A Huygens’ Metasurface Lens for Enhancing the …...antenna and the waveguide antenna with the...
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A Huygens’ Metasurface Lens for Enhancing the Gain of Frequency-Scanned Slotted Waveguide Antennas Michael Chen, George V. Eleftheriades The Edward S. Rogers Department of Electrical and Computer Engineering University of Toronto Toronto, Ontario, Canada M5S 3G4 Ariel Epstein Andrew and Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa 3200003, Israel Abstract—Lenses at the microwave/millimeter-wave frequen- cies can be used to improve the performance of antennas. However traditional dielectric lenses suffer from high reflections and large physical thickness. To combat these issues, we propose a Huygens’ metasurface lens design which can perform the desired lensing effects while minimizing reflections and keeping a low profile. The proposed metasurface utilizes a wide variety of unit cells to accurately model the theoretical boundary conditions necessary for a focusing wave transformation. An example of a metasurface cylindrical lens is designed to improve the gain of a 40λ long frequency-scanned slotted waveguide antenna operating in the frequency range of 33.4GHz to 35.2GHz. The proposed metasurface is designed to increase the gain of the feed antenna while maintaining its scanning capabilities. I. I NTRODUCTION Lenses are crucial devices for manipulating electromagnetic waves. By utilizing the material properties and geometry of lenses, electromagnetic energy can be focused from a diverg- ing source. While traditional utilization of lenses often occurs at optical frequencies, microwave/millimeter-wave frequency lenses are also sought after. One utilization of such lenses is their application in enhancing antenna radiation patterns. These lens antennas utilize a feed antenna at the focal plane of the lens. Similar to optical lenses, microwave lenses can be realized from dielectric materials with curved geometries. However, some disadvantages of using pure dielectric lenses include their typical bulky size and reflections which occur due to the mismatch at their air and dielectric interfaces. While techniques exist to reduce the thickness and mismatch of dielectric lenses [1], [2], a true matched and thin dielectric lens is still difficult to achieve. Metasurfaces, which are the 2D equivalent of metamaterials, are thin structures composed of electrically small scatterers [3], [4]. These scatterers or unit cells are electrically small and can manipulate incident electromagnetic waves to produce desired effects. Such metasurfaces can achieve a variety of wave manipulations, such as refraction and polarization control, with minimal reflections, while maintaining a low profile [3]. In this paper, we propose the design of a metasurface lens to collimate a 40λ long frequency-scanning slotted waveguide antenna centered at 34.3GHz. The waveguide antenna which produces a fan beam has a bandwidth of 1.8GHz which scans continuously with frequency from 0 ◦ to -20 ◦ in the H-plane. To improve the gain of the waveguide antenna, a metasurface lens is designed to collimate the fan beam into a pencil beam without disturbing its scanning capabilities. The lens is composed of a three-layer printed design placed at the focal plane of 3λ at 34.3GHz away from the waveguide antenna and has a width of 15λ in the E-plane or collimation plane. II. UNIT CELL DESIGN AND PHYSICAL REALIZATION The design of the metasurface can be broken down into two steps. The first step involves finding the desired theoretical re- sponse of the metasurface. To approximate the radiation profile of the waveguide antenna, an equivalent magnetic line source can be used. By stipulating the cylindrical wave profile of the equivalent magnetic line source and the desired output plane wave, the electric/magnetic surface impedance/admittance re- quired to produce the wave transformation can be obtained [3], [4]. The second step is to then find appropriate unit cells which can model these spatially varying surface constituents to produce the desired wave transformation. Following the derivations in [5], the spatially dependent electric impedance Z se and magnetic admittance Y sm can be determined by stipulating the wave profile of the equivalent magnetic line source and the desired output plane wave. These are surface impedances/admittances required to transform the cylindrical wave from the magnetic line source to the output plane wave with small reflections. For a physical realization, the surface impedances/admittances can be translated into a microwave equivalent [Z] or [S] matrix [6]. Thereafter, physical structures can be designed by matching their response to the translated [Z] or [S] matrices. To design physical structures to model the ideal [Z] or [S] matrices, three-layer unit cells with etched metallic scatterers are proposed. The proposed unit cells consist of 3 copper layers (1/2 oz. thick) etched on two 25mil Rogers 3010 substrates. The two substrates are bonded using a 2mil Rogers 2929 bondply producing a total unit cell thickness of 1.32mm (≈ λ/7 at 34.3GHz). The lateral dimensions of the unit cells are 1mm x 1mm (≈ λ/9 x λ/9). To produce the desired response with the unit cells, the metallic features are varied geometrically. Specifically, to accommodate for the entire required phase range, a variety of metal structures including dogbones and meander lines are used (see inset Fig. 1).
