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2892 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 66, NO. 6, JUNE 2018

Binary Huygens’ Metasurfaces: ExperimentalDemonstration of Simple and Efficient Near-Grazing

Retroreflectors for TE and TM PolarizationsAlex M. H. Wong, Member, IEEE, Philip Christian , and George V. Eleftheriades, Fellow, IEEE

Abstract— This paper investigates the retroreflective propertiesof a type of periodic metasurface, which is aggressively discretizedto include only two cells per grating period. The resultantmetasurface, which we term the binary Huygens’ metasurface,dramatically simplifies the design toward highly efficient, lowcost, and robust metasurface retroreflectors. Using this discretiza-tion method, we designed, simulated, and measured two binaryHuygens’ metasurfaces that retroreflect an incident plane waveat 82.87° from broadside, for TE and TM polarized waves,respectively. The simulated results for a 2-D infinite structureshow power efficiencies of 94% (TE) and 99% (TM). Themeasured results show a power efficiency of 93% for both TEand TM polarizations. This shows that it is possible to obtain ahigh retroreflection power efficiency at an angle of choice usinga very simple (slot or patch) metasurface design. The proposeddesign methodology allows one to achieve not only retroreflectionbut also reflection to arbitrary angles, with very high efficiency,which diversifies its uses.

Index Terms— Binary surfaces, equivalence principle, Huy-gens’ sources, metasurface, retroreflector.

I. INTRODUCTION

ARETROREFLECTOR is a device that back reflects anelectromagnetic wave in the direction of incidence.The passive retroreflection of electromagnetic waves, fromradio to optical frequencies, finds a myriad of practicalapplications in communication with satellites and unmannedaerial vehicles [1]–[3], remote sensing [4], target labeling,navigation safety, and radar cross section (RCS)/visibilityenhancement [5], [6]. In these and other applications, it isoften desirable to have retroreflectors which: 1) operate atlarge angles of oblique incidence; 2) can handle TE andTM polarizations; 3) low profile; 4) lightweight; 5) low loss;and 6) can be practically manufactured. In the following,we survey prominent classes of retroreflectors in view of theaforementioned factors.

The simplest retroreflection structure is a metallic plate.Clearly, a metallic plate, with side lengths of several wave-lengths and beyond, is a strong retroreflector when the incident

Manuscript received October 29, 2017; revised February 22, 2018; acceptedMarch 4, 2018. Date of publication March 16, 2018; date of current versionMay 31, 2018. This work was supported by an NSERC Collaborative R&DGrant with Thales Canada. (Corresponding author: George V. Eleftheriades.)

The authors are with the Edward S. Rogers Sr. Department of Electricaland Computer Engineering, University of Toronto, Toronto, ON M5S 3G4,Canada (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TAP.2018.2816792

wave impinges from a direction normal to the plate, buta poor retroreflector otherwise. Other elementary metallicstructures—such as the cylinder or the sphere—have beenamply studied. As expected, they feature weaker retroreflectionstrengths, but the retroreflection levels remain the same asthe incident wave’s direction varies in the azimuthal planefor the cylinder and across all angles for the sphere [7].Perhaps, the most efficient metallic retroreflection structureis the corner cube, as illustrated in Fig. 1(a). By connectingtwo (or three) metallic plates at right angles, one formsa reflection structure where the incoming wave is reflectedtwo (or three) times and achieves retroreflection. Theoreticaland experimental works show that the corner cube providesefficient retroreflection in the range of ±15° [8], [9]. The maindisadvantages of the corner cube are: 1) the structure is large:its depth is appreciable compared to the size of the aperture;2) it cannot support retroreflection beyond a maximum angleof 45°; and 3) in some cases, it is reported to alter thepolarization of an incoming wave [8], [10]. Using a sheet builtfrom an array of 2-D array of small trihedral corner cubes,one can significantly reduces the depth of the retroreflectionstructure, and achieves appreciable retroreflection in the rangeof ±30° [11]. Nevertheless, efficient retroreflection remainsout of reach at large oblique angles.

Another class of retroreflectors involves dielectric and/orplasmonic materials. It has been found that for a randomarray of spherical (or near-spherical) scatterers, a coherentbackscattering phenomenon occurs to strengthen retroreflec-tion [12], [13]. Under favorable conditions, a retroreflectionstrength as high as 40% has been observed [12]. A similareffect occurs for random rough surfaces [14]. Essentially,these configurations encourage multiple scattering, and therebystrengthen the retroreflected wave component that achievesphase alignment across multiple paths [13]. The cat’s eyeretroreflector [see Fig. 1(b)]—a convex dielectric lens placedone focal length away from a (ideally parabolic) mirror—hasreceived considerable attention [10], [15]–[17]. Similar to thecorner cube, the cat’s eye retroreflector has a depth that is com-parable to its lateral size. However, since the wave is focusedto a considerably smaller area at the location of the mirror, thisconfiguration is useful for performing switching and encodingon an electromagnetic signal. Biermann et al. [10] havedemonstrated a cat’s eye retroreflector with a multistage lens,which achieved highly efficient retroreflection across the rangeof ±15°. Lundvall and Nikolajeff [17] demonstrated a cat’s eye

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WONG et al.: BINARY HUYGENS’ METASURFACES 2893

Fig. 1. Retroreflection devices. (a) Metallic corner cube. (b) Cat’s eye retroreflector. Black line: metallic mirror. (c) Luneburg lens backed by a metallicmirror. In (a)–(c), arrows outline representative trajectories of electromagnetic rays. (d) Eaton’s lens. Reprinted by permission from Macmillan Publishers Ltd.:Nature Materials [19], copyright 2009. (e) Four-element Van Atta patch antenna array. (f) Various metallic gratings that include the echellet grating (top),the groove grating (middle), and the strip grating (bottom). Gray: metal. Green: dielectric substrate. (g) Representative metasurface from [23]. Reprinted withpermission from American Association for the Advancement of Science.

