Full-duplex Reflective Beamsteering Metasurface Featuring Magnetless Nonreciprocal Amplification
FFull-Duplex Reflective Beamsteering MetasurfaceFeaturing Magnetless Nonreciprocal Amplification
Sajjad Taravati and George V. Eleftheriades The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University ofToronto, Toronto, Ontario M5S 3G4, CanadaEmail: [email protected]
Nonreciprocal radiation refers to electromagnetic wave radiation in which a structure pro-vides different response under the change of the direction of the incident field. Modernwireless telecommunication systems demand versatile apparatuses which are capable of full-duplex nonreciprocal wave processing and amplification, especially in the reflective state.Here, we propose full-duplex reflective beamsteering metasurfaces for magnetless nonrecip-rocal wave amplification. To realize such a unique, extraordinary and versatile functional-ity, we propose a completely new architecture in which a chain of series cascaded radiat-ing patches are integrated with nonreciprocal phase shifters, providing an efficient mech-anism for wave reception, signal amplification, nonmagnetic nonreciprocal phase shiftingand steerable wave reflection. Having accomplished all these functionalities in the reflec-tive state, the metasurface represents a conspicuous apparatus for efficient, controllable andprogrammable wave engineering for wireless telecommunications. Such an ultrathin reflec-tive metasurface can provide directive and diverse radiation beams, and steerable beams bysimply changing the bias of the gradient active nonmagnetic nonreciprocal phase shifters. a r X i v : . [ phy s i c s . a pp - ph ] J a n he proposed structure provides large wave amplification and is immune to undesired timeharmonics, yielding a highly efficient full-duplex reflective beamsteering apparatus.1 Introduction Over the past decade, the advent and development of metasurfaces has led to significant advancesto wave processing in modern telecommunication and optical systems . However, conventionalstatic metasurfaces are restricted by the Lorentz reciprocity theorem which significantly limitstheir applications as versatile wave shapers and wave processors in modern wireless communica-tion systems. Ferrite-based magnetic materials have been used for nonreciprocity implementationbut they are cumbersome, costly, are not compatible with printed circuit board technology, andare not suitable for high frequency applications and future generation telecommunication systems.It is an object of this study to overcome some of the above-noted disadvantages. Lately, therehas been a substantial scientific attraction to magnetless active metasurfaces for nonreciprocalwave processing . Magnet-free nonreciprocal metasurfaces and metamaterials provide hugedegrees of freedom for arbitrary alteration of the wavevector and temporal frequency of electro-magnetic waves . They may be classified into two main categories, that is, space-time-modulated and transistor-loaded metasurfaces and metamaterials. Amongthese nonreciprocity approaches, transistor-based nonreciprocity is of high interest thanks to itsimmense capability for efficient nonreciprocal electromagnetic-wave amplification while breakingthe time reversal symmetry.Active metasurfaces provide huge degrees of freedom for arbitrary and unidirectional al-2eration of the wavevector and amplitude of electromagnetic waves . They representa class of compact dynamic wave processors for extraordinary transmission of electromagneticwaves. Reflective active metasurfaces represent a class of metasurfaces for simple and advancedwave tailoring . They can be installed on a wall or inside a device like a cell phoneor a laptop to provide a diverse range of wave engineering.This paper proposes a low-profile reflective metasurfaces for nonreciprocal wave engineer-ing and electromagnetic wave radiation control. The proposed reflective metasurface is capableof providing full-duplex unidirectional wave amplification and beam-steering. We introduce anoriginal metasurface architecture in which a chain of series cascaded radiating patches are inte-grated with nonreciprocal phase shifters, providing an efficient mechanism for wave reception,unilateral signal amplification, nonmagnetic nonreciprocal phase shifting and steerable wave re-flection. Such a unique, extraordinary and useful functionality has not been reported previouslyand is expected to find various applications in modern telecommunication systems. We provide thetheory, simulation and experimental results of full-duplex nonreciprocal-beam-steering and waveamplification of these reflective metasurfaces. Such metasurfaces may be placed on a wall, therebyamplifying, transforming and directing the radiation pattern of a source antenna or a received wavenon-reciprocally, while providing different radiation beams for the reception and reflection states.Such metasurfaces are composed of chains of transistor-based nonreciprocal phase shifters inter-connected to antenna elements.The proposed apparatus may be placed on a wall or in front of an antenna to amplify a3ave, and/or steer a beam to a desired direction, i.e., transform the radiation pattern and introducedifferent radiation patterns for waves incident from its left and right sides. The metasurface isendowed with directive, diverse and asymmetric reflection and reception radiation beams, andtunable beam shapes. Furthermore, these beams can be steered by changing the DC bias of thenovel nonreciprocal phase shifters. Moreover, there is no undesired harmonics, yielding a highconversion efficiency with significant wave amplification which is of paramount importance forpractical applications such as point to point full-duplex communications.