Transcript of A Huygens’ Metasurface Lens for Enhancing the …...antenna and the waveguide antenna with the...
A Huygens’ Metasurface Lens for Enhancing theGain of Frequency-Scanned Slotted Waveguide
AntennasMichael Chen, George V. Eleftheriades
The Edward S. Rogers Department of Electrical and ComputerEngineering
University of TorontoToronto, Ontario, Canada M5S 3G4
Ariel EpsteinAndrew and Erna Viterbi Faculty of Electrical Engineering
Technion - Israel Institute of TechnologyHaifa 3200003, Israel
Abstract—Lenses at the microwave/millimeter-wave frequen-cies can be used to improve the performance of antennas.However traditional dielectric lenses suffer from high reflectionsand large physical thickness. To combat these issues, we propose aHuygens’ metasurface lens design which can perform the desiredlensing effects while minimizing reflections and keeping a lowprofile. The proposed metasurface utilizes a wide variety of unitcells to accurately model the theoretical boundary conditionsnecessary for a focusing wave transformation. An example of ametasurface cylindrical lens is designed to improve the gain of a40λ long frequency-scanned slotted waveguide antenna operatingin the frequency range of 33.4GHz to 35.2GHz. The proposedmetasurface is designed to increase the gain of the feed antennawhile maintaining its scanning capabilities.
I. INTRODUCTION
Lenses are crucial devices for manipulating electromagneticwaves. By utilizing the material properties and geometry oflenses, electromagnetic energy can be focused from a diverg-ing source. While traditional utilization of lenses often occursat optical frequencies, microwave/millimeter-wave frequencylenses are also sought after. One utilization of such lensesis their application in enhancing antenna radiation patterns.These lens antennas utilize a feed antenna at the focal planeof the lens. Similar to optical lenses, microwave lenses canbe realized from dielectric materials with curved geometries.However, some disadvantages of using pure dielectric lensesinclude their typical bulky size and reflections which occurdue to the mismatch at their air and dielectric interfaces.While techniques exist to reduce the thickness and mismatchof dielectric lenses [1], [2], a true matched and thin dielectriclens is still difficult to achieve.
Metasurfaces, which are the 2D equivalent of metamaterials,are thin structures composed of electrically small scatterers [3],[4]. These scatterers or unit cells are electrically small and canmanipulate incident electromagnetic waves to produce desiredeffects. Such metasurfaces can achieve a variety of wavemanipulations, such as refraction and polarization control, withminimal reflections, while maintaining a low profile [3].
In this paper, we propose the design of a metasurface lensto collimate a 40λ long frequency-scanning slotted waveguideantenna centered at 34.3GHz. The waveguide antenna whichproduces a fan beam has a bandwidth of 1.8GHz which scanscontinuously with frequency from 0◦ to -20◦ in the H-plane.
To improve the gain of the waveguide antenna, a metasurfacelens is designed to collimate the fan beam into a pencilbeam without disturbing its scanning capabilities. The lens iscomposed of a three-layer printed design placed at the focalplane of 3λ at 34.3GHz away from the waveguide antenna andhas a width of 15λ in the E-plane or collimation plane.
II. UNIT CELL DESIGN AND PHYSICAL REALIZATION
The design of the metasurface can be broken down into twosteps. The first step involves finding the desired theoretical re-sponse of the metasurface. To approximate the radiation profileof the waveguide antenna, an equivalent magnetic line sourcecan be used. By stipulating the cylindrical wave profile of theequivalent magnetic line source and the desired output planewave, the electric/magnetic surface impedance/admittance re-quired to produce the wave transformation can be obtained[3], [4]. The second step is to then find appropriate unit cellswhich can model these spatially varying surface constituentsto produce the desired wave transformation.
Following the derivations in [5], the spatially dependentelectric impedance Zse and magnetic admittance Ysm can bedetermined by stipulating the wave profile of the equivalentmagnetic line source and the desired output plane wave. Theseare surface impedances/admittances required to transform thecylindrical wave from the magnetic line source to the outputplane wave with small reflections. For a physical realization,the surface impedances/admittances can be translated intoa microwave equivalent [Z] or [S] matrix [6]. Thereafter,physical structures can be designed by matching their responseto the translated [Z] or [S] matrices.
To design physical structures to model the ideal [Z] or [S]matrices, three-layer unit cells with etched metallic scatterersare proposed. The proposed unit cells consist of 3 copperlayers (1/2 oz. thick) etched on two 25mil Rogers 3010substrates. The two substrates are bonded using a 2mil Rogers2929 bondply producing a total unit cell thickness of 1.32mm(≈ λ/7 at 34.3GHz). The lateral dimensions of the unit cellsare 1mm x 1mm (≈ λ/9 x λ/9). To produce the desiredresponse with the unit cells, the metallic features are variedgeometrically. Specifically, to accommodate for the entirerequired phase range, a variety of metal structures includingdogbones and meander lines are used (see inset Fig. 1).
