
design, an infinitely thin square patch with a side lengthofw = 3
15mm is printed on top of a grounded substrate witha dielectric
constant of ε2 = 4 4 and a thickness of h = 1 95mm. The length of
the gap between adjacent patches is g = 0 6mm. Vertical conducting
paths with a diameter of via = 0 36mmare used to connect the upper
patches to the ground plane.
The infinite array performance was analyzed based on thisunit
cell using a commercial full-wave EM simulation softwareHigh
Frequency Structure Simulation (HFSS) which appliesFloquet’s
theorem of periodic boundaries. While this methodaccounts for the
mutual coupling between the array elements,it does not include the
effect of edge elements in the case offinite arrays. In the
simulation setup, periodic boundaries areused at the sides of the
unit cell of antenna array in both xand y directions, and a Floquet
port terminates the setupfrom the top. The radiating modes from the
structure sur-face propagate within air, filled between the unit
cell surfaceand Floquet port, and are absorbed from the top.
Thedipole is fed at the center by a lumped port with a
portimpedance of 16 ohms so as to match the input impedanceat
broadside. Next, the active input impedance and themagnitude of the
reflection coefficient S11 versus the scan-ning angle and the
scanning performance will be calculatedby ANSYS HFSS
simulations.
Figure 2 shows the active impedance variations dur-ing an
E-plane scan, where the solid lines are obtainedfrom HFSS
simulations, while the dashed lines will beexplained in the next
section. It can be seen that theimaginary part of an active
impedance is maintained ata small value, while the real part
remains almost con-stant within the scanning angle range of 0°−65°,
whichindicates that the array exhibits excellent impedance-matching
performance.
2 International Journal of Antennas and Propagation
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We calculate the magnitude of the reflection coeffi-cient S11 of
the HIS-ground-plane-based array duringan E-plane scan and compare
it with that of an arraywith a PEC ground plane, as shown in Figure
3, wherethe red solid line is the case of the HIS ground and
theblue solid line is the case of the PEC ground plane.The
comparison reveals that the impedance-matchingperformance of the
array with the HIS ground planeis significantly better than that of
the array with thePEC ground plane. From Figure 3, we can see
thatthe array can achieve a wide scanning angle of up to65° with
S11 < 0 4. In addition, for the case of theHIS ground plane, the
simulated scan performance ofour array in the E-plane at 10 GHz is
shown inFigure 4. We can see that the main beam of our arraycan
scan from -65° to +65° in the E-plane with a gainfluctuation less
than 3 dB and a maximum sidelobe
level (SLL) less than -10 dB. The radiation
patternscorresponding to the main beam toward 0°, ±20°,±40°, and
±65° are particularly plotted in Figure 4.By contrast, for the case
of the PEC ground, the arraycan only scan its main beam to 35° at
the same stan-dard, and scan blindness appears at 45° since the
SWmode is excited. As a result, the proposed array canscan its main
beam over the range from -65° to +65°.In the next section, we will
analyze why the proposedsystem can achieve wide-angle scanning.
3. Discussion
In the previous section, we introduced the design of aninfinite
dipole array that can achieve wide-angle scan-ning in the E-plane.
In this section, we will analyzethe relationship between the HIS
reflection phase andthe active impedance of the array via Floquet
modeanalysis to show that the reflection phase of HIS is aparameter
that is critical to the antenna’s radiation per-formance, thereby
revealing the mechanisms behind ourdesign.
3.1. Floquet Mode Analysis. In this subsection, Floquet
modeanalysis is used to calculate the active input impedance andthe
magnitude of the reflection coefficient S11 versus thescanning
angle. Then, we compare the theoretical resultsfrom the Floquet
mode analysis with those of the HFSSsimulations. Additionally, the
effect of the HIS reflectionphase is clearly shown in the
analysis.
via
l
t
b a
𝜀2
𝜀1
Z
YX
h
d
g
W
Z Y
X
Figure 1: Structure of the dipole array on the HIS ground
plane.The top figure gives a view of a unit cell of the infinite
phaseddipole array printed on the HIS ground plane. The bottom
figureshows 4-by-4 unit cells of the HIS ground plane. Some
keyparameters are as follows: the square patch size w = 3 15mm,
thegap between patches g = 0 6mm, the via size via = 0 36mm,
thedipole size l = 10 32mm (length) and t = 0 06mm (width),
thesubstrate thickness h = 1 95mm and d = 5 7mm, the
latticeconstant is a = b = 30mm, and the substrate permittivity ε1
= 2 55and ε2 = 4 4.
