Research ArticleGain Incorporated Split-Ring Resonator Structures forActive Metamaterials

Jordan Chaires, David Schumerth, Cole Drawdy, and Weiguo Yang

Department of Engineering & Technology, Western Carolina University, Cullowhee, NC 28723, USA

Correspondence should be addressed to Weiguo Yang; wyang@email.wcu.edu

Received 30 June 2015; Accepted 13 August 2015

Academic Editor: Jung Y. Huang

Copyright © 2015 Jordan Chaires et al.This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We present a systematic study of split-ring resonator (SRR) structures that are used as the basic building blocks of activemetamaterials with incorporated gain. The active split-ring resonator (aSRR) structures with gain elements can in theory havesimilar unusual electromagnetic responses such as negative effective permeability near their resonance of the artificial magneticresponse just like their passive counterparts. At the same time aSRRs can have reversed imaginary part of the effective permeabilityand, therefore, mitigate the loss of passive SRRs. We explored in detail both passive and active SRRs through analytic theory,numerical simulations, and lab experimentation and demonstrated that aSRRs can have the similar negative effective permeabilityresponses while reducing and even reversing the loss.

1. Introduction

Split-ring resonator- (SRR-) based structures are buildingblocks for metamaterials that can exhibit exotic effectiveelectromagnetic responses including but not limited to neg-ative or near-zero index of refraction [1], reverse Casimireffect [2], and perfect absorption [3]. Such exotic engineeredelectromagnetic responses can be extremely useful and mayenable many potentially revolutionary applications suchas superresolution imaging, cloak of invisibility, quantumlevitation, and conforming and electrically small antennas[2–5]. However, one fundamental drawback of the SRR-based metamaterials is their intrinsic loss due to metalsused for SRRs [6]. For most metamaterial applications suchas superresolution imaging and cloak of invisibility, suchloss is detrimental. For other applications that are moretolerant to loss, the intrinsic metal loss of the SRR-basedmetamaterials still tends to limit the practical applications tothose of metasurfaces [7, 8], where only a very thin layer ofmetamaterials is required. For bulk metamaterials, attemptshave been made to compensate the intrinsic metal loss ofSRR structures by either adding layers of gain materials orembedding the SRRs in host materials that will provide gain[9, 10]. Dong et al., for example, have explored SSRs on activesubstrate in optical wavelengths up to 610 nm [9]. According

to their approach, the heavy metal loss of the SRR structuresis compensated by the optical gain material as the substrateand left-hand resonance transmission is obtained at 20 dBreduced loss, essentially providing transparent transmission.In this approach, the absorption nature of the negative indexmaterial (NIM) is not changed; it is only compensated bythe separate layer of optical gain. Other investigators alsoexplored the similar concepts of compensating the metalloss of plasmonic structures by separate gain layers [10].Experimentally such approaches so far only have had limitedsuccesses. On the other hand, there is still a hot debatewhether or not suchmixing formula based approaches wouldwork in theory due to the spatial averaging nature of theunderlying assumptions of the effectivemedium theory.Morespecifically, the separate layers of gain materials employed inthese loss compensation approaches are all normal materialswith, for example, positive indices of refraction. While thespatial average according to the effective medium theoryapproaches reduces the effective metamaterial losses in thespectral amplitude responses, which are determined by theimaginary part of the effective index of refraction, it alsotends to reduce the negative real part of the effective indexof refraction of the NIM at the same time, which definesthe unusual effective electromagnetic responses that arerelated to the spectral phase responses. We propose here to

Hindawi Publishing CorporationAdvances in OptoElectronicsVolume 2015, Article ID 247630, 9 pageshttp://dx.doi.org/10.1155/2015/247630