Figure 1 shows the realization of the proposed reflective transistor-based metasurface. The meta-surface is formed by a set of phase-gradient cascaded radiator-amplifier-phaser supercells. Themetasurface comprises a dielectric layer sandwiched between two conductor layers. The bottomconductor layer acts as the ground plane of the patch antenna elements and also includes the di-rect current (DC) signal patch of the unilateral circuits. The top conductor layer includes patchantenna elements, transistors, and phase shifters. The dielectric layer separates the two conductorlayers from each other. Each supercell is formed by a patch antenna element, a phase shifter and aunilateral circuit. When an electromagnetic wave is received at the surface of the metasurface, themetasurface reflects a wave having an identical frequency to the frequency of the received wavebut towards a desired direction in space.The metasurface system comprises a dielectric layer interposed between two conductor lay-4igure 1: Schematic of the reflective beamsteering metasurface constituted of cascaded radiator-amplifier-phaser chains for simultaneous reflection and reception at different angles of receptionand reflection. 5rs. Each of the conductor layers is formed by a plurality of supercells embedded therein. Eachsupercell in the plurality of supercells comprises a microstrip patch radiator in electrical connectionwith a phase shifter and a unilateral transistor-based amplifier. The transistor radio frequency (RF)circuit includes two decoupling capacitors, and the DC biasing circuit of the transistor includes achoke inductor, two bypass capacitors and one biasing resistor. A DC signal biases the transistorsto create a gradient non-reciprocal phase shift profile.Figure 2 sketches the high-level architecture of the proposed reflective beamsteering meta-surface. The metasurface thickness is subwavelength. In the forward problem, denoted by “F”,the incoming wave from the right side impinges on the metasurface under the angle of incidence θ i which is inside the reception beam of the metasurface. The reception beam of the metasurfaceis governed by the gradient phase shifters in each supercell. Hence, the wave is received by themetasurface, acquires a power gain and is reflected at the desired angle of reflection θ Fr , insteadof the reflection angle θ r = − θ i corresponding to the specular angle for reflection in conventionalsurfaces. In contrast, in the backward problem, denoted by “B”, the incoming wave from the leftside impinges on the metasurface under the angle of incidence − θ i which is outside the receptionbeam of the metasurface. Therefore, the wave is not received by the metasurface and is reflected atthe reflection angle θ Br without reflection gain. Therefore, at a given frequency and for symmetricwave incidences, where θ Bi = − θ Fi , the reflective metasurface introduces different, nonreciprocaland asymmetric radiation patterns for the forward and backward incidences, i.e., θ Fr (cid:54) = − θ Br , (1)6igure 2: Functionality of the proposed reflective beamsteering metasurface.and E F (cid:54) = E B , | E ( θ Fr ) | > | E ( θ Br ) | , (2)Figure 3 describes the beamsteering mechanism, including wave incidence and reflectionfrom the cascaded supercells of the metasurface in Figs. 1 and 2. Each chain is constituted by N interconnected supercells, each of which is formed by a radiating patch element characterizedby the length L and phase shift φ p , a unilateral transistor-based amplifier characterized by thetransmission function T U and the phase shift φ U , and a gradient phase shifter characterized by thetransmission function T φ n and phase shift φ n , where < n < N . The incoming wave from theright side impinges on the metasurface under the angle of incidence θ i which is inside the reception7eam of the metasurface, governed by the gradient phase shifters in each supercell. The incidentwave is received by the radiating patch elements upon different phases corresponding to the angleof incidence θ i . Then, the received signal at the feeding ports of the patch elements may be writtenin terms of voltages as V i ,n = N (cid:88) n =1 V ,n e iβ ( N − n ) d sin( θ i ) , (3)where β is the wavenumber of the incident wave, and d denotes the distance between two adjacentelements. The reflected electric field is expressed as E ( θ r ) = N (cid:88) n =1 V o ,n e iβnd sin( θ r ) , (4)where V o ,n = V i ,n .T U .T φ n . Hence, the reflected electric field reads E ( θ r ) = N (cid:88) n =1 V ,n .T U .T φ n e iβd [( N − n ) sin( θ i )+ n sin( θ r )] , (5)which demonstrates the effect of the incident angle θ i , unilateral transistor-based amplifier transferfunction T U and the gradient phase shifters transfer function T φ n on the reflected field magnitudeand the angle of reflection θ r . We shall stress that, here V ,n is different for forward and backwardwave incidences as the metasurface provides an asymmetric reception beam which is realized byuni-directional gradient phase shifters.Figure 4 depicts a schematic of a chain of the interconnected supercells. Each supercell iscomposed of a patch antenna element, and a nonreciprocal phase shifter. The nonreciprocal phaseshifters can be either one-way or two-way. A one-way nonreciprocal phase shifter is constituted ofa unilateral device, e.g. a transistor-based amplifier, incorporated with a fixed phase shifter. Thepatch antenna elements are double-fed microstrip patch antennas to allow the flow of the reflection8igure 3: Beamsteering mechanism of the nonreciprocal reflective metasurface. A chain of seriescascade radiating patches are integrated with nonmagnetic nonreciprocal phase shifters, providingan efficient mechanism for wave reception, one-way signal amplification, nonmagnetic nonrecip-rocal phase shifting and steerable wave reflection.9f power in the desired direction inside the metasurface. However, the first and last patch antennaelements are single-fed patches. The chain of the interconnected patches and nonreciprocal phaseshifters behave differently with the incident waves from the right side and the left side.For further development of the proposed metasurface and for achieving a more versatilestructure, one may use a two-way nonreciprocal phase shifter and amplifier as illustrated in Fig. 5.Such a nonreciprocal phase shifter is formed by two power dividers, two unilateral transistor-based amplifiers, two fixed phase shifters, and four decoupling capacitors. The top and bottomphase shifters provide different phase shifts. The top and bottom amplifiers may provide equal am-plification and isolation, in the forward and backward directions, respectively. The signal enteringthe structure from the left side goes through the upper arm, experiences amplification by the topamplifier and then passes through the top phase shifter. However, the signal entering the structurefrom the right side goes through the lower arm, experiences amplification by the bottom amplifierand then passes through the bottom phase shifter. Figure 6 illustrates the detailed architecture of the fabricated reflective beamsteering metasurface.The top layer includes a set of chains of patches interconnected through one-way transistor-basedgradient nonreciprocal phase shifters. The bottom conductor layer includes two metallic sheets,one acting as the RF grounding of the patch antennas, and the other one provides the DC bias ofthe transistors. The DC bias of the transistors is supplied to the bottom-right side of the top layer,10igure 4: Nonreciprocity of the full-duplex reflective metasurface with an asymmetric receptionbeam governed by chains of series cascaded radiating patches integrated with phase shifters andunilateral amplifiers. 11 ort 1 Port 2 T φ R φ Figure 5: Two-way nonreciprocal phase shifter and amplifier composed of two amplifiers, tworeciprocal phase shifters, and two power splitters.transferred to the bottom layer through a via hole, and then supplied to each transistor through avia hole.Figure 7(a) shows a photo of the fabricated reflective metasurface. The metasurface is formedby 30 patch antenna elements, i.e., 20 double-fed and 10 single-fed patch antenna elements, and 25nonreciprocal phase shifters. Each nonreciprocal phase shifter includes a reciprocal transmission-line based phase shifter, a GAli-2+ transistor-based amplifier, two decoupling capacitors, an induc-tor