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A Metamaterial-Based Terahertz Low-Pass FilterWith Low Insertion Loss and Sharp Rejection

Zhihua Zhu, Xueqian Zhang, Jianqiang Gu, Ranjan Singh, Zhen Tian, Jiaguang Han, and Weili Zhang

(Invited Paper)

Abstract—In this paper, we present an efficient low-pass tera-hertz (THz) filter design based on MEMS technology. With a cas-caded arrangement of two functional meta-layers, we demonstratea nearly loss-free response at the lower frequency passband andsharp rejection characteristics at the higher frequency stopband,with a steep roll-off of 296 dB/THz. The bandwidth of the low-passfilter is easily tuned by scaling the structural parameters of themetamaterial unit cell. The low-pass filter works efficiently evenat oblique angles of incidence, making it attractive for practicalapplications in THz signal processing.

Index Terms—Low-pass filters, metamaterials, passband, selec-tivity, terahertz (THz).

I. INTRODUCTION

T ERAHERTZ (THz) science and technology have shownpromising applications in astronomy, imaging, spec-

troscopy, and sensing [1], [2]. Efficient terahertz sources,highly sensitive terahertz detectors, and high-performance ter-ahertz components have attracted increasing research interestin order to accomplish such application goals. Developingterahertz components with high performance is essential inmanipulating terahertz waves with well-defined characteristics.In general, however, the terahertz gap still exists largely due tothe lack of functional devices in this technologically importantfrequency regime, which has the tremendous potential to bridgethe two impactful fields, i.e., electronics and photonics. Meta-materials, on the other hand, made from artificial structures atthe subwavelength scale, enable extraordinary electromagnetic

Manuscript received June 30, 2013; revised October 02, 2013; acceptedOctober 06, 2013. This work was supported in part by the National Sci-ence Foundation of China under Grants 61107053, 61007034, 61107085,61028011, and 61138001, by the U.S. National Science Foundation underGrant ECCS-1232081, by the Major National Development Project of Sci-entific Instruments and Equipment under Grant 2011YQ150021, and by theTianjin Sci-Tech Program under Grant 11JCYBJC25900.Z. Zhu, X. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang are with

the Center for Terahertz Waves and College of Precision Instrument andOptoelectronics Engineering, Tianjin University, Tianjin 300072, China(e-mail: zzh868711@163.com; alearn1988@126.com; gjq@tju.edu.cn; ji-aghan@tju.edu.cn; tianzhen@tju.edu.cn).W. Zhang is with the School of Electrical and Computer Engineering, Ok-

lahoma State University, Stillwater, OK 74078 USA (e-mail: weili.zhang@ok-state.edu).R. Singh is with the Center for Disruptive Photonic Technologies, Nanyang

Technological University, Singapore (e-mail: ranjan.ranjansingh@gmail.com).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TTHZ.2013.2285342

Fig. 1. (a) 3-D schematic of the proposed design. (b) SEM image of m-LPF1’scross section with an inset showing higher resolution of the image. (c) A viewof the sample from the -axis. The polarization of the incident light is along the-axis.

properties and have proven to offer a unique path in developingversatile terahertz devices with the ability to control at the unitcell level [3]–[9]. Metamaterial-based devices, including filters[10], [11], modulators [12], [13], switches [14], and invisibilitycloaks [15]–[17], have been developed using conventionalphotolithography and MEMS techniques. Terahertz filtersplay an important role in applications, such as terahertz signalprocessing, imaging [1], communications [18], and biomedicaland chemical sensors [19]–[21]. Extensive efforts have beendevoted in developing various types of terahertz filters, such asband-pass [4], [22]–[25], band-stop [26], high-pass [27], lowpass [28], and tunable filters [29]–[31]. However, as one of themost important components in the filter family, the low-passterahertz metamaterial filters with an extremely low insertionloss at the passband and a sharp rejection stopband still remainunexplored.In this article, we present a new type of metamaterial based

low-pass filter functioning in the terahertz regime. The filteris designed with a straightforward structure denoted as meta-lowpass filter (m-LPF), which consists of two-layer staggeredmetallic gratings, as shown in Fig. 1(a) and (b). The design notonly exhibits a passband with insertion loss less than 1.2 dB anda stopband with rejection of about 24.6 dB, but also shows a

2156-342X © 2013 IEEE

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2 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY

Fig. 2. (a)–(e) Measured (open circle) and simulated (solid line) spectra of m-LPF1, m-LPF2, m-LPF3, m-LPF4 and m-LPF5 samples, respectively.

steep roll-off behavior with a selectivity of 296 dB/THz. Themeasured results of the filter are analyzed using rigorous nu-merical simulations and an RLC analytical model calculation.