2 Advances in OptoElectronics

mitigate the intrinsic metal loss problem of the SRR-basedmetamaterials by making the underlying SRR structuresactive, namely, incorporating gain element in them whilekeeping the unusual spectral phase response characteristicssimilar to that of their passive counterparts. This is similarto the case where the population inversion is introduced in anormally absorptive atomic system,making the same spectralresonance feature now exhibiting gain instead of loss throughthe stimulated emission. In this way, the unusual spectralphase response governed by the real part of the effective indexof refraction can be preserved but now potentially with gain.The successful demonstration of this novel concept presentedin this paperwill lead to a rich area of fundamental research ofactive metamaterials that are characteristically defined by itsactive composition of the meta-atoms. The key differentiatorof our proposed active metamaterials approach as comparedto previous metamaterial loss compensating approaches isthat we focus on making the meta-atoms themselves activewhile most other groups were using active host materials inorder to compensate the loss of the meta-atoms. In otherwords, our proposed approach fundamentally changes meta-atoms’ spectral responses, notably from loss to transparentor even gain for the spectral amplitude response while itmaintains the abnormal spectral phase response due to theresonance of the SRR structure that gives rise to its artificialmagnetic responses, leading to the possibility of negativepermeability. In contrast, other approaches try to compensatethe passive SRR’s loss by extra gain layers of normalmaterials,which, as pointed out above, may or may not succeed inachieving the goal of low loss metamaterials. Our proposedapproach to active metamaterials is fundamentally differentin this respect. We explore the single active SRR (“meta-atom”) structures and take advantage that it is possible tomaintain the abnormal dispersion relationship while makingthe meta-atoms a gain element rather than a loss element bydirectly incorporating gain in the SRR structure. The pro-posed approach also provides the benefit of the introducedactive elements, which can in turn strongly interact withthe stimulus electromagnetic fields and therefore providemeans for tunable as well as active metamaterials. Suchactive metamaterials with gain can also be incorporated withpassive metamaterials to make transparent materials withoutreducing the unusual effective electromagnetic responsesthat are related to the spectral phase responses, a.k.a. thereal part of the effective index of refraction. In this paper,we present a systemic study including analytical theory,numerical simulations, and experimental investigations ofincorporating gain element in single active SRR structures.We demonstrate that the spectral amplitude responses of theactive SRR cells can in fact exhibit gain while preservingthe unusual spectral phase responses similar to their passivecounterparts.

2. Artificial Magnetic Response fromSplit-Ring Resonators

Split-ring resonators (SRRs) have been extensively stud-ied and well understood [11]. As illustrated in Figure 1(a),

the metal ring structure provides the inductive response tothe electromagnetic field, while the gap of the split ringprovides the capacitive response. Depending on the design,double split rings can also be used to increase the capacitiveresponse so that the resonant frequency of the SRR canbe further reduced, making SRR suitable for electricallysmall antenna applications. In our study, we used the sim-plistic single ring design. Generally speaking, SRRs gaintheir special electromagnetic responses, that is, the artificialmagnetic response (AMR), through the resonance of the SRRstructures that is determined by the artificially introducedinductive and capacitive responses. Figure 1 shows a simpleSRR design (Figure 1(a)) and its lump element equivalentcircuit model for the AMR resonance (Figure 1(b)). Not allelectromagnetic resonances of SRRs are the AMR resonance.Many are higher-order electrical resonances that typicallyhavemore complicated surface current distributions. In orderto facilitate an intuitive understanding of the SRR’s AMRresonance as well as different SRR designs in general, we usethe lump element equivalent circuit model as illustrated inFigure 1(b). The transformer is used to model the electro-magnetic wave excitation, which has the sinusoidal varyingmagnetic field perpendicular to the ring. The excitation canbe modeled as the induced electromotive force (emf) in theSRR. Analysis using this equivalent circuit model yields theeffective relative permeability of the SRR as

𝜇SRReff = 1 −

𝜋

2

𝑠2𝜇0𝑟𝐶

1 + 𝑠𝑅𝐶 + 𝑠2𝐿𝐶, (1)

where 𝑟 is the inner radius of the metal ring, 𝐿 is the self-inductance of the SRR,𝐶 is the capacitance of the SRR, and 𝑅is the total resistance. The self-inductance 𝐿 is proportionalto the length of the metal ring. The capacitance 𝐶, on theother hand, is due to the dielectric gap introduced in themetalring. The total resistance 𝑅 includes metal Ohmic resistanceas well as the radiation resistance that can be used to modelthe radiation property of the SRR as an antenna. The AMRresonance frequency of the SRR is therefore 𝜔

0= 1/√𝐿𝐶.

