Optics Communications 284 (2011) 3129–3133

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Optics Communications

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Thermal broadband tunable Terahertz metamaterials

Jun Zhu a,b, Jiaguang Han a,⁎, Zhen Tian a, Jianqiang Gu a, Zhongyong Chen b, Weili Zhang c

a Center for Terahertz wave, Key laboratory of Opto-electronic Information Science and Technology, Ministry of Education,College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, Chinab School of Physics and Electronic Information,Yunnan Normal University, Kunming 650092, Chinac School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK 74078, USA

⁎ Corresponding author.E-mail address: jiaghan@tju.edu.cn (J. Han).

0030-4018/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.optcom.2011.02.038

a b s t r a c t

a r t i c l e i n f o

Article history:Received 20 December 2010Received in revised form 12 February 2011Accepted 15 February 2011Available online 12 March 2011

A thermally tunablemetamaterial comprising a periodic array ofmetallic split-ring resonatorswith anembeddedsemiconductor has been proposed. The resonance frequencies of the metamaterial are demonstrated to becontinuously tuned in the terahertz regime by increasing the temperature. The tunability is attributed to thetemperature-dependent permittivity of the embedded semiconductor and well analyzed by an equivalentcapacitor–inductor model. The proposed designs ensure broadband thermally tunable terahertz devices.

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© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Metamaterials have gained enormous interest, in recent yearsespecially, due to their unusual electromagnetic response character-istics that are rare or absent in natural materials [1–3]. The excitingemerging research on metamaterials thus promises importanttechnological and scientific advances in diverse areas and enablespromising applications in diffraction-limit imaging [4–6], cloaking [7–9], chiral devices [10–12], electromagnetically induced transparency(EIT) [13–15], etc. The large variety of applications of metamaterialscould be extended tremendously if their response characteristics canbe dynamically tuned. Tunability strategies examined thus far areelectrical control [16–18], magnetostatic control [19–23], opticalpumping [24–26], thermal control [27–29], liquid crystal inclusions[30–32], optical activity [10,11], coherent control [33] and Kerrnonlinearities [34]. In these previous works, the essential elementsare mostly split-ring resonators (SRRs) of metal, and these resonantelements can be represented by an effective inductor–capacitor (LC)resonator, where the resonance frequency ω0 is strongly dependenton the effective capacitance C and inductance L, i.e., ω0∝(LC)−1/2.Tunability is introduced by ensuring that another component is madefrom an electro-optic material, liquid crystal, ferrite, semiconductorand so on in the designs to alter L, C, or both.

Recently, incorporation of semiconductors into the LC resonator isgiven considerable attention, especially at terahertz frequencies. This isbecause in the terahertz regime semiconductors emulate metals byhaving the real parts of their relative permittivities negative. Comparedtometals, however, semiconductors have a significant advantage in thattheir relative permittivity can bemodified by changing the temperature

[27], external magnetic fields [19], pumping light intensity [25,35] andapplied voltages [18]. Hence,metamaterialsmade from semiconductorsprovide one way to be tunable and switchable in the terahertz regimeand then can be expected to be used in the practical applications.

Associated with metamaterial investigations and applications isthe need for enabling metamaterial structures to be of utmost flexibleproperties. In this work, we present a smart metamaterial exhibitingboth broadband tuning as well as small amplitude switching atterahertz frequencies but considerably consistent with theoreticalanalysis. In the presented structure, we consider incorporation of thesemiconductor into the gap of metallic SRRs, where precise patterningof semiconductors permits frequency tuning of the metamaterialresonance by changing the external temperature. Meanwhile, avariation of this design by directly pattering the semiconductorinclusions on the substrate is also given. Our studies have shown thata large blueshift of resonance frequency in the proposed structures asmuch as ~65% can be implemented with increasing temperature. Theresults presented here thus may offer a desirable and flexible designfor frequency-agile metamaterials in the terahertz regime and thencould lead to potential applications in novel terahertz devices.

