METAMATERIAL TUNABLE FILTER WITH LIQUID METAL W. M. Zhu

1, W. Zhang

1,3, R. F. Huang

2, S. K. Ting

2, G. Q. Lo

3, D. L. Kwong

3, and A. Q. Liu

1,3*

1School of Electrical and Electronic Engineering, Nanyang Technological University

50 Nanyang Avenue, Singapore 639798 2Temasek Laboratories, 5A Engineering Drive 1, Singapore 117411

3Institute of Microelectronics, 11 Science Park Road, Singapore 117685

ABSTRACT

In this paper, we demonstrate a metamaterial tunable filter with liquid metal, which can be tuned by adjusting the size and position of the air gap within the liquid metal. In experiment, it measures a 2.3 GHz tuning range for the tunable metmaterial unit with the working wavelength of 8.9 GHz. The tuning of 5 × 5 unit array is also demonstrated. Different from traditional metamaterials [1, 2], the metal patterns of the tunable metamaterial filter are liquid state which can be reshaped once fabricated. The liquid state metal pattern not only advances in flexible tuning method, but also results in large tuning range for vast applications, such as tunable filter, accelerometer and optical switch. INTRODUCTION

Artificial materials, such as metamaterials, are intensively studied due to their extraordinary optical properties, such as negative refraction and hyperlens [1, 2], which have vast applications in bio-sensor and imaging typically hampered by the diffraction limit. Tunable metamaterials can be rationally designed to achieve optical anisotropy [3-13] that can be altered by changing the refractive index of the surrounding media or by engaging the electrical or thermal effects in the liquid crystals. At the same time a substantial progress has been made in developing metamaterials with unit cells reconfigurable with micro-actuators [14, 15]. Their tunablilities are fundamentally limited by the pre-defined patterns of the solid metal. Some tunable metamaterials with liquid metal are demonstrated by shifting the liquid metal plug or just simply fill the air channel with mercury [16], which have similar tuning mechanisms as micromachined actuation and phase change materials. Tunable metamaterials composited of conductive liquid, such as mercury, galinstan and carbon nano-tube solutions, are seldom discussed because the difficulties of defining and controlling the shape of the liquid.

Microfluidics technology has been intensively used to form and transport liquid plugs within micro channels, which can also be used to construct tunable metamaterials with liquid metal. The geometry of the metamaterial elements is determined by the shape of the channels where the liquid metal is confined within. The metamaterial elements can be tuned by pumping the liquid metal plugs to the channels with different shapes. Therefore, tunable metamaterials with liquid metal are possibly to be tuned by remolding the liquid metal to any shape with equivalent volume. This tuning mechanism is different from other structural reconfigurable metamaterials, which reshape the metamaterials element by changing the relative positions of the pre-defined metal patterns. In this paper,

donut-shaped channels are used to demonstrate the tuning of the liquid metal metamaterials element via pressure and acceleration, which has potential applications as tunable filter, accelerometer and optical switch. This paper is organized as the following. Firstly the design of the liquid metal metamaterials is given. Then followed by the numerical analysis and experimental characterization. Finally, the results are discussed.

DESIGN OF THE METAMATERIALS

Figure 1: Schematic and working principle of Tunable metamaterials based on liquid metal (a) Overview of the tunable metamaterials. (b) Schematic of the tunable unit cell of the metamaterials. (c) Graph of the tunable unit cell at initial state when the liquid metal is sealed within the PDMS channel (d) the rotation of the air gap after the tunable unit has been accelerated at vertical direction (e) tunable unit with pressure applied. The air gap becomes small when the pressure applied on the tunable unit is increasing. The graph shows the gap is tuned by the pressure.

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The schematic and the working principle of the tunable metamaterials with liquid metal are shown in Figure 1. The tunable metamaterials unit consists of 3-µL liquid metal (mercury) and 0.7-µL air, which are sealed within the circle-shaped polydimethylsiloxane (PDMS) with the radius of 3 mm. The PDMS channels are fabricated using the SU-8 hard mask and bonded with a PDMS substrate. The height of the PDMS channels are 100 µm. Both the cover PDMS and substrate PDMS have the thickness of 2 mm. The liquid metal forms a split ring pattern due to the constraint of the PDMS channel. The initial size of the air gap can be adjusted by controlling the volume of the liquid metal during the fabrication process. The angle between the symmetry axis and the long side wall of the PDMS cover is defined as the rotation angle θ, which can be tuned by accelerating the metamaterials element towards the directions, which are different from the symmetry axis of the metamaterials element. The size of the air gap is defined as the arc angle of the gap Φ, which can be tuned by applying pressure to the PDMS chip and change the height of the channels. Fig. 1(a) and (b) shows the schematic of the unit array and single unit structure, respectively. The unit array is consists of 10 × 10 liquid metal plugs within donut shaped channels. Fig. 1(c) shows the graph of the initial state of the metamaterials unit when the symmetry axis of the ring is along the long side wall of the substrate. Fig. 1(d) shows the change of the rotation anlge after the tunable metamaterials unit has been accelerated at vertical direction, which is along the short side wall of the metamaterials unit. Fig. 1(e) shows the tunable unit with pressure applied. The air gap Φ becomes smaller when the pressure applied on the tunable unit cell is increasing, which shows that the gap of the split ring formed by the liquid metal can be controlled by the pressure. NUMERICAL ANALYSIS

The numerical analysis of the tunable metamaterials at different rotation angle is shown in Figure 2. Figure 2(a), Figure 2(b) and Figure 2(c) shows the transmission spectra when θ = 0°, θ = 45° and θ = 90°, respectively. The inserts show the contour map of the surface current of the first two resonance modes of each rotation angle. The bright regions show the high intensity of the surface current while the dark regions represent the opposite. The input source is set to have TE01 mode shape to comply with the experiment setup. Therefore, the electric field is along the short side wall of the PDMS substrate while the magnetic field is not parallel to the surface of the metamaterials unit cell, which is different from the linear polarized incident EM waves used frequently in the characterization of metamaterials in free space. Nevertheless, the magnetic field component penetrate through the split ring is very weak and cannot form a strong resonance within the frequency region ranging from 8 to 12 GHz. Therefore, the transmission dips shown in Figure 2 are due to the electric resonances within the split rings.

