A Study Of a Wide-Angle Scanning Phased Array Based On a High-Impedance Surface Ground Plane

Transcription

1 1 A Study Of a Wide-Angle Scanning Phased Aay Based On a High-Impedance Suface Gound Plane Tian Lan, Qiu-Cui Li, Yu-Shen Dou, Xun-Ya Jiang axiv: v1 [physics.app-ph] 15 Jan 2019 Abstact This pape pesents a two-dimensional infinite dipole aay system with a mushoom-like high-impedance suface (HIS) gound plane with wide-angle scanning capability in the E-plane. The unit cell of the poposed antenna aay consists of a dipole antenna and a fou-by-fou HIS gound. The simulation esults show that the poposed antenna aay can achieve a wide scanning angle of up to 65 in the E-plane with an excellent impedance match and a small S11. Floquet mode analysis is utilized to analyze the active impedance and the eflection coefficient. Good ageement is obtained between the theoetical esults and the simulations. Using numeical and theoetical analyses, we eveal the mechanism of such excellent wide scanning popeties. Fo the ange of small scanning angles, these excellent popeties esult mainly fom the special eflection phase of the HIS gound, which can cause the mutual coupling between the elements of the eal aay to be compensated by the mutual coupling effect between the eal aay and the mio aay. Fo the ange of lage scanning angles, since the suface wave (SW) mode could be esonantly excited by a high-ode Floquet mode TM 1,0 fom the aay and since the SW mode could be conveted into a leaky wave (LW) mode by the scatteing of the aay, the adiation field fom the LW mode is nealy in phase with the diect adiating field fom the aay. Theefoe, with help fom the special eflection phase of the HIS and the designed LW mode of the HIS gound, the antenna aay with an HIS gound can achieve wide-angle scanning pefomance. Index Tems High impedance sufaces (HISs), phased aays, wide-angle scanning, suface waves(sws). I. INTRODUCTION Geneally, the main beam of a plana phased aay cannot effectively scan to lage angles due to the mutual coupling among the antenna elements and the excited suface waves (SWs), which can cause the eflection coefficient S11 to incease apidly [1]. Seveal diffeent appoaches have been applied to impove the adiation pefomance of plana phased aays, such as a subaay technique fo suppessing SWs [2], inhomogeneous substates [3], educed suface wave (RSW) antenna elements [4], and defected gound stuctues [5]. In ecent yeas, thee has been inceasing inteest in utilizing high-impedance suface (HIS) [6] stuctues in aay design. Because of thei unique eflection phase and bandgap chaacteistics, HISs povide a new degee of feedom in antenna design; fo example, HISs ae widely used as the gound planes of aays to suppess SW geneation using the HIS gap [7] [9]. They can also be placed between aay elements [10], [11] to This wok was suppoted by the National Natual Science Foundation of China unde Gant , and the National Key Reseach and Development Poject of China unde Gant 2016YFA , 2018YFA These authos ae with the Depatment of Light Souce & Illuminating Engineeing, Fudan Univesity, Shanghai , China ( jiangxunya@fudan.edu.cn). educe the mutual coupling between those elements to extend the scanning ange of the beam. Recently, eseaches have exploed whethe the SW modes suppoted by HISs can help to impove cetain aspects of the adiation pefomance of antennas o antenna aays. In [12], it is shown that the TE SW is esonantly excited and the edge adiation is favoable fo boadening the bandwidth and maintaining the adiating patten in the bandwidth. Li et al. [13] poposed that one dipole antenna and two paasitic elements be placed in close poximity to a finite HIS gound. Using the advantage of TE SW popagation on an HIS and the HIS edge adiation, a wide beam tilting towad the endfie diection is achieved. Then, Li et al. [14] designed an HISbased linea aay with eight dipoles wheeby the HIS edge adiation of the SW suppoted by the HIS is also utilized to achieve wide-angle scanning in the H-plane. Thus, these woks demonstate that an HIS SW that causes HIS edge adiation can impove the adiation pefomance fo single elements o small aays on an HIS. Howeve, this method cannot be applied to a lage aay on an HIS since the impotance of edge adiation will be significantly educed with an inceasing numbe of aay elements, and scan blindness may occu because the SW can absob lage amounts of adiating enegy. Fo lage antenna