For the metamaterial built with the SRR as the buildingblocks and a filling ratio of 𝐹, one has approximately for theeffective relative permeability of the metamaterial

𝜇eff = (1 − 𝐹) 𝜇host + 𝐹𝜇SRReff . (2)

These simplified theoretical analyses are in consistence withprevious studies of SRRs in the literature.

Figure 2(a) shows a simulation of the real and imaginaryparts of the effective permeability of a hypothetical case of𝑟 = 12mm, 𝐿 = 24 nH, 𝐶 = 1 pF, and 𝑅 = 10Ohm.TheAMR resonance frequency is around 1GHz.The effectivepermeability of the SRR determines the magnetic field insidethe SRR given a fixed electromagnetic wave excitation. Theinduced surface current in the SRR will give rise to theinduced electromagnetic waves and the far-field scatteredwave from the SRR is the superposition of the inducedelectromagnetic wave and the original excitation wave. Forexample, in the direction of the original wave propagation,the complex number 𝜇eff means that the induced wave and

Advances in OptoElectronics 3

(a) Split-ring resonator

R

CI1

−

+

(b) Lump element equivalent circuit

Figure 1: (a) A simple design of the split-ring resonator (SRR). The metal ring provides the magnetic field response while the dielectric gapprovides the capacitive response and together SRR demonstrates a distinct resonance response referred to as the artificial magnetic response.(b) The lump element equivalent circuit model for the SRR’s artificial magnetic response.

0 0.5 1 1.5 2

0

2

4

6

8

Frequency (GHz)

Real partImaginary part

−4

−2

𝜇SR

Reff

(a)

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−50

−40

−30

−20

−10

0

10

20

20lo

g|𝜇

SRR

eff−1|

(dB)

(b)

Figure 2: AMR resonance of the SRR. (a) Effective permeability. Solid curve shows the real part of the effective relative permeability. Dashedcurve shows the imaginary part. (b) The far-field scattered wave response that clearly exhibits the AMR resonance.

the original wave will add up with a phase shift and this mayresult in attenuation in the propagation in that particulardirection. In addition, in the spectral range where the realpart of the effective permeability is negative, it is possibleto make a negative index of refraction (NIM) material ifsimilar negative electrical responses can be incorporated. Inthe research of themetamaterials built from SRRs, it is alwaysdesired to locate the actual AMR resonant frequency inducedby the SRR. It is, however, not always an easy task to doso since the far-field transmission responses of the SRR, forexample, may exhibit many resonance features that may notbe related to the desired AMR resonance. Identifying withoutambiguity the actual AMR resonance is therefore a criticaltask in design and optimization of SRR-based metamaterials.

Consider the special case of the propagation of scatteredwaves in the orthogonal direction where there is no propa-gation of excitation waves (e.g., in the direction along which

the electric field of the excitationwave oscillates or polarized);the scattered wave is solely determined by the induced mag-netic field inside the SRR and proportional to the magnitudeof |𝜇SRReff − 1|, which has the characteristics of a second-order high-pass filter response. This configuration provides aconvenient far-field characterization method for SRRs AMRand its far-field effects. The characterization requires only totake far-field measurements perpendicular to the directionof propagation of the excitation wave on the SRR plane.One should be expecting a second-order high-pass filter typeresponse for the scattered wave and the AMR frequency, forexample, can be identified from the characteristic response.This special far-field scattered wave response is shown inFigure 2(b) for the same hypothetical SRR as in Figure 2(a).If different far-field configurations are used, AMR is typicallyblended with other higher-order electrical and/or magnetic

4 Advances in OptoElectronics

Z

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−137.50

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Setup1: sweep1dB(rEX)

Setup1: sweep1dB(rEX)

dB(rEX)Setup1: sweep1

dB(rEX)Setup1: sweep1

dB(rEX)Setup1: sweep1

Curve info

𝜙 = “10deg.” 𝜃 = “90deg.”