III. LENS PHYSICAL REALIZATION AND SIMULATIONRESULTS
The realized metasurface contains 131 unit cells in thecollimation plane yielding a total width of 131mm (≈ 15λat 34.3GHz). These unit cells are then repeated 350 timesin the scanning plane to cover the entirety of the 40λ longslotted waveguide antenna. A 1D periodic simulation viaHFSS of the lens cross section excited with a magnetic linesource is conducted as shown in Fig. 1. Although there areedge effects due to the finite size of the metasurface, theoverall transformation from a cylindrical wave to a plane waveis clearly seen. Additionally the overall antenna directivitypattern, line source with metasurface, for the entire frequencyband is shown in Fig. 2. As seen, the metasurface lensis able to collimate the isotropic radiation of the magneticline source into a narrow beam for the desired frequencyrange. Furthermore, the achieved directivity improvement ofthe metasurface is maintained for the entire frequency band of33.4GHz to 35.2GHz.
Metasurface
≈ λ/7
≈ λ/9 ≈ λ/9
Fig. 1. Fullwave simulation of a 15λ metasurface above a magnetic linesource. Inset: An example of a unit cell used for realizing the metasurface.
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34.4GHz
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34.7GHz
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Fig. 2. Fullwave simulation of metasurface lens antenna directivity vs.frequency.
IV. FAR-FIELD MEASUREMENTS
Following the verification of the metasurface lens fromsimulation, a prototype was fabricated and tested (see insetFig. 3). Utilizing an anechoic chamber, the far-field realizedgain pattern of the overall antenna, slotted waveguide antennaand metasurface lens, were characterized. Comparison of a
few measured E-plane patterns of the standalone waveguideantenna and the waveguide antenna with the metasurface lenscan be seen in Fig. 3. Examining the experimental results,it is clear that the metasurface lens is able to collimate thewide fan beam from the slotted waveguide antenna into anarrow pencil beam. As a result of the collimation, the gainof the waveguide antenna was increased by upwards of 10dB.Throughout the frequency range and the corresponding beamangles, the metasurface is able to increase the gain by 6dBto 10dB. While the losses were not possible to be quantifieddue to experimental difficulties, based on the measured gainimprovements, the overall losses are expected to be low.
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Slotted Waveguide Antenna 35.0 GHzSlotted Waveguide Antenna 35.1 GHzSlotted Waveguide Antenna 35.2 GHzSlotted Waveguide with Metalens 35.0 GHzSlotted Waveguide with Metalens 35.1 GHzSlotted Waveguide with Metalens 35.2 GHz
Fig. 3. Far-field measurement of the realized gain pattern of the colimationplane (E-plane). Inset: Close-up of a section of the fabricated metasurface.
V. CONCLUSION
Lenses are very useful devices in all regions ofthe electromagnetic spectrum. However, traditionalmicrowave/millimeter-wave lenses suffer from high reflectionsand large thickness. In this paper we have presented a methodof alleviating these issues by proposing a Huygens’metasurface lens design. An example of a metasurfacecylindrical lens designed to improve the gain of a frequencyscanned slotted waveguide antenna in the range of 33.4GHzto 35.2GHz was demonstrated. More results includingthe scanning-plane characteristics will be presented at theconference.
REFERENCES
[1] H. D. Hristov, ”Millimeter-wave Fresnel-zone plate lens and antenna”,IEEE Trans. on Microw. Theory Techn., vol. 42, no. 12, December 1995.
[2] H. Yi, S. Qu, K. Bo, C. H. Chan, ”3-D printed discrete dielectric lensantenna with matching layer”, Proceedings of ISAP 2014, pp. 115-116,December 2014.
[3] M. Selvanayagam and G. V. Eleftheriades, ”Discontinuous electromag-netic fields using orthogonal electric and magnetic currents for wavefrontmanipulation”,Opt. Express, vol. 21, no. 12, pp. 14409-14429, June2013.
[4] C. Pfeiffer and A. Grbic, ”Metamaterial Huygens’ surfaces: tailoringwave fronts with reflectionless sheets”, Phys. Rev. Lett., vol. 110, no.19, p. 197401, May 2013.
[5] A. Epstein, G. V. Eleftheriades, ”Passive lossless Huygens metasurfacesfor conversion of arbitrary source field to directive radiation”, IEEETrans. and Antennas and Propag., vol. 62, no. 11, pp. 5680-5695,November 2014 .
[6] A. Epstein, G. V. Eleftheriades, ”Huygens metasurfaces via the equiv-alence principle: design and applications”, J. Opt. Soc. Am. B, vol. 33,no. 2, February 2016.