aays and infinite aays, is it possible to find a design wheeby the SW mode suppoted by the HIS gound can impove the wide-angle scanning pefomance? To the best of ou knowledge, thee is no elevant eseach on this topic. In this pape, we will design a two-dimensional infinite dipole aay system with a mushoom-like HIS gound plane. With the unique eflection phase chaacteistics of the HIS gound plane, this aay can achieve a wide scanning angle of up to 65 in the E-plane with a small S11. Then, we will analyze the elationship between the eflection phase of the HIS and the active impedance of the aay by Floquet mode analysis, demonstate that the eflection phase of HIS is a paamete that is citical to the antenna s adiation pefomance, and eveal the mechanisms behind ou design. We find that thee ae two mechanisms suppoting the wideangle pefomance in such infinite aays: (i) The coupling effect between eal antenna elements and the mio antenna elements with an HIS as the gound can cancel the mutual coupling between the eal antenna elements. This canceling ensues the vey good adiation pefomance fo a small scanning angle ange (ii) Fo lage scanning angles of 20-65, the downwad high-ode Floquet adiating field fom the antenna aay can excite the SW mode of the HIS, and with peiodic scatteing of the antenna aay, such an SW

2 2 z y x y t x d h b a ₁ ₂ g via l w Fig. 1. Stuctue of the dipole aay on the HIS gound plane. The top figue gives a view of a unit cell of the infinite phased dipole aay pinted on the HIS gound plane. The bottom figue shows 4-by-4 unit cells of the HIS gound plane. Some key paametes ae as follows: the squae patch size w = 3.15 mm, the gap between patches g = 0.6 mm, the via size via = 0.36 mm, the dipole size l = mm (length) and t = 0.06 mm (width), the substate thickness h = 1.95 mm and d = 5.7 mm, the lattice constant is a = b = 30 mm, and the substate pemittivity ε 1 =2.55 and ε 2 =4.4. mode can be tansfomed into a leaky wave (LW) mode [15]. Due to the specially designed eflection phase of the HIS, the adiation fom the LW mode can be coheently added to the diect upwad adiating field fom the antenna aay in a wide angle ange. The imaginay pat of the active impedance is theeby maintained at a small value, while the eal pat emains almost constant ove a wide scanning angle ange. This pape is stuctued as follows. An infinite twodimensional dipole aay with a mushoom-like HIS gound plane is poposed, and the simulation esults of the active impedance and eflection coefficient S11 of ou design ae pesented in Sec II. Then, we use Floquet mode analysis to calculate the active impedance and the eflection coefficient S11 of the system and show the elationship between the eflection phase of the HIS and the active impedance of the aay in Sec III-A. The mechanisms of the excellent pefomance of ou design ae analyzed in detail in Sec III-B and Sec III-C. Finally, we conclude ou pape in Sec IV. II. DIPOLE ARRAY DESIGN BASED ON HIS GROUND PLANE AND HFSS SIMULATIONS In geneal, to ensue excellent adiation pefomance, we hope that the field eflected by the gound plane will be inphase with the diect adiation field of the antenna aay. Howeve, fo taditional design with the PEC as gound, we can only guaantee the in-phase popety fo one angle (e.g., the zeo scanning angle) since the eflection phase is a constant. The phase diffeence between the eflected field and the diect adiating field inceases when the scanning angle becomes lage. Because the eflection phase of HIS vaies with the incident angle, it is possible to achieve the in phase popety within a cetain ange of scanning angle if we design a special HIS as gound. In addition, because of its complex and unique eflection phase, the SW mode of HIS gound can be vey diffeent fom the taditional SW mode of PEC which will weaken the adiation pefomance of aays in geneal. We will show that the SW mode of the HIS can geatly impove the adiation pefomance of antenna aays unde cetain design. Afte optimization of the paametes of dipole antenna, the HIS gound and the dielectic substate between them, we design a two-dimensional infinite dipole aay, and the simulation model of the unit cell of ou design is shown in Fig. 1. This unit cell consists of a dipole antenna pinted on substate back by the fou-by-fou HIS gound plane. The lattice constant is a = b = λ/2 = 30 mm, whee λ denotes the wavelength in fee space at the opeation fequency 10 GHz. The length