and a bypass capacitor. A total number of 25 Gali-2+ unilateral transistor-based amplifiers, 25choke inductors of 15 nH, 25 bypass capacitors of 100 pF and 50 decoupling capacitances of 3 pFare used. The metasurface is fabricated as a two-layer circuit, i.e., two conductor layers and onedielectric layer, made of Rogers RO4350 with 30 mils height.The metasurface comprises a dielectric layer sandwiched between two conductor layers,12ormed by an array chain of supercells. Supercells are comprised of patch antenna elements andnon-reciprocal tunable phase shifters. When an electromagnetic wave at a given frequency im-pinges on the metasurface, the metasurface amplifies the wave instantly and reflects the wave to adesired direction, having an identical frequency to the frequency of the incident wave. The feedingline supporting the DC bias of the unilateral amplifiers is embedded inside the bottom conductorground-plane layer. The specifications of the supercells may be varied via a DC signal to con-trol the properties of the reflected wave, including the angle of reflection and the amplitude of thereflected wave. Each supercell comprises one reciprocal phase shifter, one unilateral transistor-based amplifier, one choke inductance, two decoupling capacitances, and one bypass capacitor.The choke inductance prevents leakage of the incident electromagnetic wave to the DC biasingpath, and the decoupling capacitances prevent leakage of the DC bias to the RF path of the nextsupercell.Figures 7(b) and 7(c) show a schematic diagram illustrating the experimental demonstrationof the nonreciprocal radiation beam reflective metasurface. The measurement set-up consists ofthe fabricated reflective metasurface, an absorber for holding the metasurface, a vector networkanalyzer, a DC power supply and two horn antennas.
Figure 8 illustrates full-duplex operation in the proposed reflective nonreciprocal-beam metasur-face. Here, the incoming wave from the right side impinges on the metasurface and reflects to the13igure 6: Architecture of the fabricated reflective beamsteering metasurface.14 a)(b) (c)
Figure 7: Experimental demonstration. (a) A photo of the fabricated metasurface. (b) and (c)Measurement set-up. 15igure 8: Full-duplex nonreciprocal-beam reflection and reception of the reflective metasurface.left side and is received by the main RX and TX port at the left side of the metasurface upon theangle of reception θ RX . However, the transmitting wave from the main RX and TX port impingeson the metasurfaces and reflects under the reflection angle θ TX (cid:54) = θ RX while experiencing a muchlower gain. As a result, the metasurface functions as a full-duplex nonreciprocal-beam apparatus,where simultaneous reflection and reception at different angles is achieved.Figures 9(a) to 9(h) plot the full-wave simulation results illustrating the nonreciprocal re-flective beamsteering mechanism of the proposed metasurface. Here, the reflection gain of themetasurface for forward wave incidence is set to 1 for the sake of presentation so that both incidentand reflected waves can be seen. As we see in these figures, the metasurface introduces differentangles of reflection for each angle of incidence.Figure 10(a) plots the experimental results demonstrating the nonreciprocal full-duplex beam16igure 9: Full-wave simulation results for nonreciprocal reflective beamsteering for (a)-(d) forwardwave incidence, and (e)-(h) backward wave incidence for nonreciprocity examination. (a) θ i = 80 ◦ .(b) θ i = 70 ◦ . (c) θ i = 60 ◦ . (d) θ i = 50 ◦ . (e) θ i = − ◦ . (f) θ i = − ◦ . (g) θ i = − . ◦ . (h) θ i = − ◦ . 