Tunable left-handed metamaterial based on electrorheological fluids

Yong Huang, Xiaopeng Zhao *, Liansheng Wang, Chunrong Luo

Institute of Electrorheological Technology, Department of Applied Physics, Northwestern Polytechnical University, Xi’an 710072, China

Received 28 December 2007; received in revised form 21 January 2008; accepted 22 January 2008

Abstract

A tunable left-handed metamaterial consisting of a periodic array of the left-handed dendritic structure units infiltrated with electro-rheological fluids is demonstrated. Experimental results show that the passband can move from the original 8.50–10.60 GHz to 7.16–8.39 GHz after electrorheological fluids are infused. When a dc (direct current) electric field of 666 V/mm is applied, the passband movestoward lower frequency of within 7.08–8.30 GHz. This method provides one convenient way to design adaptive metamaterials.� 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science inChina Press. All rights reserved.

Keywords: Left-handed metamaterials; Dendritic model; Electrorheological fluids; Omnidirection

1. Introduction

Electric permittivity e and magnetic permeability l aretwo fundamental electromagnetic parameters describingthe electromagnetic response of continuous medium. Mostof the naturally existing substances have positive permittiv-ity and permeability. Veselago firstly studied theoreticallythe electromagnetic properties of substances with simulta-neously negative permittivity and permeability which werereferred to as left-handed metamaterials (LHMs) [1]. How-ever, there is no such material in nature. Therefore, theresearch of LHMs is almost in stagnancy. Decades later,Pendry et al. proposed that the array of metallic wires [2]and split ring resonators [3] (SRRs) can produce a negativepermittivity and a negative permeability, respectively. Inparticular, after negative refraction was experimentally ver-ified by Smith et al. [4], studies on LHMs have attractedmuch attention on their peculiar electromagnetic propertiesand have become an attractive topic in the area of physicsand electromagnetism.

Electrorheological fluids (ERF), a kind of smart materi-als, are suspensions of polarizable dielectric particles dis-persed in insulating liquid, which can abruptly changefrom liquid to solid upon the application of an externalelectric field (E field) due to structural change when theparticles align themselves along the field direction to formchains. ERF have the characteristic of being anisotropicdielectric, i.e. the dielectric constant increases along thefield direction while it decreases in the transverse direction[5–7]. Moreover, the dependence of the resonance fre-quency of the SRRs on the substrate permittivity has beenstudied in some papers. With the increasing permittivity ofthe substrate, the resonant frequency of the SRRs movestoward lower frequency [8]. Therefore, this property ofERF may be utilized to dynamically control the positionof passband of the LHMs by applying an external E field.

The traditional SRRs are a two-dimensional (2D) aniso-tropic medium, which is disadvantageous to design the iso-tropic LHMs. In addition, the majority of researchmethods on the LHMs and the negative permeabilitymetamaterials are static and passive, which enormouslyrestrict their practical applications. Concerning these defi-ciencies, the feasibility of dynamically tunable electromag-netic behaviors in negative permeability metamaterials and

1002-0071/$ - see front matter � 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited

and Science in China Press. All rights reserved.

doi:10.1016/j.pnsc.2008.01.033

* Corresponding author. Tel./fax: +86 02988495950.E-mail address: xpzhao@nwpu.edu.cn (X. Zhao).

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Progress in Natural Science 18 (2008) 907–911

LHMs has been studied by several methods, such as E field[9,10], optical excitation [11], defect effect [12], loading var-actor [13], adjusting the permittivity of the substrate orvarying the substrate thickness [14]. However, so far, nostudy is reported on analyzing the omnidirectional reso-nance of this dendritic model, which simultaneously has�e and �l, and using ERF to realize the tunable passbandof this unitary dendritic. In this letter, we will propose akind of dendritic model which is easier to cancel electro-magnetic coupling than the traditional SRRs. The simu-lated results show that this left-handed model has the 2Disotropic property. Furthermore, we demonstrate theeffects of electrorheological fluids on the passband of theperiodic dendritic array.

2. The left-handed dendritic model

As is well known, most of the LHMs are realizedthrough combining the SRRs and wires. Furthermore,some unitary structures, such as the S-shaped resonatorsor X-shaped resonators, have been proposed. We haveproposed a kind of quasi-periodic dendritic model (Fig.1(a)), and our theoretical and experimental studiesproved that the dendritic model has negative permeabilityin the microwave and infrared domain [15–17]. Whenappropriately adjusting the parameters of the dendriticstructure, we can obtain the LHMs based on the unitarydendritic structure, which can simultaneously realize �eand �l in the same frequency range. The simulations,negative refractive index and planar focus experimentsverified that the dendritic structure has left-handed prop-erties [18].