and width of the infinitely thin dipole ae l = mm and t = 0.06 mm espectively. The egion between dipole and HIS is filled with dielectic substate with the thickness d = 5.7 mm and the pemittivity ε 1 = Fo HIS design, an infinitely thin squae patch with a side length of w = 3.15 mm is pinted on top of a gounded substate with a dielectic constant of ε 2 = 4.4 and a thickness of h = 1.95 mm. The length of the gap between adjacent patches is g = 0.6 mm. Vetical conducting paths with a diamete of via = 0.36 mm ae used to connect the uppe patches to the gound plane. The infinite aay pefomance was analyzed based on this unit cell using a commecial full-wave EM simulation softwae High Fequency Stuctue Simulation (HFSS) which applies Floquet s theoem of peiodic boundaies. While this method accounts fo the mutual coupling between the aay elements, it does not include the effect of edge elements in the case of finite aays. In the simulation setup, peiodic boundaies ae used at the sides of the unit cell of antenna aay in both x and y diections, and a Floquet pot teminates the setup fom the top. The adiating modes fom the stuctue suface popagate within ai, filled between the unit cell suface and Floquet pot, and ae absobed fom the top. The dipole is fed at the cente by a lumped pot with a pot impedance of 16 ohms so as to match the input impedance at boadside. Next, the active input impedance, the magnitude of the eflection coefficient S11 vesus the scanning angle and the scanning pefomance

3 3 Fig. 2. Active input impedance of the dipole aay on HIS gound plane shown in Fig. 1 duing an E-plane scan, whee solid lines ae obtained fom HFSS and dashed lines ae calculated fom Eq. 1. will be calculated by ANSYS HFSS simulations. Fig. 2 shows the active impedance vaiations duing an Eplane scan, whee the solid lines ae obtained fom HFSS simulations, while the dashed lines will be explained in the next section. It can be seen that the imaginay pat of active impedance is maintained at a small value, while the eal pat emains almost constant within the scanning angle ange of 0 65, which indicates that the aay exhibits excellent impedance-matching pefomance. We calculate the magnitude of the eflection coefficient S11 of the HIS-gound-plane-based aay duing an E-plane scan and compae it with that of an aay with a PEC gound plane, as shown in Fig. 3, whee the ed solid line is the case of the HIS gound and the blue solid line is the case of the PEC gound plane. The compaison eveals that the impedance-matching pefomance of the aay with the HIS gound plane is significantly bette than that of the aay with the PEC gound plane. Fom Fig. 3, we can see that the aay can achieve a wide scanning angle of up to 65 with S11 < 0.4. In addition, fo the case of the HIS gound plane, the simulated scan pefomance of ou aay in the E-plane at 10 GHz is shown in Fig. 4. We can see that the main beam of ou aay can scan fom -65 to +65 in the E-plane with a gain fluctuation less than 3 db and a maximum sidelobe level (SLL) less than -10dB. The adiation pattens coesponding to the main beam towad 0, ±20, ±40, ±65 ae paticulaly plotted in Fig. 4. By contast, fo the case of the PEC gound, the aay can only scan its main beam to 35 at the same standad, and scan blindness appeas at 45 since the SW mode is excited. As a esult, the poposed aay can scan its main beam ove the ange fom -65 to +65.In the next section, we will analyze why the poposed system can achieve wide-angle scanning. Fig. 3. Compaison of the eflection coefficient in the E-plane scan fo the dipole aay on the HIS gound plane and PEC gound plane, whee the solid lines ae obtained fom HFSS and the dashed lines ae calculated fom Eq. 1. Fo the case of the PEC gound plane, not only is the HIS gound eplaced by the PEC, but also the dipole size is tuned to have a esonance at boadside. Fig. 4. Simulated patten scanning chaacteistics in the E-plane at 10 GHz with the main beam pointing diection of θ = 0, ±20, ±40, ±65, espectively. III. D ISCUSSION In the pevious section, we intoduced the design of a infinite dipole aay that can achieve wide-angle scanning in the E-plane. In this section, we will analyze the elationship between the HIS eflection phase and the active impedance of the aay via Floquet mode analysis to show that the eflection phase of HIS is a paamete that is citical to the antenna s adiation pefomance, theeby evealing the mechanisms behind ou design.

