Following our recent theoretical studies [M. G. Silveirinha, C. A. Fernandes,
Phys. Rev. B, 78, 033108, 2008], it is experimentally verified that an array of
crossed metallic wires may behave as a nonresonant material with extremely
large index of refraction at microwaves, and may enable the realization of
ultra-subwavelength waveguides.Comment: accepted for publication in Applied Physics Letters (in press).
  Applied Physics Letters (in press) (2008

Carla R. Medeiros

Carlos A. Fernandes

Jorge R. Costa

Mário G. Silveirinha

Pozar D. M.

English

arXiv

WOS:000260571800103 (Nº de Acesso Web of Science)Following our recent theoretical studies [M. G. Silveirinha and C. A. Fernandes, Phys. Rev. B78, 033108 (2008)], it is experimentally verified that an array of crossed metallic wires may behave as a nonresonant material with extremely large index of refraction at microwaves and may enable the realization of ultrasubwavelength waveguides

Silveirinha, Mário G.

Fernandes, Carlos A.

Costa, Jorge R.

Medeiros, Carla R.

Repositório do ISCTE

Experimental demonstration of a structured material with extremeeffective parameters at microwavesMário G. Silveirinha,1,a Carlos A. Fernandes,2 Jorge R. Costa,2,3 and Carla R. Medeiros21Department of Electrical Engineering-Instituto de Telecomunicações, University of Coimbra,3030 Coimbra, Portugal2Instituto Superior Técnico-Instituto de Telecomunicações, Technical University of Lisbon, 1049-001 Lisbon,Portugal3Departamento de Ciências e Tecnologias da Informação, Instituto Superior de Ciências do Trabalho e daEmpresa, 1649-026 Lisboa, PortugalReceived 10 September 2008; accepted 10 October 2008; published online 30 October 2008Following our recent theoretical studies M. G. Silveirinha and C. A. Fernandes, Phys. Rev. B 78,033108 2008, it is experimentally verified that an array of crossed metallic wires may behave asa nonresonant material with extremely large index of refraction at microwaves and may enable therealization of ultrasubwavelength waveguides. © 2008 American Institute of Physics.DOI: 10.1063/1.3012373The design of materials with unusual electromagneticproperties has received a lot of interest in recent years,mainly because of the great potentials of structures with si-multaneously negative permittivity and permeability.1 How-ever, materials with extreme parameters or extreme proper-ties, such as near zero permittivity, extreme anisotropy, orvery large permittivity, may also have interesting applica-tions in many problems such as tunneling through narrowchannels and bends,2 subwavelength imaging,3 realization ofmagnetic materials in the visible domain,4 and cloaking.5In a recent work,6 we have reported that a compositematerial formed by crossed metallic wires may have ananomalously strong interaction with electromagnetic wavesand may enable the realization of materials with extremelylarge positive index of refraction. The geometry of agrounded slab of the structured material is depicted in Fig.1a. It was theoretically predicted in Ref. 6 that suchgrounded slab may interact with a wave with electric fieldpolarized along the x-direction as a material with very largepositive permittivity. This result is rather surprising sincesystems formed by long metallic wires are typically thoughtas materials with negative permittivity. Here, we experimen-tally verify the results of Ref. 6 and demonstrate that theproposed material may enable the realization of ultrasub-wavelength waveguides.To this end, a prototype of the structured material wasfabricated using a layer by layer design and printed circuittechniques Fig. 1b. In our planar design, the metallicwires are replaced by printed metallic strips. The material isformed by an array of 97 layers of 1.6 mm thick FR4 boards,for which the experimentally determined permittivity aroundthe 1.3 GHz design frequency was h=4.3 with loss tangenttan =0.02. The boards of FR4 have been printed with par-allel metallic strips with width ws=0.83 mm. The metallicstrips are tilted by 45° with respect to the interfaces, andthus the strips in adjacent FR4 boards are mutually orthogo-nal. The lattice constant is a=3.2 mm, and the height of thesubstrate is L=2.6a=8.32 mm. As illustrated in Fig. 1a,the metallic strips are supposed to be connected with goodOhmic contact to a metallic ground plane. In practice, suchconfiguration may be difficult to reproduce using