AN ABSORPTIVE FILTER USING MICROFLUIDIC SWITCHABLE METAMATERIALS

B. Dong1,3, W. M. Zhu1, Y. H. Fu1, J. M. Tsai2, H. Cai2, D. L. Kwong2, E. P. Li3, E. Rius4 and A. Q. Liu1†

1School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 2Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research)

11 Science Park Road, Singapore Science Park II, Singapore 117685 3Institute of High Performance Computing, A*STAR (Agency for Science, Technology and Research)

1 Fusionopolis Way, Singapore 138632 4Laboratoire des Sciences et Techniques de l’Information, de la Communication et de la Connaissance

(Lab-STICC), University of Brest, Brest 29238, France

ABSTRACT In this paper, the microfluidic switchable absorptive

metamaterials (MMs) filter in the gigahertz region is designed. It consists of a microfluidic network between the electrical resonator and the metal plate. The absorption frequency of the tunable MMs absorber can be tuned by pumping different liquids into the microchannel using the microfluidic technology. Based on the designed absorptive MMs, the absorptive peak can be shifted by introducing a microfluidic layer with frequency tunability up to 20% and absorption change up to 90%. By introducing the tunability in absorption frequency of MMs, it has great potential in the applications of filter and sensor / detector for biomedical applications. KEYWORDS

Metamaterials, microfluidics, filter, perfect absorption

INTRODUCTION

Metamaterials (MMs) were first proposed in 1960s by Vesalago [1]. It started to draw more and more attention after the first experimental demonstration of MMs in 2001 [2]. MMs are artificial materials that can provide properties, which are not readily available in nature, such as negative refractive index [2]. MMs have attractive applications in different fields and are used to design super lens, antenna, slow light and absorber.

Perfect absorber has been realized by two layers MMs [6 – 7]. Normally, there is a dielectric layer between the metal layers. Therefore, by changing the properties of the dielectric layer, the properties of the MMs can be modified. Switchable MMs have been realized via several methods, such as the micromachined switchable MMs [3 – 4], and light induced switchable MMs [5]. Comparing with these methods, microfluidic technology may be more attractive and can be used to change the properties of the dielectric layer. Microfluidic technology with the flexible control of liquids makes it possible to integrate with the MMs, and provides the tunability and flexibility of MMs.

This paper presents a switchable absorptive MMs filter in the gigahertz region by integrating a microfluidic network as the tunable dielectric layer. The absorption spectra under different conditions are simulated and discussed to optimize the design and present the

(b)

(a)

Figure 1: (a) Schematic diagram of microfluidic switchable MMs absorptive filter array. (b) The unit cell of MMs. (c) The electrical resonator.

Glass

MetalPlate

PDMS

MicrofluidicChannel

Electrical Resonator

LiquidDroplet

(c)

M3P.129

978-1-4577-0156-6/11/$26.00 ©2011 IEEE Transducers’11, Beijing, China, June 5-9, 2011530

flexibility of the switchable absorptive MMs filter.

STRUCTURAL DESIGN Figure 1(a) shows the overview of the microfluidic

switchable MMs absorptive filter array. The microfluidic tunable MMs absorptive filter consists of three parts: the top electrical resonator, the middle microfluidic network, and the bottom metal plate. The electrical resonator consists of two split ring resonators, which is able to response to the electrical field. The metal pad, paired with the electrical resonator, form anti-parallel surface currents induced by the magnetic field. Only TE mode, which means electrical field parallel to the central wire of the electrical resonator, can couple into the structure, and thus induce high absorption.

The unit cell is shown in Fig. 1(b), which has a size of 10 mm × 6 mm. The structure consists of four layers with a 700-µm thick glass wafer as the substrate. A 20-µm thick aluminum was deposited on the substrate, and acts as the metal plate. Subsequently, 500-µm polydimethylsiloxane (PDMS) was deposited as the second layer. Another 1500-µm thick layer PDMS with the microfluidic channel was then bonded with the pre-deposited PDMS layer. Next, another 20-µm thick layer of aluminum, which was the electrical resonator, was deposited. The schematic of the electrical resonator is shown in Fig. 1(c). The diameter outΦ of the ring is 5

mm, with the ring width w and the gap g to be 1 mm. As a result, the two aluminum layers are separated by the PDMS with microfluidic channel. The microchannel is embedded in the 2-mm thick PDMS, with height of 1 mm and width of 5 mm. Liquid droplet injected into the microfluidic channel has a diameter of 5 mm. By pumping liquids into the microchannel, the resonance of the MMs can be tuned.