4 4 A. Floquet Mode Analysis In this subsection, Floquet mode analysis is used to calculate the active input impedance and the magnitude of the eflection coefficient S11 vesus the scanning angle. Then, we compae the theoetical esults fom the Floquet mode analysis with those of the HFSS simulations. Additionally, the effect of the HIS eflection phase is clealy shown in the analysis. Accoding to Floquet mode analysis [16], the active input impedance Z FL of an infinite antenna aay with a geneal gound can be obtained by ( ) Z FL (k x0, k y0 ) = 4 l 2 k 2 ymn ab π 2 y TE + k2 xmn m= n= mn ymn TM [ ] cos(kxmn l/2) sin c(kymn t/2) 1 (k xmn l/π) 2 k0 2 k+2 zmn with (1) ymn TE = Ymn TE+ jymn TE- cot(kzmnh θmn/2) TE (2) Y TE+ mn = ωɛ 0 k + zmn Y TMmn = ωɛ 0ɛ k zmn (3) Fig. 5. Reflection phases of the Floquet modes eflected at the HIS vesus the scanning angle, whee the blue (ed) solid line is the eflection phase of the m = 0(m = 1)-ode Floquet mode, and the emaining eflection phases ae appoximately equal to zeo. ymn TM = Ymn TM+ jymn TM- cot(kzmnh θmn/2) TM (4) Y TM+ mn = k+ zmn ωµ 0 Y TEmn = k zmn ωµ 0 (5) k xmn = k x0 + 2mπ a k zmn = k ymn = k y0 + 2nπ b (6) k 2 k 2 xmn k 2 ymn (7) whee k is the wavenumbe in a medium o in fee space, θmn TE/TM ae the eflection phases of the Floquet modes eflected by a geneal gound, e.g., the HIS in ou design. In Eq. 6, k x0 and k y0 ae phase pogession factos elated to the intended diection of adiation. If (θ, φ) ae angles in spheical coodinate system elated to the intended diection of adiation, then k x0 = k 0 sin θ cos φ k y0 = k 0 sin θ sin φ (8) We note that the tem in Eq. 1 with the eflection phase of the HIS gound shows the contibution of eflected waves to the active impedance. Fom Eq.1, we can calculate the active impedance and eflection coefficient S11 and compae the esults with those of the HFSS simulations. If the esults fit vey well, then we have confidence that ou analysis is coect. Howeve, in ode to calculate the active impedance, we must fist obtain the eflection phases θmn TE/TM of the HIS. We calculate the eflection phases of diffeent odes of Floquet modes using EastWave commecial softwae based on the finite-diffeence time-domain (FDTD) method. We can then bing the eflection phases θmn TE/TM into Eq.1 and obtain the contibution to the active impedance fom all Floquet modes, as shown by the ed and blue dashed lines in Fig. 2. Meanwhile, we can calculate the eflection coefficient S11 by Eq. 1. We find that the theoetical esults ae in good ageement with the simulation esults. Moeove, fom the Fig. 6. Contibution of TM 0,0 and TM 1,0 mode to the active impedance of the aay, whee the dashed lines ae obtained with only the contibutions of the two modes and the solid lines ae the esults of the dashed lines in Fig. 2 calculated esults, we find that the most impotant Floquet modes fo ou antenna aay which can affect the impedance and S11 ae the TM 0,0 mode and the TM 1,0 mode. This finding is easy to undestand fo two easons. The fist is that we conside only E-plane scans in this wok, so the TM modes dominate the fa-field adiation. The second is that except fo the TM 0,0 mode and the TM 1,0 mode, all TM modes ae evanescent waves in all scanning angle anges, and they contibute only small petubations of the active impedance and S11.

5 5 The calculated esults of the eflection phases of the TM 0,0 mode and the TM 1,0 mode ae shown in Fig. 5. We can see that the eflection of the TM 0,0 mode decays almost linealy with the scanning angle within the ange of 0 20, which is vey impotant fo the excellent adiating popeties fo small scanning angles. Fo the TM 1,0 mode, its field is an evanescent wave so that the eflection phase is zeo when the scanning angle is smalle than 20. Once the scanning angle is lage than 20, the field of the TM 1,0 mode popagates in the substate mateial and the eflection phase of this mode is no longe zeo. With the eflection phases, the contibutions fom both the TM 0,0 mode and the TM 1,0 mode on the active impedance ae shown by the dashed lines in Fig. 6. The eal pat of the active impedance obtained fom Eq.1 with the contibutions of only these two modes is in good ageement with the esult obtained fom all modes, while the changing tend of the imaginay pat of the impedance is essentially the same as that with the contibutions of all modes. Theefoe, thee must be some basic mechanisms which suppot such good ageement. In the