2. Results and discussion

The schematic views of the proposed structures are shown inFig. 1. The essence of the chosen structure is a conventional two-gapSRR with linear dimensions of length D=36 μm, linewidthW=6 μm,gap G=3 μm and thickness t=200 nm. For the sake of definiteness,let us consider the planar SRR made from Al printed on an isotropicquartz substrate. The quartz substrate of a relative permittivity 3.78 is640 μm thick. By inserting semiconductor InSb patches of lengthM=8 μm andwidth G=3 μmwithin the two side gaps, we obtain theunit cell of the design as shown in Fig. 1(a). The unit cell was arrangedin a square lattice with a period of 50 μm, as shown in Fig. 1(b). All

Fig. 1. (a) A unit cell of the proposed structure with normal incident electromagnetic field. The structure parameters are: D=36 μm,W=6 μm, G=3 μm,M=8 μm and t=200 nm.(b) Schematic of a square array of SRRs printed on the substrate with a period of 50 μm.

3130 J. Zhu et al. / Optics Communications 284 (2011) 3129–3133

dimensions in our design are typical for terahertz metamaterials[11,19,25].

Computer simulations of the spectral response of the chosenstructure were performed using the commercial software CSTMicrowave Studio, which is a 3D full-wave solver that employs thefinite integration technique. In the simulation, the metamaterial wastaken to be entirely surrounded by air and open boundary conditionswere employed along the propagation direction [11,18,36–38]. Themodel was set with the SRR gap along the incident E field in order toexcite the fundamental LCmode resonance, as shown in Fig. 1. A lossy-metal model is utilized for Al, the conductivity of which isσAl=3.77×107 S/m [39]. In the simulations with CST, two waveguideports are used as the excitation and collection, respectively. Thenormal incident electromagnetic wave is excited from the freespace,goes through the sample on the substrate of actual thickness, and thenis collected in freespace. The open boundary conditions are employedalong the propagation direction. The transmission is determinedbased on the ratio of electric field. In the far-infrared terahertz regimeand within our studied temperature ranges between 160 and 350 K,the complex-valued relative permittivity of InSb can be givenapproximately by the simple Drude model [40–46]:

ε ωð Þ = ε∞−ω2p = ω2 + iγω

� �ð1Þ

where ω is the angular frequency; ε∞ represents the high-frequencyvalue; γ is the damping constant; and the plasma frequencyωp =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNe2 = ε0m�p

depends on the intrinsic carrier density N, theeffective massm* of free carriers, the electronic charge e, and the free-space permittivity ε0. It is worthy of note that the damping constant γof InSb is proportional to the electron mobility μ as γ=e/m*μ, whichin turn depends on temperature. Therefore, if the temperaturechanges largely, γ will change with temperature and then willinfluence on the absorption of InSb. However, in our studied casebetween 160 and 350 K within the frequency regime ranging from 0.1to 2.0 Thz, the electron mobility changes little [41–46] withtemperature and it is thus reasonably assumed that γ is a constant,which is consistent with the experimental report [40]. On the otherhand, the plasma frequency ωp of InSb depends strongly on thetemperature T (in Kelvin). When the temperature is between 160 and350 K, the energy gap of InSb changes very little with temperature,and the intrinsic carrier density N (in cm−3) in InSb can be describedadequately by the relationship [41–43]:

N = 5:76 × 1014T3=2 exp −0:26 = 2kBTð Þ ð2Þ

where kB is the Boltzmann constant. A variation in N due to a variationin T thus changesωp. Consequently, in the far-infrared portion of theterahertz regime, ε(ω) of InSb is very sensitive to T. Hence, formetamaterials comprising InSb inclusions, we can expect thattemperature variations can cause substantial variations in the opticalresponse characteristics. It is worth noting that in our studied cases,the carrier density calculated by the used model of Eq. (2) are in goodagreement with those calculated by an empirical model proposed byOszwaldowshi and Zimpel [42,47].