0 15 30 45 60 75 90Scanning angle (deg)
−50
−25
0
25
50
Impe
danc
e (oh
ms)
E-plane scanning
HFSS Re(Z)HFSS Im(Z)
Theoretical Re(Z)Theoretical Im(Z)
Figure 2: Active input impedance of the dipole array on
HISground plane shown in Figure 1 during an E-plane scan,
wheresolid lines are obtained from HFSS and dashed lines are
calculatedfrom equation 1.
3International Journal of Antennas and Propagation
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According to Floquet mode analysis [16], the active
inputimpedance ZFL of an infinite antenna array with a
generalground can be obtained by
with
yTEmn = YTE+mn − jY
TE−mn cot
k−zmnh − θTEmn
2, 2
YTE+mn =ωϵ0k+zmn
YTM−mn =ωϵ0ϵrk−zmn
, 3
yTMmn = YTM+mn − jY
TM−mn cot
k−zmnh − θTMmn
2, 4
YTM+mn =k+zmnωμ0
,
YTE−mn =k−zmnωμ0
,5
kxmn = kx0 +2mπa
,
kymn = ky0 +2nπb
,6
kzmn = k2 − k2xmn − k
2ymn, 7
where k is the wavenumber in a medium or in free space,θTE/TMmn
are the reflection phases of the Floquet modesreflected by a
general ground, e.g., the HIS in our design.In equation 6, kx0 and
ky0 are phase progression factorsrelated to the intended direction
of radiation. If θ, ϕ areangles in spherical coordinate system
related to the intendeddirection of radiation, then
kx0 = k0 sin θ cos ϕ,
ky0 = k0 sin θ sin ϕ8
We note that the term in equation 1 with the reflectionphase of
the HIS ground shows the contribution of reflectedwaves to the
active impedance.
From equation 1, we can calculate the active impedanceand
reflection coefficient S11 and compare the results withthose of the
HFSS simulations. If the results fit very well,then we have
confidence that our analysis is correct. How-ever, in order to
calculate the active impedance, we must firstobtain the reflection
phases θTE/TMmn of the HIS.
We calculate the reflection phases of different orders ofFloquet
modes using EastWave commercial software basedon the
finite-difference time-domain (FDTD) method. Wecan then bring the
reflection phases θTE/TMmn into equation 1and obtain the
contribution to the active impedance fromall Floquet modes, as
shown by the red and blue dashed linesin Figure 2. Meanwhile, we
can calculate the reflection coef-ficient S11 by equation 1. We
find that the theoretical resultsare in good agreement with the
simulation results. More-over, from the calculated results, we find
that the mostimportant Floquet modes for our antenna array which
can
−60 −40 −20 0 20 40 60Theta (degree)
−30
−20
−10
0
10
20
30
40
Gai
n (d
B)
−80 80
Figure 4: Simulated pattern scanning characteristics in the
E-planeat 10GHz with the main beam pointing direction of θ= 0°,
±20°,±40°, ±65°, respectively.
0 15 30 45 60 75 90Scanning angle (deg)
0
0.2
0.4
0.6
0.8
1
Refle
ctio
n co
effici
ent
E-plane scanning
HFSS S11 withHIS groundHFSS S11 withPEC ground
Theoretical S11 withHIS groundTheoretical S11 withPEC ground
Figure 3: Comparison of the reflection coefficient in the
E-plane scanfor the dipole array on the HIS ground plane and PEC
ground plane,where the solid lines are obtained fromHFSS and the
dashed lines arecalculated from equation 1. For the case of the PEC
ground plane, notonly is the HIS ground replaced by the PEC but
also the dipole size istuned to have a resonance at broadside.
ZFL kx0, ky0 =4ab
l2
π2〠∞
m=−∞〠∞
n=−∞
k2ymnyTEmn
+ k2xmn
yTMmn
cos kxmnl/21 − kxmnl/π
2sin c kymnt/2k20 − k
+2zmn
,
1
4 International Journal of Antennas and Propagation
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affect the impedance and S11 are the TM0,0 mode and theTM−1,0
mode. This finding is easy to understand for two rea-sons. The
first is that we consider only E-plane scans in thiswork, so the
TMmodes dominate the far-field radiation. Thesecond is that except
for the TM0,0 mode and the TM−1,0mode, all TM modes are evanescent
waves in all scanningangle ranges, and they contribute only small
perturbationsof the active impedance and S11.
