Tunable Left-Handed Metamaterial Based on Electrorheological Fluids

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Progress in Natural Science 18 (2008) 907–911 www.elsevier.com/locate/pnsc

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 electrorheological 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 moves toward lower frequency of within 7.08–8.30 GHz. This method provides one convenient way to design adaptive metamaterials. Ó 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.

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

1. Introduction Electrorheological fluids (ERF), a kind of smart materials, are suspensions of polarizable dielectric particles dis- Electric permittivity e and magnetic permeability l are persed in insulating liquid, which can abruptly change two fundamental electromagnetic parameters describing from liquid to solid upon the application of an external the electromagnetic response of continuous medium. Most electric field (E field) due to structural change when the of the naturally existing substances have positive permittiv- particles align themselves along the field direction to form ity and permeability. Veselago firstly studied theoretically chains. ERF have the characteristic of being anisotropic the electromagnetic properties of substances with simulta- dielectric, i.e. the dielectric constant increases along the neously negative permittivity and permeability which were field direction while it decreases in the transverse direction referred to as left-handed metamaterials (LHMs) [1]. How- [5–7]. Moreover, the dependence of the resonance fre- ever, there is no such material in nature. Therefore, the quency of the SRRs on the substrate permittivity has been research of LHMs is almost in stagnancy. Decades later, studied in some papers. With the increasing permittivity of Pendry et al. proposed that the array of metallic wires [2] the substrate, the resonant frequency of the SRRs moves and split ring resonators [3] (SRRs) can produce a negative toward lower frequency [8]. Therefore, this property of permittivity and a negative permeability, respectively. In ERF may be utilized to dynamically control the position particular, after negative refraction was experimentally ver- of passband of the LHMs by applying an external E field. ified by Smith et al. [4], studies on LHMs have attracted The traditional SRRs are a two-dimensional (2D) aniso- much attention on their peculiar electromagnetic properties tropic medium, which is disadvantageous to design the iso- and have become an attractive topic in the area of physics tropic LHMs. In addition, the majority of research and electromagnetism. methods on the LHMs and the negative permeability metamaterials are static and passive, which enormously restrict their practical applications. Concerning these defi- * Corresponding author. Tel./fax: +86 02988495950. ciencies, the feasibility of dynamically tunable electromag- E-mail address: [email protected] (X. Zhao). netic behaviors in negative permeability metamaterials and

1002-0071/$ - see front matter Ó 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.2008.01.033 908 Y. Huang et al. / Progress in Natural Science 18 (2008) 907–911

LHMs has been studied by several methods, such as E field 3. The 2D isotropic property of the dendritic structure [9,10], optical excitation [11], defect effect [12], loading var- actor [13], adjusting the permittivity of the substrate or 3.1. Simulation section varying the substrate thickness [14]. However, so far, no study is reported on analyzing the omnidirectional reso- The traditional SRRs have an asymmetric gap, which nance of this dendritic model, which simultaneously has can easily produce the electromagnetic couple [19,20], Àe and Àl, and using ERF to realize the tunable passband namely E field and magnetic field (H field) jointly couple of this unitary dendritic. In this letter, we will propose a a magnetic polarization. It is a restriction to design the kind of dendritic model which is easier to cancel electro- 2D or 3D isotropic LHMs by using the SRRs and wires. magnetic coupling than the traditional SRRs. The simu- However, the highly symmetric quasi-periodic dendritic lated results show that this left-handed model has the 2D model has the 2D isotropic property to a certain extent, isotropic property. Furthermore, we demonstrate the and it provides a feasible way to design the multidimen- effects of electrorheological fluids on the passband of the sional isotropic metamaterials. periodic dendritic array. To prove the 2D isotropic property of the dendritic structure, electromagnetic resonances were simulated by 2. The left-handed dendritic model using commercial software CST Microwave Studio involv- ing the cases of parallel incident and normal incident. The As is well known, most of the LHMs are realized thickness of the metal is t = 0.03 mm and that of the sub- through combining the SRRs and wires. Furthermore, strate is 1 mm (e = 4.65). The other dimensions of the den- some unitary structures, such as the S-shaped resonators dritic structure are a = 2 mm, b = 0.9 mm, c = 0.9 mm, and or X-shaped resonators, have been proposed. We have h =45°. In the simulation, the number of unit cell proposed a kind of quasi-periodic dendritic model (Fig. employed was chosen as 1 in order to limit the computa- 1(a)), and our theoretical and experimental studies tional cost of simulations, and the boundary conditions proved that the dendritic model has negative permeability were defined by setting periodic boundary conditions on in the microwave and infrared domain [15–17]. When the transverse boundaries and open conditions on two appropriately adjusting the parameters of the dendritic ports. structure, we can obtain the LHMs based on the unitary dendritic structure, which can simultaneously realize Àe 3.1.1. Normal incident mode and Àl in the same frequency range. The simulations, The relative orientation of the electromagnetic excita- negative refractive index and planar focus experiments tion is shown in Fig. 1(b). The distribution of surface cur- verified that the dendritic structure has left-handed prop- rent shows that the positive and negative charges erties [18]. accumulate 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 the surface current under normal incident; (c) distribution of the surface current under parallel incident. The arrows indicate the instantaneous current direction. Y. Huang et al. / Progress in Natural Science 18 (2008) 907–911 909 the E field direction to produce the electric resonance, H field, respectively. The sample was placed between two which is excited by the E field. Because the H field parallels horn antennas at a distance of 20 cm, and the scattering to the surface of the dendritic structure, it hardly contrib- parameters were measured by a network analyzer utes to the electric polarization. Because of the symmetry, AV3618. The transmission spectra of the dendritic struc- the magnetic moments with the opposite direction pro- ture with and without electrodes were measured under par- duced by two circle currents counteract each other to a allel incidence. Fig. 2(c) shows that the two electrodes, great extent, which thereby avoids cross-polarization. which are loaded along the orientation of the E field or When we rotate the dendritic structure with 45°,90°, the H field, have little influence on the transmission spec- 135°, 180°, 225°, 270°, 315° and 360° along its normal, trum of the sample. The results indicate that the dendritic the results show that the states of the rotated and non- structure has the 2D isotropic property, which may provide rotated dendritic cell are completely overlapped and the the references on how to choose the loaded manner of the polarization modes are maintained constantly. Hence, we electrodes in our subsequent experiment. think that this structure can realize 2D isotropic property The polarization modes of the copper hexagonal SRRs to a certain extent. are also studied in contrast to the 2D isotropic property of the dendritic structure. The experimental setup is the 3.1.2. Parallel incident mode same as that of Fig. 2. The loaded manner of the electrodes Fig. 1(c) shows the orientations of the E-field, H-field, and the results are shown in Fig. 3. The transmission spec- and the wave vector. The dendritic branches can produce trum of the hexagonal SRRs has great difference under the four circle currents with the same direction on its surface, influence of the electrodes loaded along the y axis. On the which is excited by the H field component. The entire cell contrary, the measured transmission spectrum is little influ- is similar to four coupled SRRs, which can exhibit mag- enced by the electrodes loaded along the x axis. While the netic resonance. The electric resonance and the distribution orientations of electromagnetic wave vary, the polarization of surface current is the same as that of the dendritic struc- modes are different due to the asymmetrical gaps of the ture for the normal incident. The surface current excited SRRs. When the electrodes are loaded along different ori- jointly by the E field and H field is shown in Fig. 1(c), entations, the polarization modes of the SRRs are different, and the left-handed effect could be realized. namely the hexagonal SRRs model has the 2D anisotropic In the same way, the polarization modes are unaltered property. though the model is rotated. Hence, the 2D isotropic property can be proved again. 4. Tunable passband of the dendritic structure based on ERF