Fig. 2(a) shows the simulated frequency-dependent amplitudetransmission t(ω) of the studied metamaterial at various tempera-tures. At a low temperature 160 K, the intrinsic carrier density in InSbis N~0.94×1014 cm−3 and the semiconductor displays typicaldielectric features. The resonance of the chosen structure ismanifested as a sharp transmission dip around 0.92 Thz. If thetemperature is increased, the intrinsic carrier density in InSb isenhanced and thus induces remarkable shift of resonance. At 290 K,the resonance blueshifts to 1.07 Thz, where the carrier density isN~1.57×1016 cm−3 and InSb shows typical metallic features. As thetemperature is further increased to 350 K, the carrier density N isenhanced to 5.76×1016 cm−3 and the resonance is then dramaticallyshifted to 1.34 Thz. Therefore, a fairly broadband blueshift, as much as50%, has been achieved without changing the transmission amplitudevisibly as temperature is increased from 160 to 350 K.

As a comparison, Fig. 2(b) illustrates the simulated transmission ofthe SRRs patterned on a silicon substrate, where the SRRs keepthe same dimensional parameters as those on quartz substrate and thesilicon has a permittivity 11.96 [36–38,48]. Compared to the simulatedresults in Fig. 2(a), the presented results in Fig. 2(b) show that theresonance of the metamaterial depends on the substrate and thewhole resonance frequency is totally shifted towards lower frequencywhen we change the substrate from quartz to silicon. This result isreasonably consistent with the previous experimental observations[49]. But similar tunable characteristics are also found when wechange the temperature. As shown in Fig. 2(b), the resonancefrequency significantly blueshifts from0.56 to 0.85 Thz as temperatureincreased from 160 to 350 K. These results demonstrate well that thetunability is mainly dominated by the properties of the inserted InSb.

Clearly, the transmission characteristics of the proposed structurechange significantly with temperature and the temperature-depen-dent characteristics can be attributed to the increase in the density offree carriers in InSb by thermal excitation as the temperatureincreases. To clarify the nature of the frequency tuning in theproposed metamaterial structure, the electric field distributions atthe resonance frequency under different temperatures are calculated.

(a)

(b)

Fig. 2. Simulated transmission of the chosen designwith quartz substrate (a) and siliconsubstrate (b) at different temperatures ranging from 160 to 350 K, respectively. Theinserted patches are made of InSb, whose relative permittivity is given by Eqs. (1) and(2) with ε∞=15.68, m*=0.015me, me=9.1×10−31 kg, andγ/2π=0.05 Thz [40–43].

3131J. Zhu et al. / Optics Communications 284 (2011) 3129–3133

Fig. 3 shows the electric field distributions of the design patterned onquartz substrate at 160, 290 and 350 K, respectively. The significantchanges of the resonance of the metamaterial due to increase oftemperature can be reflected clearly from the variations of the electricfield distributions around the outer two gaps of SRRs. As mentionedabove, the resonance in the studied SRR structure can be representedby an effective LC resonator, where the outer two metallic gapsprovide appreciable capacitive responses. When temperature isincreased, the inserted InSb shows more metallic features and thus

Fig. 3. Distribution of electric fields at the LC resona

does not benefit the capacitive response. As a result, the electric fieldshows notable attenuation with increasing temperatures.

The frequency tunability in the proposed metamaterial can befurther derived from the capacitance C control on the basis of theanalogy with an equivalent LC circuit of SRR as shown in the inset ofFig. 4(a). The resonance frequency of the metamaterials behaving as aresonator can be estimated as:ω0 = α=

ffiffiffiffiffiffiLC

p, here α is the propor-

tional coefficient. The inductance L is proportional to the SRR area andinverse to the SRR thickness as [50]:

L =μ0D

2

t: ð3Þ

The capacitance C is due to the gap and can be calculated as [50]:

C =ε0εeff tW

Gð4Þ

where εeff is the effective permittivity of the materials contributing tothe gap. By substituting L and C, we then obtain:

ω0 = αcD

ffiffiffiffiffiffiffiffiffiffiffiffiffiG

W εeff

sð5Þ

in which c = 1 =ffiffiffiffiffiffiffiffiffiffiε0μ0

pis the speed of light in the vacuum. In our

design with fixed geometry parameters, L is considerably harder to bechanged and the tuning frequency is ascribed to the change of C, i.e.,the change of εeff.