retroreflector with an array of microlenses and micromirrors.This device was relatively low profile, and achieved efficientretroreflection across an angular range of ±30°. By replacingthe convex lens and the lens–mirror spacing with a Luneburglens [18], one arrives at the Luneburg lens retroreflector[see Fig. 1(c)], which when properly designed can facilitateefficient retroreflection across a wide angular range of about±50° [9]. While the Luneburg lens retroreflector has seensome practical applications, it is limited by its large size, heavyweight, and relatively expensive fabrication. More exoticmetallodielectric retroreflectors have been proposed, whichinclude an Eaton lens [19] [see Fig. 1(d)] and a retroreflectionsuperscatterer [20] implemented through the transformationoptics approach, and a plasmonic superscatterer which isessentially a superdirective small antenna, impedance matchedby metal and dielectric shells of precise thickness [21], [22].While interesting and potentially efficient, these proposalsrequire very high precision in the dimension and permittivityof the materials involved. Their practicality is yet to be provedbeyond proof-of-principle laboratory demonstrations.

The Van Atta array is a practical and low-profile wideangle retroreflector for RF electromagnetic waves [24], [25].Fig. 1(e) shows a four-element Van Atta array with properconnections amongst the antenna patches. The antennas onthe surface are designed to efficiently couple to the incidentand reflected waves; the crossed transmission line connectionsreverse the phase front on the surface of the retroreflector.Thus together, the antennas and their connections serve toreverse the phase front along the surface of the retroreflector,and thereby achieve retroreflection. The Van Atta array has

been shown to work in 1-D and 2-D configurations [25] andon both planar and curved surfaces [26]. A wide angularbandwidth of over ±60° has also been demonstrated [9].However, the Van Atta array suffers a few drawbacks. First,unlike many previous devices, the Van Atta array relies onthe near-resonant operation of antenna elements. Hence, itsoperation bandwidth is limited by the antenna elements, and itsangular range is limited by the element factor. Similarly, dueto limitations from the antenna elements and the transmissionlines, it is difficult to imagine its extension to frequenciesbeyond the millimeter-wave regime. Additionally, the criss-crossed connections between antenna elements greatly compli-cate antenna routing as the array size increases. This makes theVan Atta array impractical for a retroreflector with an aperturelength of several wavelengths and beyond.

When the incident wave direction is known, a metallicgrating can be designed as a practical, low profile, and efficientretroreflector. Gratings used for retroreflection purposes areknown as blazed gratings; three prominent kinds of blazedgratings are depicxted in Fig. 1(f) and explained as follows.Traditional echelette gratings have been designed to sup-port blazed reflection [27], however, it has been found thattheir saw-tooth edges lead to spurious undesired diffractionand limitations, particularly for retroreflecting TM waves.Gratings featuring metallic grooves, on the other hand, arefound to support efficient retroreflection for both TE and TMwaves [28], [29]. It has since been found that a metallicstrip grating atop a metal-backed substrate [30], [31] func-tions similar to the metallic groove grating [30], and hence,can serve as efficient retroreflectors for both TE and TM


polarizations [32]–[34]. However, a few reports have emergedon the usage of these retroreflectors at large angle incidenceof beyond ±60°, thus their effectiveness for near-grazingincidence is yet to be investigated.

More recently, the metasurface [Fig. 1(g)] has emergedas a versatile tool in electromagnetic wavefront manipula-tion [23], [35]–[39]. By tuning the surface impedance asa function of position, various wavefront operations havebeen demonstrated [40], which modify the amplitude [41],phase [41], [42], polarization [43], [44], and propagationdirection [42], [45] of an incident wave. Specifically, meta-surfaces with linear phase variants have been demonstrated:they represent low profile and cost-effective structures, whichcan perform retroreflections at selected angles. Additionally,they provide more freedom in waveform manipulation than agrating which is inherently 1-D. Nevertheless, to date mostdemonstrated metasurfaces feature finely discretized surfaceimpedance profiles implemented by element cells of sizeλ/8 or smaller. This means that the scaling of these metasur-faces for use at higher frequencies will involve high-precisionfabrication, which may drive up the fabrication cost, reducethe metasurface’s robustness, or render impossible altogetherthe scaling of the technology. Moreover, the near-grazing angleoperation of a metasurface has seldom been reported, and itspower efficiency is yet to be investigated.

In this paper, we report the design and demonstration ofnear-grazing angle retroreflection metasurfaces for both TEand TM polarizations. Our proposed structure is a subwave-length array of rods (for TE) and slot (for TM) backed bya ground plane, etched onto a dielectric substrate. The pro-posed metasurface synthesizes a grating with an ultra-coarsediscretization of two cells per grating period. Such aggressivediscretization alleviates, as much as possible, the need forsmall features, and paves the way to a simple metasurfaceretroreflector that is highly efficient, robust, cost-efficient, andeasily scalable to millimeter-wave and tetrahertz frequencies.The rest of this paper is organized as follows. In Section II,we formulate our problem and present our metasurface designmethodology. In Section III, we show designs and full-wavesimulation results for the TE and TM retroreflection meta-surfaces. For the TM case, we also examine the origin ofspurious effects that are not observed for the TE counterpart.In Section IV, we report monostatic and bistatic RCS exper-imental results which validate simulations and demonstratethe operation of both metasurfaces. Finally, in Section V,we conclude our findings.