II. SIMULATION AND EXPERIMENT

The designed structure is schematically illustrated in Fig. 1.We first etched the periodic slits on one side of a 500- m-thickn-type silicon substrate ( and resistivitycm) with depth m, width m, and period

m by using standard photolithography process followed bywet etching. A gold film with thickness nm was thenthermally evaporated onto the corrugated surface with a slowerspeed to avoid covering the metal film onto the side walls ofthe slots. The scanning electron microscope (SEM) images ofthe fabricated sample are shown in Fig. 1(b) and 1(c). A higherresolution image [inset of Fig. 1(b)] displays the sharpness ofthe side wall. Four other samples were also fabricated, with allgeometric parameters (except the substrate thickness ) scaledby a factor of , 10/6, 8/6, and 4/6 with respect to thefirst sample of . The samples with , 10/6, 8/6, 1,and 4/6 are referred to as m-LPF1, m-LPF2, m-LPF3, m-LPF4,and m-LPF5, respectively.All the samples were experimentally characterized by use

of photoconductive-antenna-based terahertz time-domain spec-troscopy with an 8-F confocal configuration [32], [33]. Tera-hertz wave polarized along the direction excited the metama-terial filter sample at normal incidence. We measured the trans-mission through all m-LPFs, , where

and are the Fourier transformed spectra of thetransmitted sample signal and reference pulses, respectively. Ablank silicon substrate was used as the reference.Fig. 2 illustrates the transmittance spectra of all the five struc-

tures. When the corresponding parameters are scaled, the trans-mittance spectra reveal a nearly flat passband with differentcut-off frequencies . It is easily identified that for(m-LPF4), the pass-band region has an insertion loss of dBup to 1.08 THz with dB cut-off frequency of THz.Then the insertion loss suddenly drops to dB at 1.23 THz,corresponding to a 0.07 THz transition bandwidth. The mea-sured data also showed a very steep roll-off behavior.As the metamaterial structural features were scaled down

from (m-LPF1) to (m-LPF5), the 3 dBcut-off frequency varied from 0. 58 to 1.74 THz with lowinsertion losses, as shown in Fig. 2. The transition width (adrop in transmission from 90% to 10%) in all of our m-LPFs

Fig. 3. (a) Equivalent transmission-line model of samples. (b) Calcu-lated results of m-LPF4 with and without any inductive coupling.

is 110 GHz which compares very well with the terahertzBragg LPFs as shown in [29]. Therefore, by scaling the size ofthe structural features, we could optimize the cut-off frequencyaccording to the requirements for a particular application.

To elucidate the electromagnetic properties of the proposedstructures, 3D full-wave numerical simulations were carried outusing CST Microwave Studio. The unit cell shown in Fig. 1(a)was reproduced in the simulations with periodic boundaryconditions. The silicon substrate was modeled as a losslessdielectric medium with relative permittivity , whilegold was simulated with a conductivity of S/m.Despite minor fabrication defects, such as mismatched dimen-sions, the simulation results presented in Fig. 2(a)–2(e) agreewell with the measured data.In order to better understand the mechanism of low-pass fil-

ters characterized here, we resort to the transmission-line-RLCmodel [34] to analyze the structure, as shown in Fig. 3(a). ,, , , , and represent the corresponding imped-

ances of air, upper metal layer, coupling interaction, silicon slitlayer, lower metal layer, and silicon substrate. We use these pa-rameters to model the total transmission through the fabricatedmetamaterial samples. The model is separated into two

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ZHU et al.: A METAMATERIAL-BASED THz LOW-PASS FILTER 3

Fig. 4. (a)–(e) Measured results of cascaded samples for m-LPF1, m-LPF2, m-LPF3, m-LPF4 and m-LPF5, respectively; the inset in (a) illustrates the cascadedarrangement.

sections in order to simplify the calculation. For the first sec-tion, as shown in Fig. 3(a), we have

(1)

For the second section

(2)

The corresponding transmission and the reflection coefficientfor the two sections can then be estimated by [34]

(3)

Specially, for the upper layer impedanceand for the lower layer ,

in which , , , , , and are equivalent resistance,inductance, and capacitance of the upper and lower layers, re-spectively. The interaction between two layers was modeled by

as the impedance in Fig. 3(a).The total transmittance is given by [35]

(4)

where is the phase difference due to the exis-tence of the etched silicon film; and are the thickness andequivalent refractive index of the thin film, respectively.With this model, we fit the measured transmittance data and

the results are shown in Fig. 3(b).We found excellent agreementbetween analytical model, numerical simulations and measure-ments, which verifies our analytical model. Thus the theoret-ical analysis presented here reveals the importance of the in-ductive coupling between the top and the bottom meta-surfaces.Without accounting for this coupling, a simple sum of two grat-ings could have only given-a transmission spectrum with worse

Fig. 5. (a)–(d) Measured results at various angles of oblique incidence form-LPF4 ; the angle between the wave vector of the incident terahertzwave and surface normal of the meta filter are 5 , , and 15 , respectively.

selectivity and an inferior roll-off performance as indicated bythe red circle in Fig. 3(b) for m-LPF4.