From the simulated results, we can see that when we change thesubstratematerials or the properties offilling InSb, both of themwouldhave a significant influence on the resonance frequency. Therefore, notonly the fillingmaterials contribute to εeff but also substratematerials.Taking this factor into account, we can calculate εeff using a simpleeffective medium model as [51–54]: εeff= fεsub+(1− f)εInSb, here f isthe filling factor denoting the contribution ratio from substrate andfilling materials. The solid circles in Fig. 4(a) represent the analyticallypredicated resonance frequency with Eq. (5), which is in goodagreement with the simulated results. In the calculation, εInSb isusing the average value around the resonance frequency because thisvalue changes small around the resonance frequency. Being consistentwith the simulated results, the analytical predication clearly revealsthat the thermal tunability of the studied metamaterials originatesfrom the variations of εeff. The changes of permittivity of the insertedInSb due to the temperature give rise to the change of the value ofcapacitance C and thus result in a remarkable blueshift of theresonance frequency.

For greater flexibility and with a view towards application, itwould be ideal to consider a variant of the proposed design. In Fig. 4(b), we present the simulated transmissions of one possible variantdesign at various temperatures. Unlike our previous design, here, a

nce under 160 K (a), 290 K (b) and 350 K (c).

L CC

(a)

(b)

Fig. 4. (a) The solid circles are calculated resonance frequency for the chosenmetamaterials at different temperatures. The open squares are simulated resonancefrequency. The calculation is based on Eq. (5) and the simple effective medium modelεeff= fεsub+(1− f)εInSb. Parameters: D=36 μm, W=6 μm, G=3 μm, f=0.98, andα=0.31 for the design with a quartz substrate of εsub=εquartz=3.78 and f=0.98,and α=0.33 for the design with silicon substrate of εsub=εSi=11.96 are taken intoaccount, respectively. εInSbis an average value around the resonance frequency(±0.03 Thz). (b) Simulated temperature-dependent transmission of the variant design.The inset is the equivalent LC circuit.

3132 J. Zhu et al. / Optics Communications 284 (2011) 3129–3133

150-nm-thick InSb thin layer is deposited on the quartz substratedirectly spacing the metallic SRR and the substrate. Following ourexpectations, similar frequency tunabilities are achieved as ourprevious structure. When temperature increases from 160 to 350 K,the resonance frequency then blueshifts from 0.90 to 1.49 Thz — ashift more than 65%, demonstrating an alternative approach to endowthermally tunable Thz metamaterials.

3. Conclusions

In conclusion, we have proposed and analyzed a thermally tunablemetamaterial operating in the terahertz regime. Our computersimulations have shown that the resonance frequency of themetamaterial constituted by an array of metallic SRRs with embeddedsemiconductor InSb can be tuned by changing the temperature. Wedemonstrated that a broadband tuning range more than 50% can beachieved. The shifts obtainable are quite consistent with the analyticalpredictions based on an equivalent LC model, where variablecapacitances due to the variation of the relative permittivity of theembedded InSb allow shifting of the metamaterial resonance. The

design proposed here is more amenable to fabrication and also offersgreater flexibility in applications of frequency-agile terahertz devices.

Acknowledgments

We acknowledge the fruitful discussions with Prof. A. Lakhtakia(Pennsylvania State University, USA). This work was supported by theU.S. National Science Foundation (Grant no. ECCS-0725764), theNational Science Foundation of China (Grant nos. 61028011,61007034, and 60977064), the Tianjin Sci-Tech Program (Grant nos.09ZCKFGX01500 and 10JCYBJC01400), and the MOE 111 Program ofChina (Grant no. B07014).

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