𝜙 = “30deg.” 𝜃 = “90deg.”

𝜙 = “50deg.” 𝜃 = “90deg.”

𝜙 = “70deg.” 𝜃 = “90deg.”

𝜙 = “90deg.” 𝜃 = “90deg.”

(b)

Figure 3: 3D HFSS simulation of single SRR. (a) HFSS 3D SRR simulation setup. (b) Far-field scattered field responses at different locationson the 𝑥𝑦-plane exhibiting the characteristic resonance that give rise to the artificial magnetic response (AMR) of the SRR structure alongwith other higher-order electrical resonance responses.

responses, adding to the difficulty to single out the far-fieldAMR effects.

3. Numerical Simulations ofSingle SRR Far-Field FAMR Effects

Extensive numerical simulations of single SRR using theHFSS 3D solver have been performed for far-field effects ofAMR. The basic simulation setup is shown in Figure 3(a).The excitation electromagnetic wave is propagating alongthe 𝑥-axis (the green axis in the figure). The electricalfield of the excitation waves is polarized along the 𝑦-axis(blue). The magnetic field is along the 𝑧-axis (red) and isperpendicular to the SRR surface. The far-field scatteredwaves are measured in the 𝑥𝑦-plane. Since the excitationwaves have the electrical field that is parallel to the 𝑦-axis, thefar-field scattered waves in 𝑦 direction, for example, are solelydetermined by the induced magnetic field excited inside theSRR. As the result, the far-field radiation pattern measuredat a location that is on the 𝑦-axis will exhibit a second-orderhigh-pass (SOHP) filter characteristic spectral response at theSRR’s AMR resonance frequency. The numerical simulationcovers a wide frequency range from 100MHz to 12GHz.Figure 3(b) shows the simulation results of 10mm SRR.As shown in Figure 3(b), the typical frequency responsescan be characterized by two dominant features. The firstdominant feature is a clear SOHP filter type characteristicwith the resonance frequency in the 1.5 GHz range. Thisfeature does not shift in frequency for different scatteringdirections, which is expected for the AMR resonance of theSRR.The second dominant feature is the periodic dips in thepassband of the SOHP filter. These periodic dip features havethe frequency period that increases with the scattered angle

and they are attributed to the SRR’s higher-order electricalresonances that determine its radiation impedance. Thehigher-order electrical resonant responses also give rise to thedirection dependent nature of the radiation impedance of theSRR.The qualitative distinction between the AMR resonanceand other resonances related to the radiation characteristicsof SRR is important as the optimal design of the SRR-based metamaterial structure will require a match betweenthese two features. In comparison, Figure 4 shows a far-fieldscattered field spectral responses of a full ring (no dielectricgap) in the 𝑦 direction and clearly there is lack of the second-order high-pass filter type response that is characteristicfor the AMR resonance. Obviously, in theory, the AMRresonance is expected to disappear without the dielectric gapthat introduces the loop capacitance. The response of the fullring changes to a first-order high-pass type as expected withno indication of the AMR resonance. The same size of full-ring resonator still exhibits similar impedance matching typeof periodic spectral responses in the passband due to higher-order electrical resonances.