next two subsections, the mechanisms of the excellent pefomance of the aay with the HIS gound plane will be analyzed in detail. B. Effect of the HIS Gound Plane in a Range of Small Scanning Angles In this subsection, we demonstate how the HIS gound plane impoves the scanning pefomance of the antenna aay ove the ange of small scanning angles 0 20 consideing the special eflection phase of the HIS. Fo the small scanning angles, the dominant mode is the TM 0,0 mode because the field of the TM 1,0 mode is still an evanescent wave. Fist, we make a naive assumption that the eflection phase of the TM 0,0 mode fom the HIS gound is constant, i.e., it is maintained at the value of zeo scanning angle 37 fo of the othe modes still change in thei oiginal manne. Then, we can calculate the active impedance vesus the scanning angle using Eq.1 and the esult is shown by the dashed lines in Fig. 7. Compaed with the oiginal calculated esults shown by the solid line in Fig. 7, we can see that if the HIS eflection phase of TM 0,0 mode wee a constant simila to PEC, the oiginal excellent popeties such as the almost-constant eal pat and the nealy-zeo imaginay pat at scanning angles less than 20, would be destoyed. Clealy, the only explanation fo such destuction is that the changing HIS eflection phase vesus the scanning angle shown by the blue line in Fig. 5 is vey citical fo small scanning angles. Fom the view of an image antenna, we can moe clealy see the effect of the eflection phase of an HIS. We emphasize that thee ae two diffeent appoaches to study the physical effects of the eflected field fom the gound. One appoach is to study the eflected field diectly as we did befoe. The othe appoach is to intoduce the image antenna (o image antenna aay) whose adiating field is substituted by the eflected field with the exact same phase and magnitude. Hence, the effect of the eflected field on the eal antenna aay could be viewed as the coupling between the eal antenna aay and the image any scanning angle, while the eflection phases θ TE/TM mn Fig. 7. Effect of θ0,0 TM on active impedance in a small scanning angle ange. The dashed line is the case whee the eflection phase of θ0,0 TM is a constant, while the solid lines ae the same as the esults of the dashed lines in Fig. 2. Fig. 8. Simplified stuctue of the dipole aay, whee a, b, and c ae eal dipoles; a, b, and c ae image dipoles, and an HIS gound plane is placed at z = 0. antenna aay. To clealy show the coupling effects on the active impedance, we simplify the infinite two-dimensional aay to the model shown in Fig. 8, whee a, b, and c ae eal dipoles on an infinitely lage gound with eflection phase θ. Without the gound plane, the impedance of antenna b could be obtained by: Z 0 b,in =Z b + Z ab e jθ ab + Z cb e jθ cb (9) whee Z b is the self-impedance, Z ij is the mutual impedance between elements i and j, and θ ij is the input cuent phase diffeence between elements i and j. It is well known that the Zb,in 0 changes with the scanning angle since the input cuent phase diffeence θ ij changes with the scanning angle. With a gound, image dipoles a, b, and c should be intoduced and the active impedance of element b is: Z b,in =Z b + Z ab e jθ ab + Z cb e jθ cb + Z a be j(θ ab+θ ) + Z b be jθ + Z c be j(θ cb+θ ) (10) Fom eq. 10, we can see that the active impedance of antenna b vaies with the scanning angle if the eflection phase of the

6 6 suface is constant. Howeve, fo an HIS, the eflection phase deceases almost linealy with the scanning angle as shown by the blue line in Fig. 5. With inceasing scanning angle, the change caused by Z ab e jθ ab +Z cb e jθ cb could be canceled by the change caused by Z a be j(θ ab+θ ) + Z b be jθ + Z c be j(θ cb+θ ). In othe wods, the mutual coupling effect between elements of a eal aay at small scanning angles can be compensated by the mutual coupling effect fom the mio aay, theeby geatly impoving the adiation pefomance of the antenna aay with an HIS gound. C. Effect of the HIS Gound Plane Ove a Range of Lage Scanning Angles In the pevious subsection, the impoving of adiation efficiency in small scanning angles is explained. In this subsection, we will demonstate the new mechanism of the HIS gound plane in impoving the scanning pefomance of the antenna aay ove a ange of lage scanning angles, and eveal the effect of the LW mode. Fist, we detect the effect of the eflection phase of the HIS on the TM 1,0 Floquet