Figure 2(a) shows the transmission spectrum, when the symmetry axis of the split ring is parallel to the long side wall of the substrate, which is perpendicular to the incident electric field. The air gap is located only on the left arc of the donut channel, which results in the asymmetry

distribution of the surface current between the left and right side of the split ring. The transmission dip at 9.4 GHz is due to the strong Fano resonance which is induced by the interference of the asymmetry surface currents between the left and ring arc. A circular current mode is formed instead of the dipole resonances, which are usually observed in the symmetry split ring structures. The surface current induced by 10-GHz incident EM wave is also shown in Figure 2(a), which shows the strength of the maximum ON-resonance surface current is two orders of magnitude larger than that of the OFF-resonance surface current.

More transmission dips are shown in Figure 2(b) when the rotation angle is changed to 45° because the location of the air gap not only induces the asymmetry between the left and right arcs but also induces the asymmetry between the up and bottom arcs. The surface currents plotted in the inserts of the Figure 2(b) show hybrid resonance modes, which are neither circular mode nor dipole mode.

Figure 2: Numerical analysis of the transmission modes at different acceleration angle. (a) θ = 0° (b) θ = 45° and (c) θ = 90°.The inserts show the contour map of the surface current of the first two resonance modes of each acceleration angle, which shows the symmetry resonance mode shape at θ = 0° and θ = 90°.. The transmission dips are due to the resonance modes of the surface currents.

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Figure 2(c) shows the transmission spectrum when the symmetry axis of the split ring is parallel to the incident electric fields. Both of the two transmission dips at 10.6 GHz and 11.4 GHz respectively are induced by the dipole resonance modes which are shown in the inserts of Figure 3(c). Therefore, the resonance modes of the surface current are strongly dependent on the rotation angle of the split ring. EXPERIMENTAL RESULTS

The experimental characterization has been carried out by two steps using Agilent Vector Network Analyzer (VNA) N5230A. First, the transmission of the single metamaterials unit is measured using the X-band rectangular waveguide The metamaterials unit is placed in the metal connector with the size of 10.16 mm × 22.86 mm × 9.6 mm. The propagation direction of the TE10 mode is perpendicular to the surface of the liquid metal split ring. Then the transmission of the unit array of 10 × 10 units are measured using the linear polarized source from the free space, which has the frequency range of 10 to 20 GHz. The electric field orientation of the free space characterization is the same as that of in the X-band rectangular waveguide.

(a)

(b)

Figure 3 Measured transmission spectra at (a) different pressure applied when the rotation angle is fixed at θ = 45° and (b) different acceleration angle when the air gap sized is fixed at Φ = 60°.

Figure 3(a) shows the measurement results of the tunable metamaterials unit at different air gap size Φ. The red, blue and green lines represent the transmission spectra of the metamaterials unit when the air gap is approximately from 60° to 15° as the pressure applied is increasing. The resonance dip is blue shifted from 8.9 GHz to 11.3 GHz when the rotation angle θ of the air gap is increasing. Figure 3(b) shows the measurement results of the transmission spectra at different rotation angles when the air gap size Φ is fixed at 60°. The red, blue and green lines represent the transmission spectra when the rotation angle θ is 15°, 30° and 45°, respectively. The resonance dips also blue shift during the rotation of the split ring unit of the liquid metal metamaterials.

Figure 4: Measured transmission spectra of the unit cell array under different pressure. The transmission dips red shifts when the pressure is increasing. The transmission spectra of the unit cell array of the liquid metal metamaterials are characterized under linear polarized incidence when the electric field is parallel to the symmetry axis of the split ring unit. Figure 4 shows the measured transmission spectra of the metamaterials unit array under different pressure. The applied pressure results in the decreasing of the air gap size Φ since the liquid metal is pushed toward the air gap region. The resonance dip is red shifted from 13.26 GHz to 13.12 GHz when the air gap size Φ is changed approximately from 60° to 15° under different pressures applied. CONCLUSIONS In conclusion, a tunable metamaterials filter with liquid metal is designed, fabricated and experimentally demonstrated. The liquid metal patterns of the tunable metamaterials can be tuned by both pressure and acceleration which is different from any reported tuning mechanisms for tunable metamaterials. The liquid metal unit of the metamaterials can be remolded to arbitrary shape so that the optical properties of the metamaterials can be precisely controlled according to any specific applications, which has potential applications not only in the controllable filtering and luminance but also in sensor and detection.

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ACKNOWLEDGEMENTS This work was supported by the Science &

Engineering Research Council (SERC) of Singapore with project Metamaterials Programme: Nanoplasmonics (Grant No. SERC 092 154 0098).

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CONTACT

*A. Q. Liu, Tel: +65-67904336; eaqliu@ntu.edu.sg

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