3.2. Experiment 4.1. Samples and experimental setup

To prove the 2D isotropic property of the dendritic Using shadow etching technique, the metal dendritic structure, we experimentally studied the transmission units were etched on a 1-mm-thick Fr-4 circuit board mate- behaviors of the dendritic sample under different test con- rial with the permittivity of 4.65 and were arrayed to a ditions. Fig. 2 shows the schematic illustration of the exper- LHM with the lattice constant of 8.96 mm. Then the den- imental setup. Two plastic electrodes with a distance of 1 dritic array was placed in a water-proof paper cell filled cm were loaded along the orientations of the E field and with 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 the orientation of the H field; (b) the electrodes loaded along the orientation of the E field; (c) the transmission spectra of the dendritic sample with two electrodes loaded along different orientations. 910 Y. Huang et al. / Progress in Natural Science 18 (2008) 907–911

Fig. 3. Schematic diagram of the loaded manner of the electrodes and corresponding transmission spectra. (a) The electrodes loaded along the orientation of 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 electrodes loaded along different orientations. form the sample (Fig. 4). The dimensions of the dendritic field (666 V/mm). The results are shown in Fig. 5, from unit were identical with the parameters of the prior which we can see that there is a passband in the transmis- simulation. sion curve for each case. In case (1), the left-handed trans- The scattering parameters were measured by a network mission passband appears within the range of 8.50– analyzer AV3618 and the sample was placed between two 10.60 GHz and the transmission peak is located at horn antennas with a distance of 20 cm. The microwave 10.07 GHz with a bandwidth of 2.10 GHz. In case (2) propagates along the z axis with the E field parallel to and case (3), the transmission curves are kept unchange- the x axis and the H field parallel to the y axis. The adja- able. Whereas in case (4), the LH passband of the dendritic cent plastic electrodes connected to a dc power supply were sample redshifts toward lower frequencies, i.e. from 8.50– separated by 9 mm and the dc E field is perpendicular to 10.60 GHz to 7.16–8.39 GHz with a maximum of the dendritic structure, i.e. along the y axis. 7.84 GHz, which indicates that the peak location moves 2.24 GHz toward lower frequencies and the bandwidth 4.2. Results and analyses decreases to 1.23 GHz. In case (5), the LH passband redshifts from 7.16–8.39 GHz to 7.08–8.30 GHz, the transmis- The transmission spectra with the parallel incidence sion peak appears at 7.79 GHz, which indicates that the were measured under the following five cases: (1) The den- peak location moves 49 MHz toward lower frequencies dritic array was placed in free space; (2) the dendritic array and the bandwidth is about 1.22 GHz. was placed in the cell; (3) the dendritic array was combined Because the dielectric constant of the ERF is larger than with four plastic electrodes; (4) the dendritic array was that of the air, the electric and magnetic resonance frequen- combined with electrodes and ERF; (5) the dendritic array cies shift toward lower frequencies and still overlap around was combined with electrodes and ERF under the dc E a low frequency [18]. As is well known, dielectric loss of the

Fig. 4. Schematic diagram of the electrically tunable passband of metamaterial consisting of dendritics and inﬁltrated ERF. (The shadow part denotes the electrode, and a dendritic strip is laid between two electrodes with a space of 9 mm). Y. Huang et al. / Progress in Natural Science 18 (2008) 907–911 911

Acknowledgements

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

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