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Hybridization band gap based smart antennas : deep

subwavelength yet directional and strongly decoupled

MIMO antennas

Geoffroy Lerosey1,*

, Christian Leray2, Fabrice Lemoult

1, Julien de Rosny

1, Arnaud Tourin

1and Mathias Fink

1

1Institut Langevin, ESPCI ParisTech - CNRS UMR 7587, 10 rue Vauquelin, 75005 Paris, France, geoffroy.lerosey@espci.fr

2Time Reversal Communications, Parc Saint Christophe, 10 Avenue de lEntreprise 95861 Cergy Pontoise Cedex

Abstract In this paper, we show how the concept of

hybridization band gaps can be utilized to create antennas for

MIMO applications. Those strongly decoupled antennas present

at the same time a very small form factor and a very low

correlation. To that aim, we first explain briefly the concept of

hybridization between a resonator and the free space waves

continuum. Then we expose the methodology we use to design

multi-ports antennas based on that concept. We present

numerical and experimental results of 2 ports MIMO antennas at

2.45 GHz, printed on a PCB, whose areas are smaller than

2.6*2.6 cm2. The two ports display experimentally peak gains of

a about 4 dB, efficiencies of 80%, a coupling lower than 30 dB

and a correlation lower than 0.1.

Smart antennas, compact antenna arrays, MIMO antennas,

electromagnetic band gap antennas, photonic crystals,

metamaterials

I. INTRODUCTION

It is well known that in order to be efficient for MIMOcommunications, antenna arrays must present very lowcorrelation coefficients. This can be achieved by separating theantennas of the array by a distance higher than half awavelength at the operating frequency [1]. Yang has proposed,

based on a structure investigated by Sievenpipper, to decoupleeven better patch antennas from surface waves usingmushroom type electromagnetic band gap structures [2,3].There has also been some proposals in order to decoupleantennas using slabs of metamaterial which present an effectivenegative permeability or permittivity [4]. Yet none of thoseapproaches ensure antennas with a very small form factor. Herewe propose a very general approach based on the concept ofhybridization band gaps that permit to design antennas with

any type of resonant element. Using those subwavelengthresonant elements, it is possible to design antenna arrays which

present a small form factor and low correlations and inter-antenna coupling. In the first part of the paper, we explain theconcept of hybridization in terms of Fano resonances, andunderline why resonant elements create band gaps that forbidthe propagation of waves. Then we demonstrate that resonantslits in metal planes can be used as resonant elements to realizea very subwavelength two port antenna. We first shownumerical and experimental results of a 1.5 cm wide and 2.6cm high linearly polarized antenna that can be printed on a

PCB substrate and present a decoupling of about 20 dB andgains of about 3.5 dB. Then we further improve our approach

by designing a simple two port antenna that is at the same timevery small (2.6*2.6 cm2), efficient (85%), whose correlation isvery low (0.1), and which provides an enormous decoupling of

about 30 dB in a typical laboratory room. Such antenna couldfind many applications for MIMO applications in small sizevolumes or on PCB boards where multiple systems have toshare the same spectrum such as Zigbee and WIFI in verysmall form factors.

II. HYBRIDIZATION BAND GAPS

A. Metamaterials and photonic crystalsIn a recent paper [5], we have shown that there is a very

close relation between metamaterials and photonic crystals.Those two different kinds of manmade materials are notgoverned by the same phenomena, but they can present the

same properties. In the case of photonic crystals, interferencesbetween scattered and transmitted waves, known as Bragginterferences, can result in the inhibition of the propagation ofwaves in certain frequency ranges. One very interesting featureof photonic crystals [6] is that since propagating waves onlygovern their properties, one can locally modify these materialswithout destroying the band gaps they offer, in order forinstance to create cavities, filters, waveguides, and so on. Thesecrystals, although presenting many applications, can verylimitedly be used in the radio frequency domain since theirtypical scale is of the order of the wavelength. Metamaterials[7], on the contrary, present much smaller spatial scale. This isdue to the fact that their unit cell is generally resonant, andhence can have a typical width much smaller than the

wavelength. They are usually used for their effectiveproperties, for instance negative permeabilities orpermittivities, and hence as slabs or bulky pieces. This can beexplained by the common belief that the unit cells ofmetamaterials are strongly near field coupled, and that no localmodification of a metamaterial can be done, such as changing asingle or a few unit cells, without altering the properties of thewhole material. Hence, there has been no tentative to transposethe concepts explored in the photonic crystal field to that ofmetamaterials. In the antenna community, electromagnetic

band gap materials (EBG) have been proposed independentlyto decouple antennas, which present spatial scales relatively

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smaller than those of photonic crystals. Again, the latter areusually used as isolating surface between antennas, and thetypical separation between uncoupled antennas remains quitelarge, of the order of half a wavelength, even though thecoupling can be drastically reduced.