THEORETICAL ANALYSIS

The MMs can be treated as uniform materials with constant electromagnetic properties. Light incidences normally from the top. The absorption at frequency is calculated by ( ) 1 ( ) ( )A T Rω ω ω= − − , which means that the absorption can be increased by minimizing both the transmission ( )T ω and reflection ( )R ω . Both the transmission and reflection of the incidence light can be eliminated by satisfying the impedance matching condition ( ( ) 1Z ω = ), which is determined by the position, the shape and the refractive index of the liquid droplets. By treating the middle microfluidic layer as an effective medium, MMs can be characterized by the electric permittivity (ε ) and magnetic permeability (μ). Impedance matching is achieved by fine tuning of and μ, which then be realized by tuning the liquid droplets.

The electric permittivity of water at gigahertz is modeled by 1st order Debye model, [8] which is expressed as

( )ˆ1

S

Diε εε ω ε

ωτ∞

∞−

= ++

(1)

where sε is the static permittivity and equal to 78.36,

ε∞ is equal to 5.2, and the relaxation time Dε is 8.27 ps.

The dispersion curve of water is shown in Fig. 2. Water at gigahertz has higher refractive index as compared to that at visible light range. Thus, water can be utilized to modulate the resonance between the metal layers significantly.

The simulation is done using the commercial finite difference time domain solver (Microwave studio, CST 2009). Electromagnetic wave was incident normally and both the reflected and the transmitted signals are recorded. S-parameters are detected on both sides and the absorption is calculated by

2 211 12( ) 1 ( ) ( )A S Sω = − − .

The absorption spectrum of the microfluidic switchable filter is shown in Fig. 3(a). The absorption reaches more than 98% at 9.485 GHz. The surface current is shown in Fig. 3(b) with the arrow showing the

(a)

Figure 2: Dispersion curve of the water at Gigahertz.

Figure 3: (a) Absorption spectrum and (b) surface currents of microfluidic switchable MMs filter.

(b)

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direction of the surface current induced by the electrical field. Since the permittivity of water is relatively high in the GHz region, water absorbs most of the energy, which is known as dielectric loss.

In this paper, two tuning mechanisms are demonstrated, one is by shifting the position of the droplets, and another is by changing the size of the droplets.

Figure 4(a) shows the mechanism of shifting the position of the droplet in a unit cell. By changing the pressure in the microfluidic channel, it is possible to drive the droplet to move. Thus, the droplets in the microfluidic channel can be controlled and stopped precisely at various positions. Since the resonance between the metal patterns is coupled mainly via water, the droplet shift (D as the displacement from the center of the unit cell) can be used to control the resonance. The surface current density with D = 1.5 mm (dotted line) is shown in Fig. 4(b). The surface

current density is higher as compared to the surface current density at Fig. 3(b). Therefore, the position of the water can affect the resonance frequency in the electrical resonator.

The absorption spectra at various D are shown in Fig. 4(c). The droplet moves from the center to the edge along the microchannel, and shifting the resonance frequency to high frequency region. By shifting the droplet by 1.5 mm, the absorption at 9.485 GHz drops from approximately 100% to 55%, with approximately 50% of incidence wave reflected back. The same phenomena are observed at 10.38 GHz. Thus, the ON/OFF states can be switched by detecting the absorption via the tuning of droplet position.

Figure 5(a) shows the mechanism of switching the MMs by tuning the droplet size. The droplets’ diameter (

wΦ ) in the microfluidic channel can be fine controlled

and pumped into the channel. The surface current density shown in Fig. 5(b) confirms that smaller droplet (dotted

(b)

(a)

Figure 4: The tuning of microfluidic switchable MMs absorptive filter via varying droplet shift (D). (a) Schematic diagram of the tuning mechanism; (b) average surface current density at D = 1.5 mm; and (c) absorption spectra at various P.