II. METASURFACE DESIGN METHODOLOGY

In this paper, we adopt a surface impedance approach tometasurface design, demonstrated in [39], [45], and [46].In this section, we first determine the necessary impedance(and reflection coefficient) profile for the retroreflection meta-surface, then examine the effects of discretization on theperformance of the metasurface.

A. Surface Impedance Analysis

Fig. 2 illustrates plane wave diffraction with a generalizedmetasurface for both the TM and TE incident polarizations.

Fig. 2. Diagrams of (a) TM and (b) TE single-plane wave reflection off ametasurface at z = 0.

We will find the necessary impedance profile for this surface,and thereafter specialize to the case of retroreflection, whereθr = −θi .

We shall analyze the TM case [Fig. 2(a)] in detail. In theillustration of [Fig. 2(a)], the incident and reflected planewaves can be described, respectively, as

Ei = Ei0 exp(− jk0(sin θi y − cos θi z))· (cos θi ŷ + sin θi ẑ),

Hi = Ei0η

exp(− jk0(sin θi y − cos θi z))x̂ (1)

and

Er = Er0 exp(− j (k0(sin θr y + cos θr z) + φ))· (− cos θr ŷ + sin θr ẑ),

Hr = Er0η

exp(− j (k0(sin θr y + cos θi z) + φ))x̂ (2)

where k0 = 2π/λ0 is the spatial frequency and λ0 is the freespace wavelength. φ is a constant phase offset between theincident and reflected waves at y = 0, which remains arbitraryfor the moment. The fields tangential to the surface (at z = 0+)are hence described as follows:

Ei,tan = Ei0 cos θi exp(− jk0 sin θi y)ŷHi,tan = Ei0

ηexp(− jk0 sin θi y)x̂

Er,tan = −Er0 cos θr exp(− j (k0 sin θr y + φ))ŷHr,tan = Er0

ηexp(− j (k0 sin θr y + φ))x̂. (3)

We will introduce two relationships at this point that willsimplify the derivation that follows. First, we will define

��(y) = k0(sin θr − sin θi )y + φ (4)as the phase difference between the incident and reflectedplane waves. Next, we set

Er0 =√

cos θicos θr

Ei0 (5)

which relates the incident and reflected plane wave ampli-tudes for perfect reflection metasurfaces [39], [40]. Using (4)and (5), we write the surface impedance (as a function oflocation on the metasurface) which will generate the desired


reflection upon the prescribed incidence

Zs,TM = Etan · ŷHtan · x̂ =(Ei,tan + Er,tan) · ŷ(Hi,tan + Hr,tan) · x̂

= η cos θi√

cos θr − cos θr√cos θi e− j��(y)√cos θr + √cos θi e− j��(y) . (6)

For the case of retroreflection, θr = −θi ⇒ cos θr = cos θi .Redefining θ = |θi | = |θr |, we obtain

Zs,TM = η cos θ(

1 − e− j��(y)1 + e− j��(y)

)

= j Z0,TM tan(

��(y)

2

) (7)

where Z0,TM = η cos θ is the wave impedance for the incidentand reflected waves in TM polarization.

It is often convenient to work with reflection coefficientsas opposed to surface impedances. In this single plane waveretroreflection scenario, one straightforwardly finds the reflec-tion coefficient as

TM = Zs,TM − Z0,TMZs,TM + Z0,TM = −e

− j��(y). (8)

One can find corresponding relationships for the TE polar-ization following a procedure very similar to the one describedearlier. We refer the interested reader to [39] where reflectionwith this polarization is discussed in more detail. Followingthe analysis outlined earlier, we find that for the TE polar-ized single-wave reflection scenario [Fig. 2(b)], the surfaceimpedance as

Zs,TE = η√cos θi cos θr

√cos θr + √cos θi e− j��(y)√cos θi − √cos θr e− j��(y) . (9)

Specifically, for retroreflection, (9) reduces to

Zs,TE = − j Z0,TE cot(

��(y)

2

)(10)

where Z0,TE = η/ cos θ is the wave impedance for TEpolarized incident and reflected waves. The correspondingreflection coefficient is

TE = Zs,TE − Z0,TEZs,TE + Z0,TE = e

− j��(y) = −TM. (11)

Relationships akin to (6) and (9) have been derived, to var-ious degrees of generality, in [39] and [45]. Additionally,one may simplistically (and correctly) assume from gratingtheory that the desired reflection coefficient profile is that of alinear phase gradient, as shown in (8) and (11). Nevertheless,the preceding analysis shows, with the full rigor of Maxwell’sequations, that it is possible to retroreflect all the power froman incident plane wave, at any incidence angle and witheither polarization. Moreover, such perfect retroreflection isachieved using an aptly designed passive metasurface withsurface impedances described by (6) and (9), or equivalentlywith reflection coefficients described by (8) and (11).

Fig. 3. Transformation of a plane wave’s transverse (y-directed) wave vector,as it is reflected from a periodic metasurface. Arrows: spatial frequenciesof possible spectral components, but their lengths do not reflect the relativeamplitudes of these components.

B. Discretization Effects

Next, we examine the degree of discretization suitablefor our realization of the retroreflection metasurface. Whilstmost metasurfaces are designed in a continuous manner,their implementations are often facilitated by discretizing intosubwavelength-sized cells, each of which are implemented toachieve the requisite electromagnetic property (e.g., surfacesusceptibility or surface impedance). Individual cases, suchas [47], have shown that coarser discretization is possible forselected reflection surfaces. A coarse discretization benefitsmetasurface design in two major ways: they reduce the mutualcoupling between metasurface elements and relax tolerancerequirements, allowing for cost-effective and robust metasur-face fabrication well into the millimeter wave frequencies.In the following, we shall provide a brief investigation towardthe proper design of an aggressively discretized retroreflectionmetasurface.