mode, shown by the ed line in Fig. 5. Similaly, at fist we assume that the eflection phase of the θ 1,0 TM of TM 1,0 mode fom the HIS gound always is zeo fo any scanning angle, while the eflection phases θmn TE/TM of all othe modes still change in thei oiginal manne. We can then calculate the active impedance vesus the scanning angle by Eq.1. The esults ae shown by the dashed lines in Fig. 9. We can see that when the scanning angle exceeds 20, the imaginay pat of the active impedance begins to deviate fom the oiginal value and fo lage scanning angles the deviating values become lage, which indicates that the coupling effect between eal antenna elements and the mio antenna elements with an HIS as the gound can cancel the mutual coupling between the eal antenna elements. It is obvious that the eflection phase of the TM 1,0 Floquet mode fom the HIS is vey citical fo lage scanning angles. The effects of the eflection phase of the TM 1,0 Floquet mode imply the new mechanism which influences the adiating popeties of the antenna aay. In the next paagaphs, we will eveal the mechanism step by step. Fist, we show that at lage scanning angles this TM 1,0 Floquet mode can excite the SW mode suppoted by the HIS substate (composed of the HIS gound plane and the dielectic laye above it, which is shown by the inset in Fig. 10). Then, we illustate that this SW mode can be conveted into the LW mode by the peiodic modulation of the aay. When the TM 1,0 esonantly excites the LW mode, the LW mode adiation is almost in phase with the diect adiating field fom the aay, so that the aay pefomance at a lage scanning angle could be excellent. Using eigenmode solve of HFSS, we can calculate the dispesion cuves of the unit cell of the HIS substate. The simulation model of the unit cell is shown as the inset in Fig.10. In the simulation setup, peiodic boundaies ae used at the sides of the unit cell, and an absobing mateial (PML) teminates the setup fom the top. The adiating modes fom the stuctue suface popagate within ai, filled between the unit cell suface and PML, and ae absobed fom the top. The Fig. 9. Effect of θ 1,0 TM on the active impedance ove a ange of lage scanning angle. The dashed line is the case whee the eflection phase of θ 1,0 TM is zeo, while the solid lines ae the same as the esults of the dashed lines in Fig. 2. two modes TM 0 and TM 1, suppoted by this HIS substate ae shown in Fig. 10 by the solid blue and ed lines. Since they ae lowe than the light line which is shown by a black dashed line, both of them ae SW modes. Geneally, the condition fo the existence of such SW modes is θ +θ up +2k z d = m 2π, whee θ is the eflection phase of the HIS gound, θ up is the phase of total eflection at the inteface between the medium and ai, k z is the wavevecto in the z diection in the substate dielectic mateial, and m is the ode of the SW modes. Clealy, the popeties of SW modes ae also influenced by the eflection phase of the HIS in a subtle way. In this pape, the woking fequency is 10 GHz and the mode of TM 0 is vey fa away fom this fequency, we neglect the TM 0 mode in this eseach. Once the popagation constant of the Floquet mode of antenna aay is equal to the popagation constant of TM 1 mode of HIS substate, TM 1 mode will be excited [1]. Howeve, this TM 1 mode can be tansfe into LW mode. Since the peiod a of the antenna aay is fou times lage than the peiod of the HIS substate, the dispesion cuve of TM 1 should be folded back if using a as the peiod, as shown by the ed dashed line in Fig. 10. Now the ed dashed line is above the light line (the black dashed line), which means the SW mode becomes the LW mode which could adiate. Actually, we have also calculated the dispesion cuves of the unit cell of the antenna aay, which is shown as an inset in Fig. 11. As we expected, the dispesion cuve of the mode 2 above the light line is like the dashed line in Fig. 10. The physical eason fo the tansfomation of the SW mode to the LW mode is shown in Fig. 12. If the SW mode TM 1 of the HIS substate could be excited by an extenal field, the SW mode will expeience the peiodic scatteing by the antenna aay and the scatteed field could be a adiating field. With all this pepaation, we now can compose all the pieces