4. Fabrication and Measurement ofSingle SRR Structures

Based on the extensive numerical simulation and theoret-ical analysis results, we fabricated and measured severaldifferent SRR structures including the ones incorporatinggain elements. The SRRs were fabricated in-house usingthe printed circuit board (PCB) router on FR4 dielectricboards. First, the passive SRRs with various sizes were mea-sured and compared to the numerical simulations. Figure 5shows the experimental setup and the dependence of theAMR resonance peak frequency on the size of the SRR

Advances in OptoElectronics 5

0.00 2.00 4.00 6.00 8.00 10.00 12.00Frequency (GHz)

)XEr(Bd

m1

m2

Curve InfodB(rEX)Setup1: sweep1

−125.00

−112.50

−100.00

−87.50

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−37.50XY plot 2 RR_rad10mm

Name X Ym1 10.0000m2 7.3000

−77.4352−38.5219

𝜙 = “90deg.” 𝜃 = “90deg.”

Figure 4: 3D HFSS simulations of the far-field responses in 𝑦direction of a full ring of the same size as in Figure 3(b).There are noAMR characteristic responses in this case as compared to the split-ring cases.

and compares the measurement results with the numericalsimulations. The experimental setup consists of a VectorNetwork Analyzer (Agilent N5230A) and a pair of matchedantennas for the frequency band of interest. The identifiedAMR resonance peak frequencies of various SRRs are plottedversus the radius 𝑟 of the SRR ring. The power law fittingsyield close approximate relations of 𝑓

0∝ 1/𝑟, which is in

agreement with the lump element equivalent circuit modeldiscussed in Section 2 for both the numerical simulationand measurement results. The measured results are also inexcellent agreement with the simulated results.

On the other hand, the active SRRs (aSRRs) need to incor-porate gain elements in the passive SRR structures.We startedwith the externally driven SRRs where we demonstrated thatthe SRRs emit efficiently in their resonant frequency rangeand the emission adds coherently to the input. Consequently,we designed a self-driven active SRR consisting of a passiveSRR connected to a circulator followed by an amplifier thatprovides the gain as shown in Figure 6(a). The circulatoris necessary here in the single ring aSRR configuration inorder to avoid the direct short circuit connection betweenthe input and output of the amplifier. The amplified signal atthe amplifier output is in turn fed to the SRR and re-emittedvia the circulator. This configuration of aSRR is capable ofcapturing the input waves in the frequency range of SRR’sresonance and then amplifying and reemitting at the samefrequency coherently, changing the amplitude response ofthe SRR structure from loss to gain, while still keeping theabnormal phase response in the interested aSRR responsefrequency range.This configuration allows one to incorporatethe gain element with a single SRR ring via the circulator andthe design is conceptually closest to the ideal aSRR where again element is incorporated into a single SRR ring structure.Conceptually, the effect of the gain incorporated can bemodeled by the negative resistance in the lump elopementcircuitmodel similar to that presented in Section 2. Replacingthe resistance 𝑅 in (1) with an effective resistance 𝑅eff that

models the combined effects of metal loss, radiation loss, andthe gain, one can have the effective relative permeability ofthe aSRR as

𝜇aSRReff = 1 −

𝜋

2

𝑠2𝜇0𝑟𝐶

1 + 𝑠𝑅eff𝐶 + 𝑠2𝐿𝐶. (3)

Figure 6(b) shows the real and imaginary parts of the effectivepermeability of a hypothetical case of 𝑟 = 12mm, 𝐿 = 24 nH,𝐶 = 1 pF, and 𝑅eff = −10Ohm. The added gain does notaffect the AMR frequency, which is determined by the self-inductance and capacitance of the split ring. Compared toFigure 2(a) which plots the effective relative permeability ofthe passive SRR, the real part stays the same, which, forexample, still provides the opportunity for negative effectivepermeability.The imaginary part, on the other hand, has beenflipped in sign. This means that, at the frequencies wherethe real part of the effective permeability can be negative,aSRRs will now exhibit gain rather than the loss as in cases forthe passive SRR structures. Figure 7 shows the measurementresults of this circulator based aSRRdesign. Figure 7(a) showsa picture of the measurement setup for this aSRR designconfiguration and themeasured amplitude andphase spectralresponses of the circulator based aSRR designwith increasingapplied voltages to the gain element (e.g., RF amplifier) areshown in Figures 7(b) and 7(c), respectively. The amplifierhas a nominal gain of 23 dB around 10GHz. As one can seefrom the amplitude spectral responses in Figure 7(b) loss ofthe resonance feature of the SRR in the vicinity of 10GHz issignificantly reduced by the increasing gain provided by thegain element. Figure 7(c) shows the phase spectral responseswhich is corresponding to the real part of the effectivepermeability.