17teering functionality for wave incidence from the angle of incidence of +80 degrees. For the for-ward problem, where the incident wave impinges on the metasurface from the right side, i.e., uponthe angle of incidence of +80 degrees, the wave is being amplified, about 16.5 dB by the meta-surface instantly and is reflected to the desired angle of reflection of -5 degrees. However, forthe backward problem, where the incident wave impinges on the metasurface from the left side,i.e., upon the angles of incidence of -5 and -80 degrees, the wave is not amplified significantly.The nonreciprocal-beam full-duplex operation in Fig. 10(a) is as follows. The main port for thereception and reflection is placed at -5 degrees. As a result, a reflection gain of +7.8 dB from -5to +32 is achieved. However, a reception gain of 16.2 dB is achieved from +80 to -5. Hence,the metasurface is capable of simultaneous reception and reflection but at different reception andreflection angles, i.e. with a reflection angle of +32 degrees and a reception angle of +80 degrees.Figure 10(b) plots the experimental results demonstrating the frequency response of the nonrecip-rocal full-duplex beam steering functionality for wave incidence from the angle of incidence of 80degrees. The isolation between the wave reflection at different angles shows that a proper waveamplification and isolation is achieved at the frequency of 5.81 GHz.Figure 10(c) plots the experimental results demonstrating the nonreciprocal full-duplex beamsteering functionality for wave incidence from the angle of incidence of +70 degrees. For theforward problem, where the incident wave impinges on the metasurface from the right side, i.e.,upon the angle of incidence of +70 degrees, the wave is being amplified about 19 dB by themetasurface and is reflected to the desired angle of reflection of -20 degrees. However, for thebackward problem, where the incident wave impinges on the metasurface from the left side, i.e.,18pon the angles of incidence of -20 and -70 degrees, the wave is amplified less than 13 dB and underangles of reflection corresponding to the opposite of angles of incidence. The nonreciprocal-beamfull-duplex operation in Fig. 10(c) is as follows. The main port for the reception and reflection isplaced at -20 degrees. As a result, a reflection gain of +12 dB from -20 to +20 degrees is achieved.However, a reception gain of 18.5 dB is achieved from +70 to -20 degrees. Hence, the metasurfaceis capable of simultaneous reflection and reception but at different reception and reflection angles,i.e. with a reflection angle of +20 degrees and a reception angle of +70 degrees. Figure 10(d) plotsthe experimental results demonstrating the frequency response of the nonreciprocal full-duplexbeam steering functionality for wave incidence from the angle of incidence of 70 degrees. Theisolation between the wave reflection at different angles shows that a proper wave amplificationand isolation is achieved at the frequency of 5.81 GHz.Figure 10(e) plots the experimental results demonstrating the nonreciprocal full-duplex beamsteering functionality for wave incidence from the angle of incidence of 60 degrees. For the for-ward problem, where the incident wave impinges on the metasurface from the right side, i.e., uponthe angle of incidence of +60 degrees, the wave is being amplified more than 21.2 dB by the meta-surface instantly and is reflected to the desired angle of reflection of -28.5 degrees. However, forthe backward problem, where the incident wave impinges on the metasurface from the left side,i.e., upon the angle of incidence of –28.5 and -60 degrees, the wave is not amplified significantly.Nonreciprocal operation of the metasurface is not only relevant to different wave amplificationfor forward and backward wave incidences, but also to angular beamsteering. The nonreciprocalbeamsteering operation of the metasurfaces is as follows. For the forward problem, corresponding19o the angle of incidence of +60 degrees, the ordinary reflection reads -60 degrees, but the wave issteered toward -28.5 degree according to the phase gradient profile of the metasurface. However,for the backward wave incidence, corresponding to the angle of incidence of -28.5 degree, the waveis reflected under the ordinary angle of reflection, i.e., +28 degrees. This is due to the fact that thenonreciprocal phase gradient profile of the metasurface mainly affects the forward waves comingfrom the right side. Figure 10(f) plots the experimental results demonstrating the frequency re-sponse of the nonreciprocal full-duplex beam steering functionality for wave incidence from theangle of incidence of 60 degrees. The isolation between the wave reflection at different anglesshows that a proper wave amplification and