III. OPTIMIZATION

To obtain a sharp-rejection bandwidth in the stopband,a back-to-back arrangement of two equal meta-layers wasemployed, as displayed in the inset of Fig. 4(a). The overallthickness is m here. We observed that the high fre-quency stopband possesses twice the attenuation (as much as

dB) as compared to the results in Fig. 2, while the inser-tion loss in the passband did not decline. The 3-dB bandwidthsof these patterns remain nearly constant, and the transition frompassband to stopband performance significantly improved witha selectivity 296 dB/THz asdefined in [36], where is the selectivity in dB/THz; isthe 3 dB-attenuation point; is the 20 dB-attenuation point;is the 20 dB stopband frequency; and is the 3 dB cut-off

frequency.To examine the angular behavior of the low-pass filters, trans-

mittance measurements were also carried out at wide angles ofincidence, defined between the wave vector of the incident ter-ahertz and surface normal of the meta filter m-LPF4. The resultsare shown in Fig. 5(a)–5(d) for various , 5 , 10 , and 15 ,

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4 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY

Fig. 6. (a)-(d) Measured results with different polarization for m-LPF4; the angle between the E-field of the incident waves and -axis are 0 ,

30 , 60 and 90 , respectively.

respectively. The transmittance spectra did not show significantvariation up to oblique incidence angle of about 15 , suggestingthat the filter can be efficiently used even if a minor misalign-ment existed between the filter and the incident terahertz wave.In addition, we investigated the polarization dependence

of the meta-filter structure, m-LPF4 as shown inFig. 6(a)–6(d). When the polarization angle between E-fieldand axis is zero, we obtain the highest transmittance pass-band. As increased to 30 , 60 , and 90 , the transmittancesdecreased sharply which showed the tremendous polarizationsensitivity of the device. . We also noticed that the cut-offfrequency was unchanged.

IV. CONCLUSION

We report on the theoretical, numerical and experimentaldemonstration of MEMS metamaterial based low-pass filterworking efficiently at terahertz frequencies. Performance ofthe meta low-pass filtering device shows low insertion loss atthe lower terahertz frequency band and sharp rejection roll-offat higher frequency stopband. A 296 dB/THz selectivityalso competes well with other existing low-pass filters [36].Meanwhile, our fabrication process tends to be more matureand stable compared with wave-guide materials. Transmis-sion-line- model explained the working mechanism ofthe meta low-pass filters. The excellent agreement betweenthe numerical simulation, analytical model and experimentalresults of the meta-filters indicate that this design could be apromising candidate for various broadband low-passes filteringin terahertz communications and imaging. The bandwidth of thefilters could be easily scaled with the geometrical dimension ofthe structures and the transmission showed large incident angletolerance. We believe that the meta low-pass filters presentedhere would function as terahertz signal processing device andwould lead the path forward for the design of active modules

of low pass filters by integrating dynamic materials such asphotodoped silicon, GaAs, superconductors and Graphene withthe metamaterial unit cell.

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Zhihua Zhu received the B.E. degree in optoelec-tronic science and technology from Tianjin Univer-sity and Nankai University, Tianjin, China, in 2011.She is currently a graduate student at the Center forTerahertz Waves, Tianjin University, Tianjin, China,under the supervision of Profs. J. Gu, J. Han and W.Zhang. Her research focuses on the PIT phenomenaand terahertz metamaterials.

Xueqian Zhang received the B. E. degree inelectronic science and technology from TianjinUniversity, Tianjin, China, in 2010, and is currentlyworking toward the Ph.D. degree in the field ofterahertz metamaterials at the Center for TerahertzWaves and College of Precision Instruments andOptoelectronics Engineering, Tianjin University.

Jianqiang Gu received the B.S. degree in electronicscience and technology, and the M.S. and Ph.D.degrees in opto-electronics technology from TianjinUniversity, Tianjin, China, in 2004, 2007, and 2010,respectively.From 2008 to 2010, he was a visiting Ph.D.

candidate in the School of Electrical and ComputerEngineering, Oklahoma State University, Stillwater,USA. Currently, he is on the faculty of the Collegeof Precision Instruments and Optoelectronics Engi-neering, and a member of the Center for Terahertz

Waves, Tianjin University, China. His current research interests includemetamaterials, surface plasmon polaritons, and material studies in the terahertzregime.

