a study of a wide-angle scanning phased array based on a ...mode of the his ground, the antenna...

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

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

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

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

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


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.


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.


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.


−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.


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.


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.

References

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[9] L. Li, C.-H. Liang, and C.-H. Chan, “Waveguide end-slotphased array antenna integrated with electromagnetic band-gap structures,” Journal of Electromagnetic Waves and Appli-cations, vol. 21, no. 2, pp. 161–174, 2012.

1.0E + 6

0.0E + 0

9.0E + 5

8.0E + 5

1.0E + 5

2.0E + 5

3.0E + 5

4.0E + 5

5.0E + 5

6.0E + 5

7.0E + 5

H field (A/m)

Z

X

(a)

Z

X

1.0E + 1

0.0E + 0

9.0E + 0

8.0E + 0

1.0E + 0

2.0E + 0

3.0E + 0

4.0E + 0

5.0E + 0

6.0E+0

7.0E + 0

H field (A/m)

(b)

Figure 13: Comparison of field distributions and energy flow directions between the LW eigenfield and the radiation field of the array at aradiation angle of 60°, where the color distribution and the arrow direction represent the magnitude of the magnetic field and thedirection of the Poynting vector, respectively. (a) LW mode eigenfield and the direction of the Poynting vector; (b) total field and thedirection of the Poynting vector of our array.


[10] F. Yunqi and Y. Naichang, “Elimination of scan blindness inphased array of microstrip patches using electromagneticbandgap materials,” IEEE Antennas and Wireless PropagationLetters, vol. 3, no. 1, pp. 63–65, 2004.

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