(c)

(b)

(a)

Figure 5: The tuning of microfluidic switchable MMs absorptive filter via varying droplet diameter (

wΦ ). (a)

Schematic diagram of the tuning mechanism; (b) average surface current density at

wΦ = 3 mm; and (c) absorption

spectra at various wΦ .

(c)

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line) can affect the distribution of the surface current by enhancing the current density right above the droplet.

The absorption spectra of the microfluidic switchable MMs by tuning the droplets’ diameter are shown in Fig. 5(c). When

wΦ becomes smaller, the resonant frequency

shifts to high frequency region. By pumping droplets with different diameters, the absorption frequency can be shifted from 9.485 GHz at

wΦ = 5 mm to 11.5 GHz at

wΦ = 3 mm. At 9.485 GHz, the absorption drops to less

than 10% with diameter reduces to 3 mm, which means that more than 90% of incidence wave can be reflected back. Therefore, the filter can be switch ON or OFF by changing the diameter of the droplets.

The demonstrated microfluidic switchable MMs absorptive filter can work at various frequencies, because the microfluidic technology can change either the position or the diameter continuously, which increase the flexibility of the MMs filter. Since the unit cell of MMs filter can be scaled to micro or nano size, the working frequency can be shifted to terahertz region or infrared region, which make this filter suitable for more applications.

CONCLUSIONS

In conclusion, microfluidic switchable MMs absorptive filter are designed and simulated. The absorption frequency of MMs can be switched by pumping liquid droplets into the microchannel, either with different diameter or stop at various positions. The microfluidic switchable MMs absorptive filter has demonstrated a frequency tuning range up to 20%. The microfluidic switchable MMs absorptive filter has merits like high tunability, high sensitivity, feasible to be integrated lab-on-chip technology and small device scale. Therefore, it has potential applications as sensor and detector for biomedical applications.

ACKNOWLEDGEMENT

This work was supported by the Environmental and Water Industry Development Council of Singapore (Grant No. MEWR C651/06/171).

REFERENCES [1] V. G. Veselago, “Electrodynamics of substances with

simultaneously negative values of ε and µ,” Soviet Physics Uspekhi-Ussr, vol. 10, pp. 509, 1968.

[2] R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science, Vol. 292, pp. 77 – 79, 2001.

[3] W. M. Zhu, H. Cai, T. Mei, T. Bourouina, J. F. Tao, G. Q. Lo, D. L. Kwong, A. Q. Liu, “A MEMS’ switchable metamaterial filter,” 23th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2010), Hong Kong, P. R. China, Jan 24 – 28, pp. 196 – 199, 2010.

[4] W. M. Zhu, A. Q. Liu, X. M. Zhang, D. P. Tsai, T. Bourouina, J. H. Teng, X. H. Zhang, H. C. Guo, H. Tanoto, T. Mei, G. Q. Lo and D. L. Kwong, "Switchable Magnetic Metamaterials Using Micromachining Processes," Advanced Materials, published online (2011)

[5] H. T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nature Photonics 2(5), 295-298 (2008)

[6] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith and W. J. Padilla, "Perfect metamaterial absorber," Physical Review Letters 100(20), (2008)

[7] B. Dong, W. M. Zhu, Y. H. Fu, J. F. Tao, D. P. Tsai, G. Q. Lo, D. L. Kwong and A. Q. Liu, “ A Microfluidic Metamaterials for Frequency Absorption by Refractive Index Tuning”, The 11th international conference on near-field optics, nanophotonics and related techniques (NFO 2010), Beijing, China

[8] Permittivity (Dielectric Constant) of Water at Various Frequencies, CRC Handbook of Chemistry and Physics, 91 Edition, 2010-2011.

CONTACT A. Q. Liu† Email: eaqliu@ntu.edu.sg Tel: (65) 6790-4336 Fax: (65) 6793-3318 URL: http://nocweba.ntu.edu.sg/laq_mems/

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