The calculated results of the reflection phases of theTM0,0 mode
and the TM−1,0 mode are shown in Figure 5.We can see that the
reflection of the TM0,0 mode decaysalmost linearly with the
scanning angle within the range of0°−20°, which is very important
for the excellent radiatingproperties for small scanning angles.
For the TM−1,0 mode,its field is an evanescent wave so that the
reflection phaseis zero when the scanning angle is smaller than
20°. Oncethe scanning angle is larger than 20°, the field of the
TM
−1,0 mode propagates in the substrate material and the
reflec-tion phase of this mode is no longer zero. With the
reflectionphases, the contributions from both the TM0,0 mode and
theTM−1,0 mode on the active impedance are shown by thedashed lines
in Figure 6. The real part of the active imped-ance obtained from
equation 1 with the contributions ofonly these two modes is in good
agreement with the resultobtained from all modes, while the
changing trend of theimaginary part of the impedance is essentially
the same asthat with the contributions of all modes. Therefore,
theremust be some basic mechanisms which support such
goodagreement. In the next two subsections, the mechanisms ofthe
excellent performance of the array with the HIS groundplane will be
analyzed in detail.
3.2. Effect of the HIS Ground Plane in a Range of SmallScanning
Angles. In this subsection, we demonstrate how theHIS ground plane
improves the scanning performance of theantenna array over the
range of small scanning angles 0°−20°considering the special
reflection phase of the HIS. For thesmall scanning angles, the
dominant mode is the TM0,0 modebecause the field of the TM−1,0mode
is still an evanescent wave.
First, we make a naive assumption that the reflectionphase of
the TM0,0 mode from the HIS ground is constant,i.e., it is
maintained at the value of zero scanning angle−37° for any scanning
angle, while the reflection phasesθTE/TMmn of the other modes still
change in their original man-ner. Then, we can calculate the active
impedance versus thescanning angle using equation 1, and the result
is shown bythe dashed lines in Figure 7. Compared with the original
cal-culated results shown by the solid line in Figure 7, we can
seethat if the HIS reflection phase of TM0,0 mode was a con-stant
similar to PEC, the original excellent properties suchas the
almost-constant real part and the nearly zero imagi-nary part at
scanning angles less than 20°, would bedestroyed. Clearly, the only
explanation for such destructionis that the changing HIS reflection
phase versus the scanningangle shown by the blue line in Figure 5
is very critical forsmall scanning angles.
From the view of an image antenna, we can more clearlysee the
effect of the reflection phase of an HIS. We empha-size that there
are two different approaches to study the
physical effects of the reflected field from the ground.
Oneapproach is to study the reflected field directly as we
didbefore. The other approach is to introduce the imageantenna (or
image antenna array) whose radiating field issubstituted by the
reflected field with the exact same phaseand magnitude. Hence, the
effect of the reflected field onthe real antenna array could be
viewed as the couplingbetween the real antenna array and the image
antenna array.To clearly show the coupling effects on the active
imped-ance, we simplify the infinite two-dimensional array to
themodel shown in Figure 8, where a, b, and c are real dipoleson an
infinitely large ground with reflection phase θr . With-out the
ground plane, the impedance of antenna b could beobtained by
Z0b,in = Zb + Zabejθab + Zcbejθcb , 9
where Zb is the self-impedance, Zij is the mutual imped-ance
between elements i and j, and θij is the input currentphase
difference between elements i and j. It is well knownthat the
Z0b,in changes with the scanning angle since theinput current phase
difference θij changes with thescanning angle.
With a ground, image dipoles a′, b′, and c′ should beintroduced
and the active impedance of element b is
Zb,in = Zb + Zabejθab + Zcbejθcb + Za′bej θab+θr + Zb′be
jθr + Zc′bej θcb+θr
10
From equation 10, we can see that the active impedance
0 15 30 45 60 75 90Scannig angle (deg)
−70
−60
−50
−40
−30
−20
−10
0
10
Refle
ctio
n ph
ase (
deg)
𝜃TM0,0𝜃TM−1,0
Figure 5: Reflection phases of the Floquet modes reflected atthe
HIS versus the scanning angle, where the blue (red) solidline is
the reflection phase of the m = 0 m = −1 -order Floquetmode, and
the remaining reflection phases are approximatelyequal to zero.