planartechnology. To avoid this difficulty, we have mimicked theground plane by printing an additional metallic strip runningalong the x-direction at the lower edge of each FR4 board.This ensures a good Ohmic contact between all the strips inthe same board. In addition, to ensure Ohmic contact be-tween the stacked FR4 boards, each FR4 board was perfo-rated at 17 specific spots next to the lower edge these spotscan be identified in the lower panel of Fig. 1, and copperwires running along the y-direction were inserted throughthese spots and soldered to the boards. Finally, the bottomface of the fabricated prototype was coated with a silverpaint. Since the spacing between the copper wires is verysmall as compared to the wavelength, such configuration ef-fectively behaves as a continuous ground plane.In order to characterize the properties of the material, wehave investigated the propagation of transverse electric TEaElectronic mail: mario.silveirinha@co.it.pt.L2ayzxaWW=155.5 mm169.7 mmyx(a)(b)hFIG. 1. Color online a A grounded metamaterial slab is placed in be-tween two horizontal dipole antennas. The structured material is formed byan array of crossed metallic wires parallel to the xoz plane and are tilted by45° with respect to the interfaces. The wires are embedded in a hostmaterial with relative permittivity h. b Photo of the fabricated prototypeformed by 97 FR4 boards printed with metallic strips.APPLIED PHYSICS LETTERS 93, 174103 20080003-6951/2008/9317/174103/3/$23.00 © 2008 American Institute of Physics93, 174103-1Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jspguided modes in the structured substrate. It is well knownthat a grounded dielectric slab with relative permittivity only supports guided modes when L0 /4−1. Thus, agrounded substrate with the same permittivity as the FR4boards only supports the TE-guided modes for frequencieslarger than 4.98 GHz. As theoretically shown in Ref. 6, thepresence of the crossed wire mesh may result in a dramaticincrease of the effective permittivity and consequently in asignificant reduction of the TE-mode cutoff frequency. Inorder to experimentally verify this property and measure thedispersion characteristic of the guided modes, the structuredsubstrate was excited by a horizontal dipole antenna orientedalong the x-direction and placed 5 mm away from themetamaterial substrate. The transmitted field was measuredby an identical dipole placed at the other end of the substratetop panel of Fig. 1. Actually, the antennas used in the ex-periment were not wire dipoles but instead were printed inFR4 boards as well. Each printed dipole is connected to thevector network analyzer VNA through a “balun” thatmakes the proper transition between the VNA coaxial cableand the coplanar printed line that feeds the dipole. In orderthat the “baluns” are not detuned by the presence of thestructured substrate, it is convenient that the dielectric boardswith the feeding circuit are oriented in such a way that theyare normal to the y-direction top right panel of Fig. 2. Thefree-space resonance frequency of the printed dipoles is ap-proximately 1.2 GHz.The phase and amplitude of the measured S-parametersare depicted in the top left and lower panels of Fig. 2, re-spectively curves a. The calibration planes are at the an-tenna SMA connectors. Note that S11 is a measure of thefraction of power accepted by the input antenna, whereasS21 is a measure of the coupling between the two dipoles. Itis important to mention that even if there is an excellentcoupling between the two dipoles, the level of S21 does notneed to be close to 0 dB, since part of the power accepted bythe input antenna is either radiated as space wave or dissi-pated in the dielectrics and metals, and only the remainingpower is received by the test antenna, being the main propa-gation mechanism of guided wave. It is seen in Fig. 2 that forfrequencies below 1.1 GHz the level of S21 is below−30 dB, showing that for these frequencies the coupling be-tween the dipoles is very low. This is understandable sincefor low frequencies the TE-guided modes are cut off. How-ever, around 1.25 GHz there is a dramatic increase in thelevel of S21 which approaches −12 dB, suggesting that thestructure may support a guided mode above 1.25 GHz, not-withstanding the electrically small thickness of the substrateL=0 /29. This property stems from the anomalously higheffective permittivity