Fig. 3 shows the transformation of a plane wave’s trans-verse (y-directed) spatial frequency as it reflects off a retrore-flection metasurface. The reflected wave’s spatial frequenciesmap straightforwardly into the angular domain through

sin θ = kyk0

for ky ≤ k0. (12)

Fig. 3 (arrows) shows the presence of spectral components, butdo not represent the amplitudes or phases of these spectralcomponents. As seen, the periodic metasurface produces aseries of diffraction orders which can, in general, reflectoff different directions. The transverse spatial frequencies ofdiffracted orders are given as

kmy = kiy + mkg = kiy + m 2π

g

(13)

where kiy represents the y-directed spatial frequency of theincident wave, while kg and g , respectively, represent thespatial frequency and the period of the metasurface.

To generate a retroreflection metasurface, one tunes the m=−1 diffraction order into the retroreflection order by choosing

g appropriately

kry = kiy − 2π

g

= −kiy ⇒ g = λ02 sin θi

. (14)

For a successful metasurface—a metasurface that implementsthe surface impedance profile (6) and/or (9)—power diffrac-tion will maximize for the retroreflection mode and vanish forother propagating modes.


With g , and thereby kg , fixed to achieve retroreflection ata predefined angle, there exists a fixed number of reflectedpropagation waves, as shown pictorially in Fig. 3 by thespectral components kry which reside within the propagationregion [−k0, k0]. The number of such diffraction orders isgiven as

N = 1 +⌊

k0 − kikg

⌋+

⌊k0 + ki

kg

⌋(15)

where �·� is the floor (round down) operator. It can bereasoned that the maximal metasurface discretization requiresat least N cells per metasurface period, to provide sufficientdegrees of freedom to tune the amplitude and phase of eachdiffraction order. (This can be mathematically proven througha Fourier analysis, which we defer to a forthcoming work.) Fora retroreflector, the discretization requirement can be furtherrelaxed to

N = 2 ×⌊

k0kg

⌉(16)

where �·� is the rounding operator. Combining (12), (14),and (16), we see that for a sufficiently large angle incidence

θi ≥ 19.5◦ ⇒ kg > 23

k0 ⇒ N = 2. (17)Hence, for angles of incidence beyond 19.5°, the retroreflec-tion metasurface can be most aggressively discretized to haveonly two cells per grating period. (This case for minimumdiscretization concurs with an earlier work [28] on blazedgratings.) We name the resultant surface a binary Huygens’metasurface—a metasurface with effective electric and mag-netic behavior comprising only two metasurface cells. As apractical design choice, we space these metasurface cells inequidistant fashion across the metasurface period (i.e., adjacentcells are spaced half a period apart). Based on this spacing,an application of (8) and (11) shows that these two cellsshould exhibit uniform reflection amplitude and 180° relativephase shift—irrespective of the desired angle of retroreflection.In Section III, we will describe the design and simulation ofTE and TM metasurfaces which achieve these properties.

III. DESIGN AND SIMULATION

Fig. 4 depicts the geometry of our desired metasurface.A typical smooth surface reflects in the specular direction,whereas our desired metasurface reflects strongly in the retrodirection. For the TE polarization, the E-field of all planewaves points to the x-direction; for the TM polarization,the H -field of all plane waves points to the x-direction. We aimto design a metasurface that emanate two diffraction orders—the specular (m = 0) and retroreflection (m = −1) orders;by appropriate metasurface design, we aim to significantlysuppress specular reflection and, hence, create an efficientretroreflector. In this paper, a 24 GHz incident wave impingeson the metasurface at a near-grazing incidence angle of θi =82.87° with respect to normal. Using (14), we obtain

g = 6.30 mm. (18)

Fig. 4. Illumination scenario of the desired metasurface, which shouldminimize specular reflection (red arrow) and maximize retroreflection (greenarrow).

Fig. 5. Single element design for the TE (electric field along x) retroreflectionmetasurface at 24 GHz. (a) Geometry of the element. Dimensions are Ux =Uy = 3.149 mm, Sz = 1.575 mm, and Py = 0.5 mm. (b) Polar plot of TE asPx is swept from 1.5 to 3 mm. (c) Top view of the two-cell TE metasurface.Dimensions are Py = 1.5 mm, Px1 = 2.16 mm, and Px2 = 2.35 mm.

Since, we wish to discretize this period into two cells,we choose a unit cell size of

Uy = g2

= 3.15 mm. (19)

A. TE Metasurface

1) Metasurface Element Design: For the TE polarization,we implement the required reflection coefficient using aground-backed dipole array. We have shown in previous worksthat: 1) this structure contains Huygens’ source characteris-tics when operated in reflection mode [41], [48] and 2) bytuning the length of the dipole, one can vary the phase ofTE by a phase range approaching 360° [41], [49], with


Fig. 6. Simulated results for the TE retroreflection metasurface at24 GHz. (a) Geometry of the finite element (1-D finite) simulation. Thex-directed (blue) faces are periodic boundaries; the y-directed and topz-directed faces are radiation boundaries; the bottom z-directed face is acopper layer. (b) Simulated scattering pattern is plotted for φ = 90° (theyz plane) (c) Simulated monostatic RCS for the metasurface (blue solid line)is plotted alongside the theoretical RCS of a metallic plate with the sameeffective aperture, placed normal to the incident radiation (red dotted line) (seeFig. 7 for further explanation).