3. The 2D isotropic property of the dendritic structure

3.1. Simulation section

The traditional SRRs have an asymmetric gap, whichcan easily produce the electromagnetic couple [19,20],namely E field and magnetic field (H field) jointly couplea magnetic polarization. It is a restriction to design the2D or 3D isotropic LHMs by using the SRRs and wires.However, the highly symmetric quasi-periodic dendriticmodel has the 2D isotropic property to a certain extent,and it provides a feasible way to design the multidimen-sional isotropic metamaterials.

To prove the 2D isotropic property of the dendriticstructure, electromagnetic resonances were simulated byusing commercial software CST Microwave Studio involv-ing the cases of parallel incident and normal incident. Thethickness of the metal is t = 0.03 mm and that of the sub-strate is 1 mm (e = 4.65). The other dimensions of the den-dritic structure are a = 2 mm, b = 0.9 mm, c = 0.9 mm, andh = 45�. In the simulation, the number of unit cellemployed was chosen as 1 in order to limit the computa-tional cost of simulations, and the boundary conditionswere defined by setting periodic boundary conditions onthe transverse boundaries and open conditions on twoports.

3.1.1. Normal incident mode

The relative orientation of the electromagnetic excita-tion is shown in Fig. 1(b). The distribution of surface cur-rent shows that the positive and negative chargesaccumulate at the two ends of the dendritic structure along

Fig. 1. Schematic representation of one unit cell of the left-handed dendritic structure. (a) One unit cell of the dendritic structure; (b) distribution of thesurface current under normal incident; (c) distribution of the surface current under parallel incident. The arrows indicate the instantaneous currentdirection.

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the E field direction to produce the electric resonance,which is excited by the E field. Because the H field parallelsto the surface of the dendritic structure, it hardly contrib-utes to the electric polarization. Because of the symmetry,the magnetic moments with the opposite direction pro-duced by two circle currents counteract each other to agreat extent, which thereby avoids cross-polarization.When we rotate the dendritic structure with 45�, 90�,135�, 180�, 225�, 270�, 315� and 360� along its normal,the results show that the states of the rotated and non-rotated dendritic cell are completely overlapped and thepolarization modes are maintained constantly. Hence, wethink that this structure can realize 2D isotropic propertyto a certain extent.

3.1.2. Parallel incident mode

Fig. 1(c) shows the orientations of the E-field, H-field,and the wave vector. The dendritic branches can producefour circle currents with the same direction on its surface,which is excited by the H field component. The entire cellis similar to four coupled SRRs, which can exhibit mag-netic resonance. The electric resonance and the distributionof surface current is the same as that of the dendritic struc-ture for the normal incident. The surface current excitedjointly by the E field and H field is shown in Fig. 1(c),and the left-handed effect could be realized.

In the same way, the polarization modes are unalteredthough the model is rotated. Hence, the 2D isotropic prop-erty can be proved again.

3.2. Experiment

To prove the 2D isotropic property of the dendriticstructure, we experimentally studied the transmissionbehaviors of the dendritic sample under different test con-ditions. Fig. 2 shows the schematic illustration of the exper-imental setup. Two plastic electrodes with a distance of 1cm were loaded along the orientations of the E field and

H field, respectively. The sample was placed between twohorn antennas at a distance of 20 cm, and the scatteringparameters were measured by a network analyzerAV3618. The transmission spectra of the dendritic struc-ture with and without electrodes were measured under par-allel incidence. Fig. 2(c) shows that the two electrodes,which are loaded along the orientation of the E field orthe H field, have little influence on the transmission spec-trum of the sample. The results indicate that the dendriticstructure has the 2D isotropic property, which may providethe references on how to choose the loaded manner of theelectrodes in our subsequent experiment.

The polarization modes of the copper hexagonal SRRsare also studied in contrast to the 2D isotropic propertyof the dendritic structure. The experimental setup is thesame as that of Fig. 2. The loaded manner of the electrodesand the results are shown in Fig. 3. The transmission spec-trum of the hexagonal SRRs has great difference under theinfluence of the electrodes loaded along the y axis. On thecontrary, the measured transmission spectrum is little influ-enced by the electrodes loaded along the x axis. While theorientations of electromagnetic wave vary, the polarizationmodes are different due to the asymmetrical gaps of theSRRs. When the electrodes are loaded along different ori-entations, the polarization modes of the SRRs are different,namely the hexagonal SRRs model has the 2D anisotropicproperty.

4. Tunable passband of the dendritic structure based on ERF

4.1. Samples and experimental setup

Using shadow etching technique, the metal dendriticunits were etched on a 1-mm-thick Fr-4 circuit board mate-rial with the permittivity of 4.65 and were arrayed to aLHM with the lattice constant of 8.96 mm. Then the den-dritic array was placed in a water-proof paper cell filledwith ERF (20 vol% pure TiO2/silicone oil suspension) to

Fig. 2. Schematic diagram of the loaded manners of the electrodes and corresponding transmission spectra. (a) The electrodes loaded along theorientation of the H field; (b) the electrodes loaded along the orientation of the E field; (c) the transmission spectra of the dendritic sample with twoelectrodes loaded along different orientations.