B. Metamaterial as hybridization band gapsIn order to explain the relation between photonic crystals

and metamaterials, we have adopted the notion ofhybridization. This phenomenon occurs when a local resonancehybridizes with the continuum of the plane waves of ahomogeneous medium, giving raise to a binding and an anti-

binding branches, that are separated by the so-calledhybridization band gap. This effect is usually rather elusively

justified by a level repulsion between the wave, that is, thephoton or the phonon, and a local resonance. This notion hasbeen particularly studied in the acoustics community, and israther unknown in the electromagnetic one. We have studiedmany unit cells of metamaterials using a willingly simplifiedquasi 1D model [5], and shown that many features of the lattercan be attributed to a far field type of coupling between unit

cells, namely, to the hybridization concept.The principal results of this study are as follow. For most

media made out of resonant and subwavelength unit cells, evenorganized on a deep subwavelength scale, at the first order only

propagating waves participate to the coupling between unitcells. The dispersive nature of the medium made of those unitcells can be attributed to a Fano interference between the waveincoming on a resonator and going through it withoutinteracting, and the wave that excites the resonator and that isre-emitted by it. Therefore, the dispersive nature of themetamaterials, which includes high permittivity or

permeability parts of the spectrum, and negative permittivity orpermeability parts of the spectrum, can be attributed solely to

far field components. This is of course not valid for all unitcells since some present high near field couplings, that is,capacitive or inductive couplings, but for most. This has a veryimportant consequence: most resonant metamaterials present

band gaps (those negative effective properties frequencywindows), which simply rely on far field components of thespatial spectrum. Conversely, most metamaterials can beunderstood just like conventional photonic crystals, albeit ofmuch smaller spatial scales, and governed by different physical

phenomena. This has led us to introduce the notion of defect inmetamaterials band gaps, and to demonstrate a very deepsubwavelength cavity in the microwave domain, withunprecedented small mode volume [8].

C. Hybridization band gaps for antenna applicationsPhotonic or microwave band gaps are obviously very useful

for many applications, and present great advantages forantenna applications, as demonstrated by electromagnetic bandgaps. Indeed, such media present the ability to stop the

propagation of waves in certain frequency ranges. Ourapproach, which uses any subwavelength resonator as a

building block for designing a subwavelength scaledhybridization band gap, takes advantage of this property. Aninternational patent application has been filled on this idea.

Basically, an hybridization band gap based on ametamaterial that can be linear, 2D, or 3D, provides thefollowing outcomes. The wave emitted by a feed that is placedin the direct vicinity of such medium cannot enter the medium,and hence tend to be emitted in the direction opposite to that ofthe band gap. This gives the possibility to engineer theradiation pattern of an antenna in order to emit waves in

preferred directions of space. Consequently, one can design

antenna arrays, each antenna emitting with quasi orthogonalradiation patterns, for example for MIMO applications. In thiscase, the MIMO takes advantages of radiation diagramdiversity, rather than from uncorrelated points in space, thatrequire a much larger spacing between the antennas. Naturally,

because the waves cannot penetrate the metamaterial, two portsplaced very closely but separated by a few unit cells of thehybridization band gap are strongly decoupled, the coupling

being lower and lower as the number of unit cells is increased.The second advantage of this approach is that since thoseresonant unit cells can be of deep subwavelength size, efficientantenna arrays with orthogonal radiation diagrams and verygood decoupling can be realized on very small dimensionscompared with the wavelength. Using a linear chain of unit

cells one can design a 2 antenna array, using a square of unitcells one obtains a 4 antenna array, and so on, without usingany polarization degree of freedom.

A very convenient way of realizing such an antenna is todesign a band gap using a given unit cell, and to use the sameunit cell as an antenna, by slightly changing its dimension suchthat its resonant frequency falls in the band gap of themetamaterial. For instance, if one creates a line of identical

passive resonant wires very closely spaced that give a band gapabove their resonant frequency, putting two shorter wires oneach side of the line gives the possibility to create a 2 antennaarray of deep subwavelength dimension, by connecting theshorter wires to an RF stage and matching their impedance. We

will give in the rest of the paper the design of two different 2antenna arrays, one very small one for WIFI MIMOapplications, and the second one even more isolated for thecoexistence of frequency overlapping communication systemin the WIFI range (e.g. WIFI and Zigbee).