5International Journal of Antennas and Propagation
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of antenna b varies with the scanning angle if the
reflectionphase of the surface is constant. However, for an HIS,
thereflection phase decreases almost linearly with the
scanningangle as shown by the blue line in Figure 5. With
increasingscanning angle, the change caused by Zabejθab + Zcbejθcb
couldbe canceled by the change caused by Za′bej θab+θr + Zb′bejθr+
Zc′bej θcb+θr . In other words, the mutual coupling effectbetween
elements of a real array at small scanning anglescan be compensated
by the mutual coupling effect fromthe mirror array, thereby greatly
improving the radiationperformance of the antenna array with an HIS
ground.
3.3. Effect of the HIS Ground Plane over a Range of
LargeScanning Angles. In the previous subsection, the improvingof
radiation efficiency in small scanning angles is explained.In this
subsection, we will demonstrate the new mechanismof the HIS ground
plane in improving the scanning perfor-mance of the antenna array
over a range of large scanningangles and reveal the effect of the
LW mode.
First, we detect the effect of the reflection phase of theHIS on
the TM−1,0 Floquet mode shown by the red line inFigure 5.
Similarly, at first we assume that the reflectionphase of the
θTM−1,0 of TM−1,0 mode from the HIS groundalways is zero for any
scanning angle, while the reflectionphases θTE/TMmn of all other
modes still change in their originalmanner. We can then calculate
the active impedance versusthe scanning angle by equation 1. The
results are shown bythe dashed lines in Figure 9. We can see that
when the scan-ning angle exceeds 20°, the imaginary part of the
activeimpedance begins to deviate from the original value andfor
larger scanning angles the deviating values becomelarger, which
indicates that the coupling effect between realantenna elements and
the mirror antenna elements with anHIS as the ground can cancel the
mutual coupling betweenthe real antenna elements. It is obvious
that the reflection
15 30 45 60 75Scanning angle (deg)
−50
−25
0
25
50
Impe
danc
e (oh
ms)
E-plane scanning
Theoretical Re(Z)Theoretical Im(Z)
Re(Z) with TM0,0 and TM−1,0 modeIm(Z) with TM0,0 and TM−1,0
mode
900
Figure 6: Contribution of TM0,0 and TM−1,0 mode to the active
impedance of the array, where the dashed lines are obtained with
only thecontributions of the two modes and the solid lines are the
results of the dashed lines in Figure 2.
0 5 10 15 20Scanning angle (deg)
−10
−5
0
5
10
15
20
Impe
danc
e (oh
ms)
Re (Z)Im (Z) Im(Z) with 𝜃TM = 37°
Re(Z) with 𝜃0,00,0
TM = 37°
Figure 7: Effect of θTM0,0 on active impedance in a small
scanningangle range. The dashed line is the case where the
reflection phaseof θTM0,0 is a constant, while the solid lines are
the same as theresults of the dashed lines in Figure 2.
a b c
a’ b’ c’
dZ = 0
Figure 8: Simplified structure of the dipole array, where a, b,
and care real dipoles, a′, b′, and c′ are image dipoles, and an HIS
groundplane is placed at z = 0.
6 International Journal of Antennas and Propagation
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phase of the TM−1,0 Floquet mode from the HIS is very crit-ical
for large scanning angles.
The effects of the reflection phase of the TM−1,0 Floquetmode
imply the new mechanism which influences the radi-ating properties
of the antenna array. In the next paragraphs,we will reveal the
mechanism step by step. First, we showthat at large scanning
angles, this TM−1,0 Floquet modecan excite the SW mode supported by
the HIS substrate(composed of the HIS ground plane and the
dielectric layerabove it, which is shown by the inset in Figure
10). Then,we illustrate that this SW mode can be converted into
theLW mode by the periodic modulation of the array. Whenthe TM−1,0
resonantly excites the LW mode, the LW moderadiation is almost in
phase with the direct radiating fieldfrom the array, so that the
array performance at a large scan-ning angle could be
excellent.