The circulator based aSRR design, although conceptuallythe closest to an ideal aSRR that incorporates gain, is notsuitable to be implemented as single board device. Thisis because when integrated on board, the bulky circulatordisrupts the electromagnetic field that the aSRR is designed torespond.The circulator based design does not lend itself wellto the active metamaterials implementation as the large arrayof aSRR unit cells would require large number of circulators,which are of high cost and difficult to be integrated in themetamaterials. Given this consideration, we experimented ona dual ring designwith a small footprint surfacemount ampli-fier in between. At 2.4GHz targeted operation frequency,the relative size of the surface mount RF amplifier (SE2574L,2mm × 2mm × 0.9mm) as compared to the SRR is verysmall. A picture of this design is shown as the inset picturesin Figures 8(d) and 8(e). The small footprint surface mountamplifier minimizes the impact of additional componentsand introduces minimal disturbance to the electromagneticfields surrounding the aSRRs. As a comparison, we alsofabricated the same dual ring structure except for the fact thatthere is no amplifier in between (see insets in Figures 8(b)and 8(c)). A picture of the near-field measurement setup isshown in Figure 8(a).The spectral responses are measured asthe calibrated 𝑆

21responses between twomonopole antennas

that are brought to the near-field range to the device. Themeasured results of dual ring SRR and aSRR are compared

6 Advances in OptoElectronics

VNA

Antenna number 1 Antenna number 2DUT

Port 1 Port 2

(a)

0

0.5

1

1.5

2

2.5

3

3.5

4

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5

3 8 13 18 23 28

Freq

uenc

y (G

Hz)

Radius (mm)

Ymeas = 17.129r−1.042

R2 = 0.9947

Ysimu = 17.689r−0.983

R2 = 0.9876

(b)

Figure 5: (a) Passive single SRR measurement setup. VNA: Vector Network Analyzer; DUT: Device Under Test. (b) Measured AMRfrequencies of single SRRs of different sizes as compared with the HFSS 3D simulation results. Solid curve: power law fitting for the measureddata set. Dashed curve: power law fitting for the simulated data sets. Both data sets find the curve fitting to be closely inverse proportional tothe ring radius. The measured results also agree very well with the simulated results.

Circulator Amplifier

(a)

0 0.5 1 1.5 2

0

2

4

6

Frequency (GHz)

Real partImaginary part

𝜇SR

Reff

−8

−6

−4

−2

(b)

Figure 6: Active SRR incorporating gain elements. (a) Conceptual design employing a circulator to incorporate a gain element with a singleSRR ring. Top: a circuit board realization of the circulator and amplifier circuit. (b) Effective permeability of ideal active SRR with theincorporated gain modeled as negative resistance. Solid curve: the real part of the effective relative permeability. Dashed curve: the imaginarypart.

in Figures 8(b)–8(e). With the passive dual ring SRR design,the AMR is shown around 2.4GHz in Figures 8(b) and 8(c).Figure 8(b) shows the spectral response of the amplituderesponse that characterizes the imaginary part of the relativeeffective permeability, while Figure 8(c) shows the phasespectral responses that characterize the real part of the rel-ative effective permeability. According to the spectral ampli-tude response shown in Figure 8(b), theAMR resonant loss ofthe single passive SRR is as deep as −50 dB, indicating a goodAMR resonance feature.The aSRR design, on the other hand,

uses the narrow band RF amplifier with the gain frequencymatched to around 2.4GHz and a typical RF gain of 25 dB.Figures 8(d) and 8(e) show the same near-fieldmeasurementson the aSRR with the amplifier turned on. The near-field 𝑆-parameter measurement directly correlates to the effectivepermeability of the single SRR and aSRR. The spectral phaseresponse of 𝑆

21corresponds to the real part of the relative

effective permeability and the spectral amplitude response of𝑆21corresponds to the imaginary part of the relative effective

permeability of the SRR/aSRR. It can be seen clearly that

Advances in OptoElectronics 7

(a)

0

5

10

10 10.5 11 11.5 12

Relat

ive

spec

tral i

nten

sity

(dB)

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−30

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−20

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(b)

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70

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10 10.5 11 11.5 12Re

lativ

e sp

ectra

l pha

se (

deg.