III. ARESONANT SLIT BASED 2ANTENNA ARRAY

A. SimulationsOur aim is to be able to design antennas such that they can

be printed on circuit board in order to be cost effective. Wechose to work with a very simple and very thin unit cell: a slitin a metal plane. We design the slit such that it presents a

resonance frequency around 2.3 GHz. We first use a set of 4 ofthose slits that will create our hybridization band gap. Thestructure without the antennas is simulated to verify theefficiency of this 4 elements band gap. Then we place 2 otherslits on each side of our metamaterial and we slightly modifytheir dimensions such that their resonant frequency falls withinthe band gap of the 4 identical elements. Finally we impedancematch the two ports of our 2 antenna array. The simulatedantenna, that is virtually printed on a 1mm epoxy PCB, isrepresented in Figure 1. At the bottom one sees the rest of the

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PCB which could contain for instance the RF part of a systemprovided that some optimization is done.

Figure 1. simulated structure with a 4 slits band gap

From the full 3D simulation realized using HFSS, weextract the S parameters of the two ports antenna which we plotin Figure 2. Clearly, even though the two antennas areseparated by only 1/8

thof a wavelength at the WIFI frequency

of 2.45 GHz, the two ports are well isolated with a S12of about15 dB. The antennas are very well adapted and present abandwidth of more than 100 MHz at 10 dB. The two ports donot show strict identical results since there is a light asymmetryin the simulated structure.

Figure 2. S parameters obtained from simulation, frequency in GHz

From those simulation, we also extract the 3Delectromagnetic field radiated in the far field. From those weare able to calculate a correlation coefficient between the twoantennas that is about 15%. Finally, we also obtain from thosenumerical studies the radiation patterns of the two antennas.We plot it for port 1 in Figure 3, that of port 2 being almostidentical except that it points in the opposite direction. Weobtain a peak gain of about 3.5 dBi and an average one ofabout 1dBi. The directive radiation patterns ensures us a gooddecorrelation between the two antennas.

Figure 3. 3D radiation diagramm of Port 1, the second being symetrical

B. Experimental resultsThe simulated antenna is then fabricated, that is, printed on

a ground plane of a PCB, as can be seen in Figure 4. Twocoaxial lines are soldered on the ports and on the ground planewhich would the circuit board on a real system, and connectedto a Network Analyzer. The antenna is measured in a typicallaboratory room and is hence subject to the fading induced bythe reflections of the obstacles present in the room.

Figure 4. Measured two ports antennaprinted on a PCB - setup in a lab room

We use this setup to measure the S parameters of our two

ports and /8 wide antenna. The antenna is not perfectlycentered on the WIFI frequency of 2.45 GHz since we did nottune it very precisely after fabrication. Nevertheless, one can

see that it presents excellent properties. Despite its very smallform factor (planar and 2.6cm*1.6cm, that is, /5*/8), it isvery well adapted, present a very wide bandwidth of more than200 MHz, and is even more decoupled than the simulatedstructure since the S12of the two antennas is close to 20 dB.We have measured the radiation patterns of those antennas (notshown here), verified that they are linearly polarized along thez axis and that their peak gain is about 3 dBi and their averagegain around 1 dBi. We have also estimated the efficiency of thetwo antennas of the structure and found efficiencies slightlyhigher than 80%.

Port 2Port 1

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Figure 5. Measured S parameters of the two ports antenna

Hence we have demonstrated a small two antenna arraywith very good efficiency, high peak and average gains andvery low correlation coefficients. Those antennas could findapplications in WIFI boards and other system using MIMOtechnology and requiring compact antennas. We will now showthat using more unit cells leads to even higher decoupling

between ports.

IV. DECREASING THE CORRELATION/COUPLING USING MORE

UNIT CELLS

A. SimulationsWe now focus on a slightly larger antenna that contains 9

slits instead of 4 between the two active elements. The

dimensions of the antenna are now 2.6cm*2.6cm, that is, (/5)2

at 2.45 GHz, schematized in Figure 6.

Figure 6. Simulated two ports antenna presenting a 9 slits band gap

Again, we simulate this structure including two activeelements that are impedance matched to 50 Ohms, and thestructure is printed on a PCB, the rest of which is copper andwould be the communications system in real applications. Weextract from the simulation the S parameters obtained usingHFSS and plot them in Figure 7. The results obtained areconsistent with that of the 4 slits antenna. The main differencesare that the bandwidth of the two antennas obtained are noweven larger than for the 4 slits cases, with about 300 MHz. Thecoupling between the antennas has decreased drastically to

reach a value between 35 and 48 dB in the WIFI band, dueto the higher number of unit cells in the hybridization bandgap.