Ranjan Singh was born in Jamshedpur, India. He re-ceived the B.E. degree in telecommunications fromBangalore University, Bangalore, India, in 2001, theM.Tech. degree in photonics from Cochin Universityof Science and Technology, Cochin, India, in 2004,and Ph.D. degree in photonics from Oklahoma StateUniversity, Stillwater, OK, USA, in the year 2009.He was a Post-Doctoral researcher at Los Alamos

National Laboratory, Los Alamos, NM, USA, during2009–2013. Currently, he is an Assistant Professorat the Center for Disruptive Photonics Technologies,

Nanyang Technological University, Singapore. His current research interestsinclude ultrafast optics, terahertz spectroscopy, terahertz plasmonic metama-terials, superconductors and transition metal oxide based metamaterials, andhigh-Q Fano resonances in metamaterials.

Zhen Tian received the B.S. degree in electronicscience and technology, the M.S. degree in physicalelectronics, and the Ph.D. degree in optical engi-neering from Tianjin University, Tianjin, China, in2004, 2007, and 2010, respectively.From 2008 to 2010, he was a visiting Ph.D.

candidate at Oklahoma State University, Stillwater,OK, USA. Currently, he is on the faculty of theCollege of Precision Instruments and Optoelec-tronics Engineering, and a member of the Centerfor Terahertz Waves, Tianjin University, China. His

current research interests include terahertz spectroscopy and surface plasmonpolaritons.

Jiaguang Han received the B.S. degree in materialphysics from Beijing Normal University, Beijing,China, in 2000, and the Ph. D degree in appliedphysics from the Shanghai Institute of AppliedPhysics, Chinese Academy of Sciences, Shanghai,China, in 2006.He was a Visiting researcher at the Japanese High

Energy Accelerator Research Organization during2004–2005. From 2006 to 2007, he was a Post-doctoral Researcher in the School of Electrical andComputer Engineering, Oklahoma State University,

Stillwater, OK, USA. In 2007, he joined the Department of Physics, NationalUniversity of Singapore, Singapore, where he was a Lee Kuan Yew ResearchFellow. Currently, he is Professor in the College of Precision Instrumentsand Optoelectronics Engineering, and a member of the Center for TerahertzWaves, Tianjin University, China. His current research interests include surfaceplasmon polaritons, metamaterials, and material studies in the terahertz regime.Dr. Han is a recipient of the Einstein Award from the Embassies of Germany

and Switzerland in 2006, and was invited to visit the German and Swiss univer-sities and research institutes.

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6 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY

Weili Zhang received the B.S. degree in laser sci-ence, and the M.S. and Ph.D. degrees in optical en-gineering from Tianjin University, Tianjin, China, in1987, 1990, and 1993, respectively.From 1993 to 1995, he was a Post-Doctoral Re-

search Associate in the Department of Physics, TheHong Kong University of Science and Technology,Hong Kong. In 1995, he joined the faculty in theDepartment of Optoelectronics Technology, TianjinUniversity. Since 2000, he was Visiting AssociateProfessor, Associate Professor, and currently Pro-

fessor at the School of Electrical and Computer Engineering at Oklahoma StateUniversity, Stillwater, OK, USA. He is also Adjunct Changjiang Professorin the College of Precision Instruments and Optoelectronics Engineeringand Director of the Center for Terahertz Waves, Tianjin University, China.

His research interests include terahertz optoelectronics, nanostructured andmicrostructured materials optics, and ultrafast lasers and phenomena.Dr. Zhang is Associate Editor of the Journal of Optoelectronics and Lasers,

Guest Editor for a number of peer-reviewed journals, including IEEE JOURNALOF SELECTED TOPICS IN QUANTUM ELECTRONICS, and Chinese Optics Letters,and member of the editorial board of Journal of Photonics,Optoelectronics Let-ters, and Chinese Optics Letters. He was the general Co-Chair for the 4th In-ternational Symposium on Ultrafast Phenomena and Terahertz Waves, Tianjin,China, in 2008. He was the Session Chair and Program Committee Member formany international conferences, including CLEO, PIERS, Optics East, SPIEDefense, Security, and Sensing, and OSA topical meetings. Dr. Zhang receivedthe first Young Faculty Award from the Ministry of Education of China in 2000,the Changjiang Scholar Award in 2010, and the Overseas Scientist ResearchAward (former NSFC-B) in 2010.