minimal loss. Fig. 5(a) shows the unit cell geometry of theproposed metasurface element. We design the element on anRT/Duroid 5880 Laminate board from Rogers Corporation,with a thickness of Sz = 1.575 mm and 17.8 μm (1/2 oz)copper cladding. The cell size is Ux = Uy = 3.15 mm, andthe dipole width is Py = 0.5 mm. We investigate the reflec-tion characteristics of this structure by performing full-waveelectromagnetic simulation using Ansys HFSS. We terminatethe unit cell with periodic boundaries in the x-direction andy-direction, with phase shifts corresponding to an incidentwave at θi = −82.87°. With a Floquet wave port from the+z boundary, we simulate the wave incidence and observethe reflection coefficient (TE) caused by the unit cell, as wesweep the dipole length from Px = 1.5 to 3 mm. Fig. 5(b)plots TE as a function of the dipole length. As expected, oneobserves a phase change approaching 360° with relatively lowloss. As noted in Fig. 5, operation points Px1 = 2.16 mm andPx2 = 2.35 mm differ in phase by about 180°. We choosethese to be the operation points for the TE retroreflectionmetasurface.

2) Periodic Metasurface Simulation: Upon choosing thedipole cell lengths Px1 and Px2, we place them adjacentto each other and simulate the scattering properties of theresultant binary Huygens’ metasurface. Fig. 5(c) shows thetop view of one period of this metasurface. Two simulationsare performed. First, we perform a 2-D infinitely periodicextension of the metasurface using the Floquet simulationdescribed earlier for the single-element analysis. From thissimulation, we find the scattered power into the retro and

Fig. 7. Effective area of the metasurface (black rectangle) which isdetermined by the projection of the horn onto the metasurface (this is shownby the blue shaded area). The effective area is calculated by multiplying thearea of the metasurface by the angle (θ ) that the horn makes with the normalof the metasurface.

specular modes to be 94% and 6%, respectively. This demon-strates very efficient retroreflection and suppression of specularreflection. Second, we truncate the metasurface to 136 cellsin the y-direction to simulate the scattering characteristicsof a finite metasurface. (We keep the simulation periodic inthe x-direction—where the fields are invariant from elementto element—to conserve computational resources.) Fig. 6(a)shows a diagram of the truncated (1-D finite) metasurfacesimulation. As shown in the diagram, we leave an appreciableair gap of λ0/2 in the ±x-direction and ±z-direction, andsimulate radiation boundaries using perfectly matched layers.Upon the illumination of a plane wave at 82.87°, Fig. 6(b)shows the simulated scattering pattern (bistatic RCS) of theresultant structure in the φ = 90° plane (yz plane). In thisscattering pattern, one clearly observes a strong retroreflectioncomponent along with a weak specular component. Fig. 6(c)shows the monostatic RCS in the φ = 90° plane (yz plane).The red dotted line indicates the power that would be reflectedby a metallic plate which: 1) occupies the same effectiveaperture as the metasurface and 2) is placed normal to theincoming wave, as shown in Fig. 7. As the size of this effectiveaperture scales with cos θ , the RCS of this plate scales withcos2 θ [7]. Since a metal plate illuminated from broadsidereflects with 100% aperture efficiency, its monostatic RCS asplotted in Fig. 6(c) provides a measure on the effectiveness ofthe metasurface, after one properly accounts for the size of theaperture, which varies with the illumination angle. At the angleof ±82°, the binary Huygens’ metasurface achieves an RCS of−0.3 dB compared to the metallic plate, which is equivalent toan aperture efficiency of 93%. Hence, very efficient retroreflec-tion is achieved at near the angle of designed retroreflection.

B. TM Metasurface

1) Metasurface Element Design: We design the TM meta-surface in a similar fashion to the TE counterpart, butwith a different metasurface element. At near-grazing angles,the electric field component of a TM polarized wave pointspredominantly in the z-(vertical) direction, which couples inef-fectively to metallic dipole strip elements on the metasurface.Instead, we seek to couple to the magnetic field using an


Fig. 8. Single element design for the TM (magnetic field along x) retrore-flection metasurface at 24 GHz. (a) Geometry of the element. Dimensionsare Ux = Uy = 3.149 mm, Sz = 3.175 mm, and Py = 1.5 mm. (b) Polarplot of TM as Px is swept from 0 to 3.149 mm. (c) Top view of the two-cell TM metasurface. Dimensions are Py = 1.5 mm, Px1 = 0.8 mm, andPx2 = 3.149 mm.

array of slots—Babinet’s equivalent to the dipole array [50].Fig. 8(a) shows a schematic of the metasurface element. In thiselement, a rectangular slot of size Px × Py is etched atopa unit cell with a thickness of Sz = 3.175 mm (125 mil),and the same periodicity as the TE counterpart (Ux = Uy =3.149 mm). As with the TE counterpart, we design themetasurface on a Rogers RT/Duroid 5880 laminate board with17.8 μm (1/2 oz) copper cladding on both sides.

We sweep the length of the slot Px , to tune the cou-pling dynamic between the ground-backed slot array and theincoming/outgoing waves, which in turn tune the reflectioncoefficient TM. Fig. 8(b) plots TM as a function of the slotlength Px as we sweep it from 0 to 3.149 mm. Simulationsare performed using the Floquet formulation as previouslyexplained for the TE metasurface element. As can be observed,TM attains near-unity magnitude, but its phase variation cov-ers over 190°, which is a notable decrease from the near 360°phase range obtained from the TE counterpart. This in largepart is due to the fact that in transforming our metasurfacefrom TE to TM operation, we retained the original substratedielectric and the ground plane, whereas in a true Babinet’sequivalent, one would replace those with a material of propermagnetic permeability and a magnetic conductor. Despite ourpractical decision to settle with a compromised Babinet’sequivalent, the reflection response, as displayed in Fig. 8(b)is sufficient for our purpose for a retroreflecting metasurfacedesign. From this plot, we choose our initial operation points

Fig. 9. Simulated results for the TM retroreflection metasurface at 24 GHz.(a) Simulated scattering pattern was plotted (the yz plane). (b) Simulatedscattering pattern with absorbers on both ends of the metasurface. (c) Simu-lated monostatic RCS for the metasurface (blue solid line) plotted alongsidethe theoretical RCS of a metallic plate with the same effective aperture,placed normal to the incident radiation (red dotted line) (see Fig. 7 for furtherexplanation).