Figure 7. Simulated S parameters of the 9 slits two ports antenna, frequency

in GHz

We have also extracted from the simulation the far fieldradiation patterns of the two antennas obtained, plotted inFigure 8. Accordingly to the results of the 4 slits antennas, eachantenna points in an opposite direction along the y axis, with a

polarization that is almost linear along the z axis. This veryhigh directivity ensures that the two antennas of the array arevery strongly decoupled and present a very low correlationcoefficient.

Figure 8. 3D radiation diagrams of Ports 1 and 2 for the 9 slits antenna,

cleary showing a very high directivity

B. Experimental resultsWe have fabricated the simulated structure using the same

approach than for the 4 slits antenna. We use an epoxy PCBwith a thin layer of copper on top. The copper is etched and theantenna printed and connected to the remaining copper of the

board. This remaining copper represents the circuitry thatwould otherwise be on top of the board and shielded fromelectromagnetic radiations. The size of the antenna is now2.6cm by 2.6cm (Figure 9). The feeders have not beenmodified in this procedure, and the impedance did not need to

be matched again compared to the previous antenna. Again, weplace this antenna in our laboratory and solder on the copperlayer two rigid coaxial lines which are then connected to the 2

ports and a Network Analyzer. Using this setup we are once

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again able to measure the S parameters of the ensemble of twoantennas decoupled by the 9 slits hybridization band gap.

Figure 9. Measured 9 slits and two ports antenna showing dimensions

The obtained S parameters, plotted in Figure 10, clearly

demonstrate that the experimental results are consistent withthe numerical ones. The bandwidth at 10 dB of the antennas isaround 300 MHz, that is, more than 12%. The decoupling

between the antennas is less than 30 dB throughout thisbandwidth, meaning that the antenna are totally uncoupled andcan be used to emit signals of different systems on the samefrequency without interfering. We believe that this couplingwould be even lower if measured in an anechoic chamber,since reflections of the walls of the room induce some of it.

Figure 10. Measured S parameters of the 9 slits two ports antenna, frequency

in MHz

Finally, we have measured the radiation patterns of our

very decoupled two antennas array on the plane perpendicularto the antenna, which are represented in Figure 11. The lattershow a very good directivity, for each antenna, each one

pointing in its direction, ensuring a very low correlationbetween those antennas measured to be lower than 0.1. Thepeak gains of the antennas is approximately of 4.5 dBi for eachantenna, for an efficiency of more than 85%.

Consequently, we have proved that adding unit cells in thehybridization band gap used can dramatically decrease thecoupling between the antennas of the array. Such antennascould find applications when two systems have to coexist on

the same location of a board and work with the samefrequency, such as WIFI and Zigbee.

Figure 11. Measured azimuthal radiations patterns of the 9 slits two ports

antenna

V. CONCLUSION

In this paper, we have proposed to use the concept of alocally modified metamaterials displaying an hybridizationband gap in order to design very compact, efficient, uncoupledand decorrelated antennas. We have explained the concept and

proved it by demonstrating a planar /5*/8 two ports antennaprinted on a PCB to be used for MIMO application on WIFIboards. This antenna has been measured and efficiencies higherthan 80%, peak gains of 3.5 dBi, coupling of 20dB andcorrelation as low as 15% have been shown. We have then

proved that by including more resonant elements in the bandgap, one can even ameliorate the decoupling between theantennas and reduce their correlation, opening possibilities forthe emission of signals of different systems on the same

bandwidth, without any interference. This approach is very

general and can be realized using any resonator, which ensuresthat many antennas can be designed based on this idea. We arecurrently working on 4 ports antennas, on multiband antennas

based on multi-resonant elements, as well as on decreasingeven more the size of our devices using even moresubwavelength resonators.

REFERENCES

[1] A. Paulraj, R. Nabar and D. Gore. Introduction to Space-Time WirelessCommunications, Cambridge Univ. Press, (2003).

[2] D. Sievenpiper et al. IEEE Trans. on Microwave Theory andTechniques, 11, 2059, (1999).

[3] F. Yang and Y. Rahmat-Samii. IEEE Trans. on Antennas andPropagation, 51, 2936, (2003).

[4] CC. Hsu et al., Antennas and Propagation Society InternationalSymposium, APS-URSI- IEEE (2009).

[5] F. Lemoult, M. Fink and G. Lerosey, Submitted to Phys. Rev. Lett.arxiv.org/pdf/1112.2524 (2011).

[6] J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade,Photonic Crystals: Molding the Flow of Light (Second Edition)(Princeton University Press, 2008).

[7] N. Engheta and R. Ziolkowski, eds., Metamaterials: physics andengineering explorations (John Wiley & Sons & IEEE Press, 2006).

[8] F. Lemoult, M. Fink and G. Lerosey, Submitted to Phys. Rev. Lett.arxiv.org/pdf/1112.2524 (2011).