Y. Huang et al. / Progress in Natural Science 18 (2008) 907–911 909

form the sample (Fig. 4). The dimensions of the dendriticunit were identical with the parameters of the priorsimulation.

The scattering parameters were measured by a networkanalyzer AV3618 and the sample was placed between twohorn antennas with a distance of 20 cm. The microwavepropagates along the z axis with the E field parallel tothe x axis and the H field parallel to the y axis. The adja-cent plastic electrodes connected to a dc power supply wereseparated by 9 mm and the dc E field is perpendicular tothe dendritic structure, i.e. along the y axis.

4.2. Results and analyses

The transmission spectra with the parallel incidencewere measured under the following five cases: (1) The den-dritic array was placed in free space; (2) the dendritic arraywas placed in the cell; (3) the dendritic array was combinedwith four plastic electrodes; (4) the dendritic array wascombined with electrodes and ERF; (5) the dendritic arraywas combined with electrodes and ERF under the dc E

field (666 V/mm). The results are shown in Fig. 5, fromwhich we can see that there is a passband in the transmis-sion curve for each case. In case (1), the left-handed trans-mission passband appears within the range of 8.50–10.60 GHz and the transmission peak is located at10.07 GHz with a bandwidth of 2.10 GHz. In case (2)and case (3), the transmission curves are kept unchange-able. Whereas in case (4), the LH passband of the dendriticsample redshifts toward lower frequencies, i.e. from 8.50–10.60 GHz to 7.16–8.39 GHz with a maximum of7.84 GHz, which indicates that the peak location moves2.24 GHz toward lower frequencies and the bandwidthdecreases to 1.23 GHz. In case (5), the LH passband red-shifts from 7.16–8.39 GHz to 7.08–8.30 GHz, the transmis-sion peak appears at 7.79 GHz, which indicates that thepeak location moves 49 MHz toward lower frequenciesand the bandwidth is about 1.22 GHz.

Because the dielectric constant of the ERF is larger thanthat of the air, the electric and magnetic resonance frequen-cies shift toward lower frequencies and still overlap arounda low frequency [18]. As is well known, dielectric loss of the

Fig. 3. Schematic diagram of the loaded manner of the electrodes and corresponding transmission spectra. (a) The electrodes loaded along the orientationof the H field; (b) the electrodes loaded along the orientation of the E field; (c) the transmission spectra of the hexagonal SRRs sample with two electrodesloaded along different orientations.

Fig. 4. Schematic diagram of the electrically tunable passband of metamaterial consisting of dendritics and infiltrated ERF. (The shadow part denotes theelectrode, and a dendritic strip is laid between two electrodes with a space of 9 mm).

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ERF is great, and so the LH bandwidth becomes narrower,the transmission power becomes smaller. Under the influ-ence of an E field, the dielectric constant of the ERFincreases along the field direction, and so the LH passbandof the dendritic sample shifts toward lower frequency.

The silicone oil is also used to infiltrate the dendriticarray, and the transmission measurement (data are notshown) shows that the passband is independent of theapplied E field, which further verifies that the above electri-cally tunable behavior is due to the change of dielectricconstant of the ERF.

5. Conclusion

In this letter, we have theoretically and experimentallydemonstrated the property of the 2D isotropic of the left-handed dendritic structure. Moreover, we have experimen-tally studied an electrically tunable LHM at microwave fre-quencies consisting of a periodic array of dendritic unitssurrounded by ERF. Based on the results and discussion,the conclusion can be drawn as follows:

(1) The electric and magnetic resonance of this model areinduced by the E field and H field, respectively. Andboth the simulated and experimental results verifythat this model has the two-dimensional isotropicproperty. The reason for this is that the model hasa fairly high level of symmetry.

(2) The experimental results show that the passband ofthe dendritic LHMs is tunable. It is found that afterinfiltrating ERF, the passband moves from 8.50–10.60 GHz to 7.16–8.39 GHz, and the passbandmoves to 7.08–8.30 GHz when the dc electric fieldof 666 V/mm is applied. The passband of the LHMscan be dynamically tuned by changing the substrateproperties.

Acknowledgements

This work was supported by the National Natural Sci-ence Foundation of China (Grant No. 50632030), NationalBasic Research Program of China (Subproject No.2004CB719805) and the Defense Basic Research Programof China.

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Fig. 5. Demonstration of the tunable LH transmission of the dendriticsample. The inset shows the LH passband region in the cases of (4) and (5)in closer detail.

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