isolation is achieved at the frequency of 5.81 GHz.Figure 10(g) plots the experimental results demonstrating the nonreciprocal full-duplex beamsteering functionality for wave incidence from the angle of incidence of 50 degrees. For the for-ward problem, where the incident wave impinges on the metasurface from the right side, i.e., uponthe angle of incidence of +50 degrees, the wave is being amplified, more than 21.7 dB, by the meta-surface instantly and is reflected to the desired angle of reflection of -20 degrees. However, for thebackward problem, where the incident wave impinges on the metasurface from the left side, i.e.,upon the angle of incidence of -20 and -50 degrees, the waves are reflected approximately under or-dinary angles of reflection and with much less power amplification. The nonreciprocal full-duplexoperation in Fig. 10(g) is as follows. The main port for the reception and reflection is placed at -20degrees. As a result, a reflection gain of +12 dB from -20 to +24 degrees is achieved. However,a reception gain of 21.6 dB is achieved from +50 to -20 degrees. Hence, the metasurface is ca-pable of simultaneous reception and reflection but at different reflection and reception angles, i.e.20ith a reflection angle of +24 degree and a reception angle of +50 degrees. Figure 10(h) plots theexperimental results demonstrating the frequency response of the nonreciprocal full-duplex beamsteering functionality for wave incidence from the angle of incidence of 50 degrees. The isolationbetween the wave reflection at different angles shows that more than 21.7 dB wave amplificationand isolation is achieved at the frequency of 5.81 GHz.Next, we show the strong nonreciprocal amplification regime of the metasurface, where θ i < ◦ . Here, more than 21 dB reflection gain for forward wave incidence is achieved whilethe backward reflection gain is less than 3dB. The metasurface is designed to present full ampli-fication for θ i = 40 ◦ corresponding to the normal reflection, i.e., θ r = 0 ◦ . Figure 11(a) plots theexperimental results demonstrating the nonreciprocal full-duplex wave amplification functionalityfor wave incidence from the angle of incidence of 40 degrees. For the forward problem, where theincident wave impinges on the metasurface from the right side, i.e., upon the angle of incidenceof +40 degrees, the wave is being amplified, about 21.6 dB, by the metasurface instantly and isreflected to the desired angle of reflection of zero degree. However, for the backward problem,where the incident wave impinges on the metasurface from the left side, i.e., under the angle ofincidence of -40 degrees, the wave is not amplified significantly.Figure 11(b) plots the experimental results demonstrating the nonreciprocal full-duplex beamsteering functionality for wave incidence from the angle of incidence of 45 degrees. For the for-ward problem, where the incident wave impinges on the metasurface from the right side, i.e., uponthe angle of incidence of +45 degree, the wave is being amplified, more than 25 dB, by the meta-21 i =+80 ( r =-5) i =-5 ( r =+32) i =-80 ( r =+74.5)17.5 (dB) (a) Transm. from +80 ° to -5 ° Transm. from +80 ° to -80 ° Transm. from -80 ° to +80 ° Transm. from -5 ° to +80 ° Freq. (GHz) T r a n s m i ss i o n m a g n i t u d e ( d B ) i s o l a t i o n (b) +90+60+300-30-60-90 5 10 15 20 (dB) i =+70 ( r =-20) i =-20 ( r =+20) i =-70 ( r =+80) (c) Transm. from +70 ° to -20 ° Transm. from +70 ° to -70 ° Transm. from -70 ° to +70 ° Transm. from -20 ° to +70 ° Freq. (GHz) T r a n s m i ss i o n m a g n i t u d e ( d B ) i s o l a t i o n (d) +90+60+300-30-60-90 5 10 15 20 i =+60 ( r =-28.5) i =-28.5 ( r =+28) i =-60 ( r =+26)22 (dB) (e) Transm. from +60 ° to -30 ° Transm. from +60 ° to -60 ° Transm. from -60 ° to +60 ° Transm. from -30 ° to +60 ° Freq. (GHz) T r a n s m i ss i o n m a g n i t u d e ( d B ) i s o l a t i o n (f) +90+60+300-30-60-90 5 10 15 20 i =+50 ( r =-20) i =-20 ( r =+24) i =-50 ( r =+42)22 (dB) (g) Transm. from +50 ° to -20 ° Transm. from +50 ° to -50 ° Transm. from -50 ° to +50 ° Transm. from -20 ° to +50 ° Freq. (GHz) T r a n s m i ss i o n m a g n i t u d e ( d B ) i s o l a t i o n (h) Figure 10: Experimental results for the angular and frequency responses, for wave incidence upondifferent angles of incidence. (a) and (b) θ i = 80 ◦ . (c) and (d) θ i = 70 ◦ . (e) and (f) θ i = 60 ◦ . (g)and (h) θ i = 50 ◦ . 22 i =+40 ( r =0) i =-40 ( r =0)