Px1 = 0.8 mm and Px2 = 3.149 mm to conduct the two-cellsimulation which is as follows.

2) Periodic Metasurface Simulation: Once we have chosenthe slot dimensions for the two unit cells that occupy a singlegrating period as shown in Fig. 8(c), we again perform aFloquet simulation that gives us the scattering parameters fora 2-D infinite extension of this binary Huygens’ metasurface.From the simulation, we find that the scattered power into theretro and specular reflection modes to be 84.3% and 15.5%,respectively. We surmise that the existence of this weak spec-ular reflection is caused by differing mutual coupling effects,now that the two elements are placed adjacent to one another.We hence attempt to reoptimize the retroreflector by tuning thelength Px1 in the Floquet simulation of the binary Huygens’metasurface. We find that retroreflection is reoptimized whenPx1 = 1.6 mm, at which point, the power efficiencies forretro and specular reflections are 99.1% and 0%, respectively.While the original and reoptimized values of Px1 seem tolargely differ, they should only affect a slight variation inthe reflection coefficient of the metasurface cell, since bothslot dimensions are quite far away from resonance. Underthis reoptimization, the simulation once again demonstratesvery efficient retroreflection and highly suppressed specularreflection.

We then truncate the metasurface to 136 cells in they-direction to simulate the scattering characteristics of a finitemetasurface. The same boundary conditions were applied as inthe case of the TE metasurface. Fig. 9(a) shows the simulatedscattered pattern of the resultant structure in the φ = 90°plane (yz plane). This again shows a strong retroreflectioncomponent along with a weak specular component. Fig. 9(c)


Fig. 10. Comparison between three 1-D finite simulations at 24 GHz.(a) 100 cell—maximum occurs at −79°. (b) 136 cell—maximum occurs at−80°. (c) 200 cell—maximum occurs at −81°.

shows the monostatic RCS in the φ = 90° plane (yz plane),and this also shows nearly 100% retroreflection at ±82° whenconsidering the effective aperture of the board, and depictedby the red dotted line that indicates the maximum power thatcould be reflected given the size of the board.

3) Spurious Reflection: When observing Fig. 9(a), it isevident that the design of the metasurface produces strongretroreflection and suppressed specular reflection. However,the spurious reflection at 37° is a little peculiar in termsof grating theory. Per grating theory, there should only betwo modes that are in the propagating regime. We, therefore,hypothesize that this could be caused by coupling of theincident wave to surface waves, which then reradiate to freespace. To test this hypothesis, we create, in simulation, a lossymaterial on both ends of the metasurface. This is done sothat if surface waves were to exist within the dielectric, theywould get absorbed by the lossy material and, therefore,will not contribute to the generation of spurious reflection.Fig. 9(b) shows the radiation pattern with this adjustment,which indeed proves that the spurious mode originates fromthe coupling into surface waves and reradiation at the edge ofthe metasurface. However, the power that is retroreflected isreduced by 0.8 dB, while the specular reflection increases by2.2 dB using this new design, and thus has its own limitations.

4) Optimization: It is important to notice that when doingfinite simulations, the retroreflection direction is not exactlythat which we designed for. If we look at Fig. 9, we see thatthe direction of the retroreflected mode is maximal at −80°,whereas the designed angle was −82.87°. The reason for thisdifference is due to the finite size of the metasurface. A wayto counteract this is by designing a metasurface with a slightlylarger angle in mind, such that when the structure is reduced toa finite size, it will align with the desired retroreflection angle.Another option is to fabricate a board that is larger, as that willalso enable the reflected angle to be closer to the −82.87°,as shown in Fig. 10. As the size of the board increases from100 cells to 200 cells, the reflected angle changes from −79°to −81°.

C. Bandwidth Analysis

While the binary Huygens’ metasurface is designed forperfect retroreflection only at a single frequency, the designmethodology of suppressing specular reflection and the usageof relatively large, nonresonant elements are a principlewhich applies over a wide operational bandwidth. Fig. 11shows the monostatic RCS for the TM metasurface fora range of frequencies surrounding the design frequencyof 24 GHz, compared against the monostatic RCS of aperfect reflector with the same physical aperture. As shown,

Fig. 11. Monostatic RCS at −82.87° as the frequency is swept from24 to 27 GHz. The frequencies (from left to right) are: 24, 24.5, 25, 26, and27 GHz. Red dashed line: reflection strength at perfect aperture efficiency.All plots are normalized such that a reflector with perfect aperture efficiencyretroreflects 0 dB upon normal incidence.

Fig. 12. Bistatic RCS at −82.87° as the frequency is swept from 24 to27 GHz. The incident angle is kept constant at −82.87°. The frequencies (fromleft to right) are: 24, 24.5, 25, 26, and 27 GHz. Red dashed line: reflectionstrength at perfect aperture efficiency. All plots are normalized such that areflector with perfect aperture efficiency reflects 0 dB toward broadside.

the binary Huygens’ metasurface retroreflects with areasonable efficiency (>−2 dB aperture efficiency) for afrequency range from 24 to 27 GHz. Within this frequencyrange, the retroreflection angle shifts from −80° to −62°,in accordance to (14). Fig. 12 shows the bistatic RCS for thissame range of frequencies, incident on the metasurface from anangle of 82.87°. One can observe that reasonable anomalousreflection (>−2 dB aperture efficiency) is also achieved forthis range of frequencies, but the reflection angle deviatesfrom the retro direction due to a beam squinting effect. Thereflection angle can be obtained by solving (12) and (13) forthe m = −1 diffraction order. As we report in [51] and [52],one can achieve perfect anomalous reflection using a binaryHuygens’ metasurface specifically designed for that purpose.