)Frequency (GHz)

−180

−130

−80

−30

(c)

Figure 7: Testing of the active SRR incorporating gain elements. (a) Testing setup for the circulator based aSRR designs. The passive SRR isconnected to the circulator and amplifier block (Figure 6(a)) via a coax cable to minimize the impact on the effective testing region of theelectromagnetic field between two probe antennas. (b) Amplitude spectral response shown as the relative spectral intensity of 𝑆

21versus the

probing frequency. (c) Phase spectral response shown as the calibrated and unwrapped phase of 𝑆21versus the probing frequency.

the imaginary part of the effective permeability due to AMRis now inversed and exhibiting gain, while the real part ofthe effective permeability due to AMR remains with thesame characteristics as the passive SRR. This result is ingood agreement with the theoretical expectation as shownin Figures 2(a) and 6(b) for the passive SRR and the activeSRR, respectively. Considering the coupling loss betweenthe radiating SRR and the monopole antenna used in themeasurement setup, the actual gain block performance isestimated to be at least 10 dB or better.These results show thatthe SRR’sAMR feature that plays critical role inmetamaterialscan be preserved while flipping the amplitude response fromloss to gain using active SRR structures. Additionally, theclose match between the responses for the passive SRRstructures and aSRR structures but with no gain also confirmsthat the small surface mount RF gain block has minimumeffects on the aSRR’s AMR responses.

5. Discussion and Conclusions

We have studied in depth the artificial magnetic responsesintroduced by the SRR in theory and through numericalsimulations, as well as experimentally. It is revealed that

the desired SRR resonances that give rise to the artificial mag-netic responses should not be confused with other radiationresonances of the SRRs, although they need to be matchedto obtain the optimized performance of the SRR-basedmetamaterials. The experimental results suggested that theactive components of the proposed aSRR need to be closelymatched to the passive SRR also.One problemencountered inthe previous investigation is that the broadband RF amplifierused with the SRR will oscillate at frequencies that are differ-ent from the desired SRR resonance. This is understandablein the sense that at the SRR resonance the radiation loss islarge for efficient reradiation SRR designs. As a result, whilethe RF amplifier gain control reduces the loss at the SRRresonance, we have not been able to reverse that loss into gain.The optimization of the single aSRR can be made, accordingto this observation, to use narrow bandwidth RF amplifiersthat only have gain around the intended SRR resonance.Thisdesign optimization requires the accurate identification ofthe SRR resonance frequencies for an optimal match and theimproved results have been demonstrated in the dual ringaSRR designs.

In conclusion, proof-of-principle investigation has shownthat the active SRR structures with incorporated gain exhibit

8 Advances in OptoElectronics

(a)

1.5 2 2.5 3 3.5Frequency (GHz)

−50

−45

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S 21

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tral

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se (d

eg.)

(e)

Figure 8: Testing of the double-ring aSRR with incorporated gain elements. (a) the near-field measurement setup; ((b) and (c)) passivering-to-ring; ((d) and (e)) with amplifier powered on.

Advances in OptoElectronics 9

significantly improved spectral amplitude responses whilepreserving their spectral phase responses.Therefore, it is verypromising for metamaterials incorporating such active SRRsto have low loss and being electrically tunable at the sametime while preserving its unusual responses similar to theirpassive counterparts.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

This research is supported by the NSF I/UCRC Center forMetamaterials from 2012 to 2014.

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