7 7 Fig. 12. Schematic illustation of the popagation paths of Edi, E0,0 and ELW, whee the oange, blue and ed lines in the fee space ae the popagation paths of Edi, E0,0 and ELW espectively, while the blue and ed lines in the substate ae the popagation paths of TM0,0 and TM 1,0. Fig. 10. Dispesion cuves of the gounded HIS substate, whee the blue and the ed solid lines ae the fist two SW modes of the HIS; the ed dashed line is the LW mode suppoted by the stuctue composed of the HIS and the dipole aay. The inset is a schematic of a unit cell of the HIS substate. mode on the scanning pefomance. As shown in Fig. 12, we decompose the adiation field of the aay in fee space into thee pats: the diect adiation field Edi of the antenna aay, the eflected field E0,0 of the TM0,0 mode and the adiation field ELW of the LW mode. Based on the obsevation that the LW mode field ELW is excited by the Floquet mode TM 1,0 in the substate, the LW mode field has the following geneal fom: γ (11) ELW = a j(ω ω0 ) + γ whee a, ω0 and γ ae the complex amplitude, eigenfequency and attenuation constant of the LW mode, espectively, and ω is the opeating fequency of the antenna aay. Then, the total adiation field Etotal can be expessed as the sum of the diect adiation field Edi, the eflected field E0,0 of the TM0,0 mode and the adiation field fom the LW mode excited by TM 1,0 : γ Etotal = Edi + E0,0 +a (12) j(ω ω0 ) + γ Fig. 11. Dispesion cuves of the HIS-based dipole aay unit cell using an HFSS simulation. The ed and blue solid lines ae the SW mode and LW mode of the unit cell espectively. The inset is a schematic of a unit cell of ou dipole aay. togethe to show the mechanism of adiation with the help of the SW mode. When the antenna aay scans at lage angles, the Floquet mode TM 1,0 becomes the popagating field and it can excite the LW mode, which is fom the SW of the HIS substate with the peiodic scatteing of the aay. Then, with the help of the LW mode, the total adiating pefomance of the antenna aay could be geatly impoved fo lage scanning angles. Finally, we qualitatively analyze the effect of the LW When the scanning angle is elatively small, Edi and E0,0 dominate the adiation field while the LW mode is difficult to excite and its contibution could be neglected. As we have discussed in Sec. III-B, the special changing of the HIS eflection phase fo the E0,0 mode can impove the scanning pefomance. When the scanning angle inceases to a value lage than 40, two conditions fo the excitation of the LW mode ae satisfied. The fist condition is that the Floquet mode TM 1,0 becomes a popagating wave in the substate and the second condition is that the LW mode eigenfequency ω0 gadually deceases and is close to the antenna woking fequency ω. Thus, ELW is almost esonantly excited by TM 1,0, and it is nealy in phase with Edi. This mechanism explains why the LW mode can help the adiation of this antenna aay. Actually, the ELW stengthens with inceasing scanning angle. At the angle ange fom 40 65, the LW mode excitation can help the antenna adiation. Howeve, when the scanning angle becomes vey lage, e.g., lage than 65, imaginay pat of the active impedance apidly gows, which means that it can absob most of the enegy adiating fom the antenna, as shown in Fig. 2. Finally, the LW excitation can geneate scan blindness at appoximately 76. To demonstate that the LW mode is tuly excited in ou model, we have shown the field and the Poynting vecto distibution of the LW mode in Fig. 13(a) and the total field of

8 8 H field [A/m] 1.0E+6 9.0E+5 8.0E+5 7.0E+5 6.0E+5 5.0E+5 4.0E+5 3.0E+5 2.0E+5 1.0E+5 0.0E+0 (a) z x H field [A/m] 1.0E+1 9.0E+0 8.0E+0 7.0E+0 6.0E+0 5.0E+0 4.0E+0 3.0E+0 2.0E+0 1.0E+0 0.0E+0 Fig. 13. Compaison of field distibutions and enegy flow diections between the LW eigenfield and the adiation field of the aay at a adiation angle of 60, whee the colo distibution and the aow diection epesent the magnitude of the magnetic field and the diection of the Poynting vecto, espectively. (a) LW mode eigenfield and the diection of the Poynting vecto, (b) total field and the diection of the Poynting vecto of ou aay. ou antenna aay at a scanning angle of 60 in Fig. 13(b). As we pedicted in Fig. 12, when the LW mode is excited by the TM 1,0 mode, the Poynting vecto should be in the diection opposite to that of the adiation in the substate, which is tue in Fig. 13(a) and 13(b). Fom Fig. 13(b), we also can see that the diect of the adiation field on the antenna suface is nealy in phase with the LW mode since both ae shown in ed. IV. CONCLUSION An infinite two-dimensional dipole aay with a mushoomlike HIS gound