While we show results only for the TM metasurface, the TEcounterpart exhibits a very similar behavior over a comparablebandwidth. Hence, the binary Huygens’ metasurfaces boast awide operational bandwidth of 11.8%, though the retroreflec-tion angle changes within this operation frequency, as dictatedby (12) and (13).

IV. MEASUREMENTS

A. TE Metasurface

The TE metasurface is fabricated with 136 cells in they-direction (the same number of cells that are used for the 1-D


Fig. 13. (a) Monostatic RCS setup with the metasurface (green) whichrotates on a stage. The effective area is shown as the area that is normalto the propagating direction of the horn. (b) Bistatic RCS setup: there arelimitations on the variable angle in this setup because the movable receiverhorn can only measure angles +4° from the fixed horn.

finite simulation), and 87 cells in the x-direction (428 mm ×275 mm). Two types of measurements are done; monostaticand bistatic RCS. Fig. 13 shows the monostatic and bistaticRCS setup.

1) Monostatic RCS: The monostatic RCS measurementsare carried out in an anechoic chamber, where we place avertically polarized, K -band horn on one end of the chamber,and place the metasurface on a rotatable stage 5.3 m awayfrom the horn. This distance corresponds to the far-field ofthe wave. The S11 signal is obtained using the time gatingfunction on the vector network analyzer (VNA) because thereflection due to the horn captured a major component to theS11 signal, and thus time gating to measure the received signalaround the time of interest allows us to measure the reflectionfrom the metasurface accurately and isolate it from the effectsof the reflections due to other sources.

The monostatic RCS measurements are then compared tothose of a copper plate with the same effective area. Fig. 14shows this comparison, where at ±81°, the retroreflectedpower is only 0.1 dB smaller than the effective copper plate,which corresponds to 98% aperture efficiency. Therefore,when considering the effective aperture, it is seen that most ofthe power is coupled into an angle very close to retroreflection.

2) Bistatic RCS: The bistatic RCS is measured with anexperimental setup depicted in Fig. 13(b). The metasurfacewas placed on a platform between two arms as shownin Fig. 15. The S21 signal received from the Rx horn ismeasured using a VNA where two steps were taken. First,an S21 background level is recorded into memory (without themetasurface on the platform), and second, we place the meta-surface on the platform and measure the S21 again with thesubtraction of the background. The resulting measurements areseen in Fig. 16 where the bistatic RCS of the TE metasurfaceis measured alongside the bistatic RCS for a copper plate ofthe same size. It can be inferred that the retroflection from themetasurface at −82.87° corresponds to 93% of the power thatspecularly reflects off a copper plate of the same size, while

Fig. 14. Monostatic RCS measurement for the TE board (blue solid line) at24 GHz, and an effective aperture (red dotted line). The angle is with respectto broadside incidence.

Fig. 15. Bistatic RCS measurement setup.

Fig. 16. Bistatic RCS measurement comparing the TE metasurface (bluesolid line) with a copper plate (red dotted line) at 24 GHz. This figure isnormalized to the specular reflection power of a copper plate.

the specular reflection of the metasurface is greatly reducedto only 10% when compared to a copper plate. We haveobtained much stronger suppression at the specular angle asevidenced by the dip at +82.87°. However, the finite size of themetasurface and the angular width of the incident beam createdappreciable reflection at an angle near the specular angle, forwhich the suppression is less dramatic. We can obtain greaterefficiency and retroreflection at the designed angle of −82.87°by increasing the size of the board.

B. TM Metasurface

The TM metasurface is also fabricated with 136 cells inthe y-direction (again the same number of cells that are usedfor the 1-D finite simulation), and 87 cells in the x-direction


Fig. 17. Monostatic RCS measurement for the TM board (blue solid line)at 24 GHz and the theoretical effective aperture (red dotted line).

Fig. 18. Bistatic measurement comparison between the TM board (blue solidline) and a copper plate (red dotted line) at 24 GHz. This figure is normalizedthe specular reflection power of a copper plate.

(428 mm × 275 mm). We measure the monostatic and bistaticRCS of this metasurface in a similar manner to its TEcounterpart.

1) Monostatic RCS: Fig. 17 shows the monostatic RCS ofthe TM board, and when it is compared to an effective copperplate at ±82.87°, there is a difference of 0.2 dB, which is anaperture efficiency of 95%. This again shows that most of thepower is coupled into the retroreflected mode. Fig. 17 is alsoconsistent with what we found in the simulation where theretroreflected power at ±82.87° and ±37° is in the range of−18 to −15 dB.

2) Bistatic RCS: The bistatic experiment is done using anincident angle of −81° rather than −82.87°, because we findthis to be the optimal retroreflection angle given the finitesize of the metasurface. Fig. 18 shows the bistatic RCS of theTM board where there is a strong retroreflected componentand a suppressed specular component. The retroflection fromthe metasurface at −81° is approximately 93% of the powerthat specularly reflects off a copper plate, while the remainingpower reflected from the metasurface is very minimal. Oncemore this shows that there is a strong coupling of the incidentwave at −81° to the retroreflected mode, whereas the specularmode is greatly suppressed.