Using eigenmode solver of HFSS, we can calculate thedispersion
curves of the unit cell of the HIS substrate. Thesimulation model
of the unit cell is shown as the inset inFigure 10. In the
simulation setup, periodic boundaries areused at the sides of the
unit cell, and an absorbing material(PML) terminates the setup from
the top. The radiatingmodes from the structure surface propagate
within air, filledbetween the unit cell surface and PML, and are
absorbedfrom the top. The two modes TM0 and TM1 supported bythis
HIS substrate are shown in Figure 10 by the solid blueand red
lines. Since they are lower than the light line whichis shown by a
black dashed line, both of them are SW modes.Generally, the
condition for the existence of such SW modesis θr + θup + 2kzd =m ×
2π, where θr is the reflection phaseof the HIS ground, θup is the
phase of the total reflection atthe interface between the medium
and air, kz is the wavevec-tor in the z direction in the substrate
dielectric material, and
m is the order of the SW modes. Clearly, the properties ofSW
modes are also influenced by the reflection phase ofthe HIS in a
subtle way. In this paper, the working frequencyis 10GHz and the
mode of TM0 is very far away from thisfrequency; we neglect the TM0
mode in this research. Oncethe propagation constant of the Floquet
mode of antennaarray is equal to the propagation constant of TM1
mode ofHIS substrate, TM1 mode will be excited [1].
However, this TM1 mode can be transferred into LWmode. Since the
period a of the antenna array is four timeslarger than the period
of the HIS substrate, the dispersioncurve of TM1 should be folded
back using a as the period,as shown by the red dashed line in
Figure 10. Now the reddashed line is above the light line (the
black dashed line),which means the SW mode becomes the LW mode
whichcould radiate. Actually, we have also calculated the
disper-sion curves of the unit cell of the antenna array, which
isshown as an inset in Figure 11. As we expected, the disper-sion
curve of the mode 2 above the light line is like thedashed line in
Figure 10. The physical reason for the trans-formation of the SW
mode to the LW mode is shown inFigure 12. If the SW mode TM1 of the
HIS substrate couldbe excited by an external field, the SW mode
will experiencethe periodic scattering by the antenna array and the
scat-tered field could be a radiating field.
With all this preparation, we now can compose all thepieces
together to show the mechanism of radiation withthe help of the SW
mode. When the antenna array scans atlarge angles, the Floquet mode
TM−1,0 becomes the propagat-ing field and it can excite the LW
mode, which is from theSW of the HIS substrate with the periodic
scattering of thearray. Then, with the help of the LWmode, the
total radiatingperformance of the antenna array could be greatly
improvedfor large scanning angles.
0 15 30 45 60 75 90Scanning angle (deg)
−50
−25
0
25
50
Impe
danc
e (oh
ms)
Re(Z)Im(Z)
𝜃TM−1,0 = 0Re(Z) with Im(Z) with 𝜃TM−1,0 = 0
Figure 9: Effect of θTM−1,0 on the active impedance over a range
oflarge scanning angle. The dashed line is the case where
thereflection phase of θTM−1,0 is zero, while the solid lines are
the sameas the results of the dashed lines in Figure 2.
15×109
10
Freq
uenc
y (H
z)
5
00 1 2
kx(𝜋/a)
TM0 modeTM1 mode
Light lineLeaky mode
3 4
Figure 10: Dispersion curves of the grounded HIS substrate,
wherethe blue and the red solid lines are the first two SW modes of
theHIS; the red dashed line is the LW mode supported by
thestructure composed of the HIS and the dipole array. The inset is
aschematic of a unit cell of the HIS substrate.