plane is designed, which can achieve a wide scanning angle of up to 65 in the elevation plane. The active impedance and S11 of the aay calculated via theoetical Floquet analysis ae in good ageement with numeical simulation esults. Two new mechanisms which suppot the excellent pefomance of such an aay at a wide scanning angle ae demonstated theoetically and numeically. In the ange of small scanning angles, these excellent popeties ae mainly fom the special eflection phase of the HIS gound, which can cause the mutual coupling between the elements of a eal aay be compensated by the mutual coupling effect fom the mio aay. Fo the ange of lage scanning angles, since the suface wave (SW) mode could be esonantly excited by high ode Floquet mode TM 1,0 fom the aay and the SW mode could be conveted into a leaky wave mode by the scatteing of the aay, the adiation field fom the LW mode is nealy in phase with the diect adiating field fom the aay. Theefoe, with the help fom the special eflection phase of the HIS and the designed LW mode on the HIS gound, the antenna aay with an HIS gound can achieve wide-angle scanning pefomance. We think these mechanisms could be widely used in the design of wide-angle scanning aays. (b) z x DATA AVAILABILITY The data used to suppot the findings of this study ae available fom the coesponding autho upon equest. CONFLICTS OF INTEREST The authos declae that thee ae no conflicts of inteest egading the publication of this pape. REFERENCES [1] D. M. Poza, Daniel H. S., Scan blindness in infinite phased aays of pinted dipoles, IEEE Tansactions on Antennas and Popagation, vol. 32, no. 6, pp , [2] Qama, Z., Riaz, L., Chongcheawchamnan, M., Khan, S. A., & Shafique, M. F. Slot combined complementay split ing esonatos fo mutual coupling suppession in micostip phased aays, IET Micowaves, Antennas & Popagation, vol. 8, no. 15, pp , [3] Tsay, W-J and Poza, David M, Radiation and scatteing fom infinite peiodic pinted antennas with inhomogeneous media, IEEE Tansactions on Antennas and Popagation, vol. 46, no. 11, pp , [4] Yazdi, Shiin Ramezanzadeh, Somayye Chamaani, and Seyed Aash Ahmadi Mutual Coupling Reduction in Micostip Phased Aay Using Stacked-Patch Reduced Suface Wave Antenna, Antennas and Popagation & USNC/URSI National Radio Science Meeting, 2015 IEEE Intenational Symposium on (pp ). IEEE. [5] Moghadas, H., A. Tavakoh, M. Salehi, Elimination of scan blindness in micostip scanning aay antennas using defected gound stuctue, AEU-Intenational Jounal of Electonics and Communications, vol. 62, no. 2, pp , [6] Sievenpipe, Dan et al., High-impedance electomagnetic sufaces with a fobidden fequency band, IEEE Tansactions on Micowave Theoy and techniques, vol. 47, no. 311, pp , [7] Adas, Enve, Fanco De Flaviis, and Nicolaos G. Alexopoulos. Integated Micostip Antennas and Phased Aays with Mode-Fee Electomagnetic Bandgap Mateials fo Scan Blindness Elimination Electomagnetics, vol. 37, no. 1, pp , [8] Donzelli, G., Capolino, F., Boscolo, S., and Midio, M. Elimination of scan blindness in phased aay antennas using a gounded-dielectic EBG mateial. IEEE Antennas and Wieless Popagation Lettes, vol 6, pp , [9] Li, L., C-H. Liang, and C-H. Chan. Waveguide end-slot phased aay antenna integated with electomagnetic bandgap stuctues. Jounal of Electomagnetic Waves and Applications, vol 21, no. 2, pp , [10] Fu Y Q, Yuan N C, Elimination of scan blindness in phased aay of micostip patches using electomagnetic bandgap mateials, IEEE Antennas and Wieless Popagation Lettes, vol. 3, no. 1, pp , [11] Azaba, A., and J. Ghalibafan. A compact low-pemittivity dual-laye EBG stuctue fo mutual coupling eduction. Intenational Jounal of Antennas and Popagation, vol. 2011, [12] Costa F et al., TE suface wave esonances on high-impedance suface based antennas: Analysis and modeling, IEEE Tansactions on Antennas and Popagation, vol. 59, no. 10, pp , [13] Li M et al., Compact suface-wave assisted beam-steeable antenna based on HIS, IEEE Tansactions on Antennas and Popagation, vol. 62, no. 7, pp , [14] Li M, Xiao S Q, Wang B Z Investigation of using high impedance sufaces fo wide-angle scanning aays, IEEE Tansactions on Antennas and Popagation, vol. 63, no. 7, pp , [15] Tami, T. Inhomogeneous wave types at plana intefaces: III-Leaky waves. Optik, vol. 38, pp , [16] Phased aay antennas: Floquet analysis, synthesis, BFNs and active aay systems, Bhattachayya Aun K., USA: John Wiley & Sons, 2006.