V. CONCLUSION

We have reported binary Huygens’ metasurfaces thatachieve strong retroreflection at near-grazing incidence for

both TE and TM polarizations. These binary Huygens’ meta-surfaces feature aggressive discretizations of only two ele-ments per grating period, implemented by ground-backeddipole (for the TE surface) and slot (for the TM surface) arrays.We have reported their design procedure, and through simula-tions and experiments, we have demonstrated their capabilityto achieve strong retroreflection and greatly suppress specularreflection. Experimental demonstration shows the achievementof retroreflection at 90%–95% aperture efficiency for bothpolarizations. In departure from contemporary metasurfaces,the binary Huygens’ metasurfaces introduced here boast thesingle-layer construction, large unit cell sizes, and simple ele-ments, which lead to advantages in relaxed precision tolerance,simple fabrication, and robust operation. These advantagesmake the binary Huygens’ metasurface an attractive candidatefor the design of next generation cost-efficient, low profile,and effective retroreflectors for millimeter-wave and tetrahertzfrequencies.

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Alex M. H. Wong (S’00–M’15) received the Ph.D.degree in electrical engineering from the Universityof Toronto, Toronto, ON, Canada, in 2014.

He then served briefly as a Postdoctoral Fellowat the University of Toronto. He is an AssistantProfessor of applied electromagnetics with theDepartment of Electronic Engineering, CityUniversity of Hong Kong (CityU), Hong Kong.He is also a member of the State Key Laboratoryof Millimeter Waves, partner Laboratory at CityU.He has advanced multiple projects in applied

electromagnetics on next-generation RF, infrared and optical metasurfaces,superoscillation-based imaging, and radar systems. His current researchinterests include metasurfaces, metamaterials, and super-resolution systems.

Dr. Wong is a member of the IEEE Antennas and Propagation Societyand Microwave Theory and Techniques Society. He has received severalaccolades which include an IEEE RWP King Award (for the best annualpublication by a young author in the IEEE TRANSACTIONS ON ANTENNASAND PROPAGATION), an URSI Young Scientist Award, a Raj Mittra Grant,IEEE doctoral research awards from the AP and MTT societies, and theNational NSERC Canada Graduate Scholarship.

Philip Christian received the B.Sc. degree in math-ematics and physics from York University, Toronto,ON, Canada, in 2014, and the M.Eng. and M.A.Sc.degrees in electrical engineering from the Universityof Toronto, Toronto, ON, Canada, in 2015 and 2017,respectively.

He is currently a Systems Engineer with ThalesCanada, Ville de Québec, QC, Canada, wherehe is involved in integrating sensors for anautonomous train platform. His current researchinterests include the field of electromagnetics, where

he focused on photonic devices and the design and simulation of reflectivemetasurfaces.


George V. Eleftheriades (S’86–M’88–SM’02–F’06) received the M.S.E.E. and Ph.D. degrees inelectrical engineering from the University of Michi-gan, Ann Arbor, MI, USA, in 1989 and 1993,respectively.

From 1994 to 1997, he was with the Swiss Fed-eral Institute of Technology, Lausanne, Switzerland.He is currently a Professor with the Departmentof Electrical and Computer Engineering, Univer-sity of Toronto, ON, Canada, where he holds theCanada Research/Velma M. Rogers Graham Chair in

Nano- and Micro-Structured Electromagnetic Materials. He is a recognizedinternational authority and pioneer in the area of metamaterials. These areman-made materials which have electromagnetic properties not found innature. He introduced a method for synthesizing metamaterials using loadedtransmission lines. Together with his graduate students, he provided thefirst experimental evidence of imaging beyond the diffraction limit andpioneered several novel antennas and microwave components using thesetransmission-line based metamaterials. His research has impacted the field bydemonstrating the unique electromagnetic properties of metamaterials; usedin lenses, antennas, and other microwave and optical components to driveinnovation in fields, such as wireless and satellite communications, defence,medical imaging, microscopy, and automotive radar. He is currently leadinga group of graduate students and researchers in the areas of electromagnetic

and optical metamaterials, and metasurfaces, antennas and components forbroadband wireless communications, novel antenna beam-steering techniques,far-field super-resolution imaging, radars, plasmonic and nanoscale opticalcomponents, and fundamental electromagnetic theory.

Dr. Eleftheriades served as a member of the IEEE Antennas and Propa-gation (AP)-Society administrative committee from 2007 to 2012. In 2009,he was elected as a fellow of the Royal Society of Canada. He was anIEEE AP-S Distinguished Lecturer from 2004 to 2009. His co-authoredpapers received numerous awards such as the 2009 Best Paper Awardfrom the IEEE MICROWAVE AND WIRELESS PROPAGATION LETTERS, theR. W. P. King Best Paper Award from the IEEE TRANSACTIONS ONANTENNAS AND PROPAGATION in 2008 and 2012, and the 2014 PiergiorgioUslenghi Best Paper Award from the IEEE ANTENNAS AND WIRELESSPROPAGATION LETTERS. He received the Ontario Premier’s Research Excel-lence Award in 2001, the University of Toronto’s Gordon Slemon Awardin 2001, and the E.W.R. Steacie Fellowship from the Natural Sciences andEngineering Research Council of Canada in 2004. He was a recipient of the2008 IEEE Kiyo Tomiyasu Technical Field Award and the 2015 IEEE JohnKraus Antenna Award, and the Research Leader Award from the Facultyof Applied Science and Engineering of the University of Toronto in 2018.He served as the General Chair of the 2010 IEEE International Symposiumon Antennas and Propagation held in Toronto, ON, Canada. He served asan Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS ANDPROPAGATION.

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