of the structured material.6 For fre-quencies above 1.35 GHz, the S21 level remains significant,even though it deteriorates with increasing frequency, in part,because the dipoles were tuned to 1.2 GHz, and thus theytend to radiate poorly for frequencies relatively far from 1.2GHz. We have experimentally verified with a different set ofprinted dipoles tuned to 1.5 GHz that the onset of propaga-tion of guided modes is still at 1.25 GHz, whereas the S21level may be improved around 1.5 GHz not shown here.Another reason for the deterioration of the S21 level is thatslightly above the cutoff frequency the guided modes be-come very confined inside the structured material, and thus itis difficult to launch the guided mode from the air region.This is supported by the extremely fast variation of the S21phase slightly above 1.25 GHz, suggesting that the guidedmode has an extremely short wavelength and consequently ishighly confined to the structured material because of the verylarge effective permittivity.The reported experimental data concur very well withthe results obtained with a full wave commercial electromag-netic simulator7 curves b in Fig. 2. In the numerical simu-lations, the ground plane was assumed continuous. The ex-cellent agreement between the numerical and experimentalresults demonstrates that our implementation of the groundplane effectively mimics an ideal continuous ground plane.In order to show that the main propagation mechanismbetween the two dipoles is indeed a guided wave, we haveplaced an 80 mm thick microwave absorber block in betweenthe two antennas, 7 mm above the prototype. The purpose ofthe absorber was to block the space wave radiated by thedipole. The corresponding measured S-parameters are shownin Fig. 2 curves c. It is seen that except near 1.25 GHz,the S21 level is little affected by the presence of the ab-sorber, consistently with our expectations that the dominantpropagation mechanism is the guided mode. The drop of theS21 close to the cutoff is understandable, since at the cutofffrequency most of the energy of the guided mode propagatesin the air region, and thus is also blocked by the absorber. Todemonstrate in a conclusive manner that the enhancement ofthe S21 level is due to the emergence of guided modes, wehave rotated the prototype by 90° so that the dipole antennasbecome orthogonal to the FR4 boards with the printed strips.In this case, it is expected that the interaction of the metallicstrips with the dipoles is very weak, and thus the prototypeshould behave in the same manner as a homogeneousgrounded substrate with the same permittivity as the FR4boards. The measured results corresponding to this scenario0.8 1.0 1.2 1.4 1.6 1.8 2.0403020100(c)S11S21S21, (d)(a)(b)(b)(d)(a)(c)Frequency [GHz]11210.8 1.0 1.2 1.4 1.6 1.840003000200010000S11, (a)S21(b) (a)Phase [deg] vs. Frequency [GHz]FIG. 2. Color online Lower panel: Amplitude of the S-parameters in dB.a Measured results. b CST MICROWAVE STUDIO full wave simulations. cMeasured results when an absorber is placed in between the two antennas.d Same as c but the prototype is rotated by 90°. Top left panel: Phase forcases a and b. Top right panel: photo of the experimental setup.174103-2 Silveirinha et al. Appl. Phys. Lett. 93, 174103 2008Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jspare depicted in the lower panel of Fig. 2 curves d, anddemonstrate that indeed the S21 level is close to −40 dB,consistent with the fact that a homogeneous dielectric sub-strate with h=4.3 only supports the TE-guided modes above4.98 GHz. The results obtained with CST MICROWAVE STUDIOcompletely confirm these findings. In Fig. 3, we plot the totalelectric field amplitude at 1.25 GHz along the midheight cutof the structured substrate for the cases in which the dipolesare parallel to either the x-axis or to the y-axis. In thesesimulations, the region in between the printed dipoles wasnot blocked by the microwave absorber. The plots demon-strate how in the case in which the dipoles are parallel to theFR4 boards panel a, the wave is able to penetrate into thestructured substrate permitting a good coupling between thetwo dipoles. This situation contrasts markedly with the casein which the dipoles are perpendicular to the FR4 boardspanel b, for which the guided mode cannot be launchedand the wave cannot propagate along the substrate.It is possible to calculate the dispersion