7International Journal of Antennas and Propagation
-
Finally, we qualitatively analyze the effect of the LWmode on
the scanning performance. As shown inFigure 12, we decompose the
radiation field of the array infree space into three parts: the
direct radiation field Edir ofthe antenna array, the reflected
field Er0,0 of the TM0,0 mode,and the radiation field ELW of the LW
mode. Based on theobservation that the LW mode field ELW is excited
by theFloquet mode TM−1,0 in the substrate, the LW mode fieldhas
the following general form:
ELW = aγ
j ω − ω0 + γ, 11
where a, ω0, and γ are the complex amplitude, eigenfre-quency,
and attenuation constant of the LW mode, respec-tively, and ω is
the operating frequency of the antennaarray. Then, the total
radiation field Etotal can be expressed
as the sum of the direct radiation field Edir, the
reflectedfield of the TM0,0 mode, and the radiation field from
theLW mode excited by TM−1,0:
Etotal = Edir + Er0,0 + aγ
j ω − ω0 + γ12
When the scanning angle is relatively small, Edir and Er0,0
dominate the radiation field while the LW mode is difficultto
excite and its contribution could be neglected. As we havediscussed
in Section 3.2, the special changing of the HISreflection phase for
the Er0,0 mode can improve the scanningperformance. When the
scanning angle increases to a valuelarger than 40°, two conditions
for the excitation of theLWmode are satisfied. The first condition
is that the Floquetmode TM−1,0 becomes a propagating wave in the
substrate,and the second condition is that the LW mode
eigenfre-quency ω0 gradually decreases and is close to the
antennaworking frequency ω. Thus, ELW is almost resonantly
excitedby TM−1,0, and it is nearly in phase with Edir. This
mecha-nism explains why the LW mode can help the radiation ofthis
antenna array. Actually, the ELW strengthens withincreasing
scanning angle. At the angle range from 40° to65°, the LW mode
excitation can help the antenna radiation.However, when the
scanning angle becomes very large, e.g.,larger than 65°, imaginary
part of the active impedance rap-idly grows, which means that it
can absorb most of theenergy radiating from the antenna, as shown
in Figure 2.Finally, the LW excitation can generate scan blindness
atapproximately 76°.
To demonstrate that the LW mode is truly excited in ourmodel, we
have shown the field and the Poynting vector dis-tribution of the
LW mode in Figure 13(a) and the total fieldof our antenna array at
a scanning angle of 60° inFigure 13(b). As we predicted in Figure
12, when the LWmode is excited by the TM−1,0 mode, the Poynting
vectorshould be in the direction opposite to that of the
radiationin the substrate, which is true in Figures 13(a) and
13(b).From Figure 13(b), we also can see that the direct of the
radi-ation field on the antenna surface is nearly in phase with
theLW mode since both are shown in red.
4. Conclusion
An infinite two-dimensional dipole array with amushroom-like HIS
ground plane is designed, which canachieve a wide scanning angle of
up to 65° in the elevationplane. The active impedance and S11 of
the array calcu-lated via theoretical Floquet analysis are in good
agree-ment with numerical simulation results. Two newmechanisms
which support the excellent performance ofsuch an array at a wide
scanning angle are demonstratedtheoretically and numerically. In
the range of small scan-ning angles, these excellent properties are
mainly fromthe special reflection phase of the HIS ground, which
cancause the mutual coupling between the elements of a realarray be
compensated by the mutual coupling effect fromthe mirror array. For
the range of large scanning angles,since the surface wave (SW) mode
could be resonantly
0 0.25 0.5 0.75 1kx(𝜋/a)
0
2
4
6
8
10
12
14
Freq
uenc
y (H
z)
×109
Light lineSW modeLW mode
Figure 11: Dispersion curves of the HIS-based dipole array unit
cellusing an HFSS simulation. The red and blue solid lines are the
SWmode and LW mode of the unit cell, respectively. The inset is
aschematic of a unit cell of our dipole array.
ELW Edir
TM−1,0Substrate
Free space
TM0,0
Er0,0
HIS
Figure 12: Schematic illustration of the propagation paths of
Edir,Er0,0, and ELW, where the orange, blue, and red lines in the
freespace are the propagation paths of Edir, E
r0,0, and ELW, respectively,
while the blue and red lines in the substrate are the
propagationpaths of TM0,0 and TM−1,0.
8 International Journal of Antennas and Propagation
-
excited by high-order Floquet mode TM−1,0 from the arrayand the
SW mode could be converted into a leaky wavemode by the scattering
of the array, the radiation fieldfrom the LW mode is nearly in
phase with the direct radi-ating field from the array. Therefore,
with the help fromthe special reflection phase of the HIS and the
designedLW mode on the HIS ground, the antenna array with anHIS
ground can achieve wide-angle scanning performance.We think these
mechanisms could be widely used in thedesign of wide-angle scanning
arrays.
Data Availability
All data included in this study are available upon request
bycontact with the corresponding author.
Conflicts of Interest
The authors declare that there are no conflicts of
interestregarding the publication of this paper.
Acknowledgments
This work was supported by the National Natural
ScienceFoundation of China under Grant 11334015 and theNational Key
Research and Development Project of Chinaunder Grants
2016YFA0301103 and 2018YFA0306201.
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