22 (dB) (a) +90+60+300-30-60-90 0 10 20 i =+45 ( r =-18) i =-45 ( r =+66)
25 (dB) (b)
Figure 11: Experimental results for nonreciprocal wave amplification. (a) θ i = 40 ◦ . (b) θ i = 45 ◦ .surface instantly and is reflected to the desired angle of reflection of -18 degrees. However, forthe backward problem, where the incident wave impinges on the metasurface from the left side,i.e., under the angle of incidence of -45 degree, the wave is not amplified significantly and is notbeam-steered.Table 1 lists a summary of the full-duplex nonreciprocal beamsteering reflective metasurfaceperformance. Figure 12(a) plots the experimental results demonstrating the beam steering functionality throughchanging the phase shift of the nonreciprocal phase shifters for wave incidence from the angle ofincidence of +30 degrees at the frequency 5.8 GHz. For the forward problem, where the incidentwave impinges on the metasurface from the right side, i.e., upon the angle of incidence of +60degrees, the wave is being amplified more than 10 dB by the metasurface instantly and is reflected23 i =+30 (3.84 V ) i =+30 (3.7 V)
13 (dB) (a) +90+60+300-30-60-90 0 5 10 i =+60 (3.84 V) i =+60 (3.6 V) i =+60 (4 V) (b) Figure 12: Experimental results for the programmable and controllable beamsteering mechanismvia adjustment of the DC bias of the transistors, for wave incidence upon the angle of incidence(a) θ i = 30 ◦ . (b) θ i = 60 ◦ .to different desired angles of reflection for the DC bias of 3.7V and 3.84V.Figure 12(b) plots the experimental results demonstrating the beam steering functionalitythrough changing the phase shift of the nonreciprocal phase shifters, by the DC bias, for waveincidence from the angle of incidence of +60 degrees at 5.8 GHz. For the forward problem, wherethe incident wave impinges on the metasurface from the right side, i.e., upon the angle of incidenceof +60 degrees, the wave is being amplified more than 10 dB, by the metasurface instantly and isreflected to different desired angles of reflection for the DC bias of 3.6V, 3.84V and 4V. Figure 13(a) shows a schematic representation of the near-field experimental set-up of the nonre-ciprocal radiation beam reflective metasurface. In this experiment, the two source horn antennas24 a) +90+60+300-30-60-90 0 10 20 i =+40 (Far-field) i =+40 (Near-field)
25 (dB) (b)
Figure 13: Experimental results for near-field efficiency of the reflective metasurface. (a) A photoof the near-field experimental set-up. (b) Near-field beam versus far-field beam of the metasurfacefor wave incidence upon the angle of incidence θ i = 40 ◦ .are placed inside the near-field zone of the metasurface and very close to the metasurface.Figure 13(b) plots the experimental results demonstrating the near-field performance of themetasurface for wave incidence from the angle of incidence of +40 degrees. This figure showsthat the metasurface provides very close results for both far-field and near-field experiments. Thisshows great performance of the metasurface in the near-field. Such a unique near-field perfor-mance, i.e, near-field wave amplification, nonreciprocity, and beam-steering, is expected to findnumerous applications in 6G indoor wireless communications.25 Discussion
The main concept of this paper is the realization of a reflective metasurface which is capable of non-reciprocal beam generation. Such a metasurface realizes full-duplex nonreciprocal-beamsteeringand amplification in the reflective state where simultaneous reception and reflection of waves areaccomplished but at different reflection angles, lacking any undesired frequency change and withdistinct reception and reflection gains. This is totally different than other proposed nonrecipro-cal metasurfaces in which the metasurface changes the spectrum of the incident waveand introduces an undesired frequency alteration. The recently proposed nonreciprocal reflectivetime-modulated metasurfaces suffer from an unwanted frequency change in the