characteristic ofthe guided modes from the experimental data. A straightfor-ward analysis shows that the propagation constant of theguided mode, ky, is such that ky 1 /W2 arg1−−arg+C, where W is the width of the substrate see Fig. 1, C isa constant chosen so that ky = /c at the cutoff frequency ofthe guided mode, and  and  are the S11 and S21 parametersreferred to the input ports of the printed dipoles, respectivelythese parameters are obtained by proper de-embedding ofthe experimental data obtained at the antenna SMAconnectors8. The extracted dispersion characteristic of theguided mode is depicted in Fig. 4 blue curve. It was as-sumed in the extraction procedure that the cutoff frequencyis 1.25 GHz, consistent with the results of Fig. 2. In Fig. 4,we have also plotted the dispersion characteristic calculatedwith CST MICROWAVE STUDIO,7 obtained by analyzing asingle cell of the periodic substrate red curve, as well as thedispersion characteristic obtained using the analytical modeldescribed in our previous work6,9 black curve. It is seenthat the results obtained with the different methods concurvery well, and that the value of kyc / may be significantlylarger than unity for frequencies slightly above the cutofffrequency. This supports the fact the guided mode becomeshighly confined in the structured material. In curve d ofFig. 4, we show the dispersion characteristic of a groundeddielectric slab 	=1, with the same cutoff frequency as theprototype. The permittivity of the equivalent dielectric slab is=53.0, which demonstrates how the crossed wire meshmay, in fact, enhance in a dramatic manner the electric prop-erties of the host medium. As discussed in Ref. 6, muchlarger values of the permittivity may be easily obtained byincreasing the density of wires. It is interesting to note thatthe slope of kyc / versus frequency is much larger for thestructured material than for the equivalent dielectric slab.This property is a consequence of the fact that the responseof the bulk structured material is anisotropic, even for propa-gation in the yoz plane. Quite remarkably, this property en-ables a greater confinement of the electromagnetic fields in-side the metamaterial slab and thus suggests interestingapplications of the proposed structure as an ultrasubwave-length waveguide.This work is supported in part by Fundação para a Ciên-cia e a Tecnologia, Grant No. POSC/EEACPS/61887/2004.The authors gratefully acknowledge technical support fromCarlos Brito, Vasco Fred, and António Almeida.1J. Pendry, Phys. Rev. Lett. 85, 3966 2000.2M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 2006.3P. A. Belov, Y. Hao, and S. Sudhakaran, Phys. Rev. B 73, 033108 2006.4C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, Phys. Rev.Lett. 99, 017401 2007.5J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 2006.6M. G. Silveirinha and C. A. Fernandes, Phys. Rev. B 78, 033108 2008.7CST MICROWAVE STUDIO 2006, CST GmbH, http://www.cst.com.8D. M. Pozar, Microwave Engineering Wiley, New York, 2006.9The model proposed in Ref. 6 assumes that the inclusions are wires andnot strips; we have taken the radius of the wires equal to R=ws, so thatthe perimeter of the cross section of the inclusions is the same.X [cm] X [cm](a) (b)FIG. 3. Color online CST MICROWAVE STUDIO simulations at 1.25 GHz forthe total electric field amplitude at the midheight of the artificial substratefor dipole antennas a parallel to the x-axis and b parallel to the y-axis. 1.0 1.2 1.4 1.6 1.8 2.002468Frequency [GHz]yk c(d) =53.(c) Analyticalmodel(a) Measured(b) MicrowaveStudio simulationsFIG. 4. Color online Dispersion characteristic of the guided mode sup-ported by the structured material. a Measured result. b Full wave simu-lation with Ref. 7. c Theoretical result. d Dispersion for a dielectric slabwith =53.174103-3 Silveirinha et al. Appl. Phys. Lett. 93, 174103 2008Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

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Experimental demonstration of a structured material with extreme effective parameters at microwaves

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Experimental Demonstration of a Structured Material with Extreme
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Experimental Demonstration of a Structured Material with Extreme Effective Parameters at Microwaves

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