spectrumof the incident wave, so that the reflected wave acquires a different frequency than the incidentwave. Such a frequency change is very impractical as the frequency conversion ratio is very smallso that one cannot achieve a practical frequency conversion functionality. However, in our pro-posed nonreciprocal-beam metasurface, the incident and reflected waves share the same frequency.Hence, the proposed metasurface is more practical. Furthermore, some of the recently proposednonreciprocal metasurfaces are transmissive structures , which are not suitable for practical ap-plications. In contrast, the proposed reflective metasurface in this study is very practical as it canbe mounted on a wall and provide a desired beamsteering and amplification.We have introduced a new architecture for reflective wave engineering comprising chainsof patch antenna elements with embedded non-reciprocal amplifying phase shifters. This archi-tecture is unique even in the case of traditional reciprocal reflect-arrays . For the proposed26on-reciprocal reflective surface, there is no inherent limit to the bandwidth as the frequency band-width of the proposed unit cells can be easily enhanced through engineering approaches for thebandwidth enhancement of patch resonators .In terms of applications, such metasurfaces can be elegantly mounted on a wall or on asmart device in a seamless way. These surfaces are capable of massive MIMO beam-forming,as no excessive RF feed lines and matching circuits are required, the metasurface functional-ity and operation can be fully controlled and programmed through biasing of unilateral devicesand phase shifters, as well as tunable patch radiators. Highly directive and reflective full-duplexnonreciprocal-beam operation is a very promising feature of the proposed metasurface to be usedfor a low-cost high capability and programmable wireless beam-forming. The metasurfaces canbecome the core of an intelligent connectivity solution for signal enhancement in WiFi , cellu-lar, satellite receivers and IoT sensors. It provides fast scanning between users while providingfull-duplex multiple access and signal coding.
We have proposed a reflective metasurface that provides the opportunity to realize full-duplex re-flection beamsteering accompanied by wave amplification. A mechanism is proposed to achievenonreciprocal beam operation in the reflection state, such that the structure can be used as a radomefor antennas or can be installed on a wall. The incident and reflected waves share the same fre-quency. The nonreciprocal phase and magnitude transitions in supercells are used to realize a radi-27ting nonreciprocal phase shifter, where the structure is immune to undesired frequency harmonics.The frequency bandwidth of the proposed supercells may be enhanced by using engineering ap-proaches for the bandwidth enhancement of microstrip patch elements and nonreciprocal phaseshifters. Given the strong capability of the proposed metasurface in both near-field and far-fieldwave amplification, nonreciprocity, and beam-steering, the structure is expected to find numerousapplications in 6G and massive MIMO indoor wireless communications.
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This work was supported in part by TandemLaunch Inc. and LATYS, Montreal,QC, Canada, and in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).The authors would like to especially thank Mr. Gursimran Singh Sethi, Co-founder and Technical Leader ofLATYS, and Dr. Omar Zahr, Director of Technology at TandemLaunch Inc., for their great help and support.
Competing Interests
The authors declare that they have no competing financial interests.
Correspondence
Correspondence and requests for materials should be addressed to Sajjad Taravati (email:[email protected]). able 1: Full-duplex nonreciprocal reflective beamsteering at 5.81 GHz.1 2 3 4 5 6 7Forward incidence angle +40 ◦ +45 ◦ +50 ◦ +60 ◦ +70 ◦ +80 ◦ Forward reflection angle ◦ − ◦ − ◦ − . ◦ − ◦ − ◦ Backward incidence angle − ◦ − ◦ − ◦ − ◦ − ◦ − ◦ Backward reflection angle ◦ +66 ◦ +42 ◦ +26 ◦ +80 ◦ +74 . ◦ Isolation level > dB > dB > dB > dB > dB > dB Forward amplification level > . dB > dB > . dB > dB > dB > dBdB