plasmon induced transparency effect through alternately

Plasmon induced transparency effect throughalternately coupled resonators in terahertzmetamaterialKOIJAM MONIKA DEVI,1,*AMARENDRA K. SARMA,1 DIBAKAR ROYCHOWDHURY,2 AND GAGAN KUMAR1

1Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam, India2Mahindra École Centrale, Jeedimetla, Hyderabad 500043, Telangana, India*[email protected]

Abstract: We analyze plasmon induced transparency (PIT) in a planar terahertz metamaterialcomprising of two C-shaped resonators and a cut-wire. The two C-shaped resonators are placedalternately on both sides of the cut-wire such that it exhibits a PIT effect when coupled withthe cut wire. We have further shown that the PIT window is modulated by displacing the C-shaped resonators w.r.t. the cut-wire. A lumped element equivalent circuit model is reported toexplain the numerical observations for different coupling configurations. The PIT effect is furtherexplored in a metamaterial comprising of a cross like structure and four C-shaped resonators.For this configuration, the PIT effect is studied for the incident light polarized in both x and ydirections. It is observed that such a structure exhibits equally strong PIT effects for both theincident polarizations, indicating a polarization independent response to the incident terahertzradiation. Our study could be significant in the development of slow light devices and polarizationindependent sensing applications.

c© 2017 Optical Society of America

OCIS codes: (160.3918) Metamaterials; (250.5403) Plasmonics.

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Vol. 25, No. 9 | 1 May 2017 | OPTICS EXPRESS 10484

#286009 https://doi.org/10.1364/OE.25.010484 Journal © 2017 Received 2 Feb 2017; revised 17 Mar 2017; accepted 29 Mar 2017; published 27 Apr 2017

Corrected: 28 April 2017

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1. Introduction

Metamaterials are artificial engineered materials having unusual electromagnetic properties [1–3].Research in metamaterials has been gaining momentum over the past decade, owing to its abilityin controlling electromagnetic wave properties through careful design [4] at the sub-wavelengthscale. Numerous structures such as planar resonators [5, 6], multi-layered structure [7, 8], holearrays [9, 10], etc. have been studied extensively for various applications. In 2008, a novel studydone by Zhang and his co-workers revealed that an electromagnetically induced transparency(EIT) like phenomenon can occur in plasmonic metamaterials [11]. EIT is a quantum interferencephenomenon occurring in a three level atomic system. In EIT, an atom that absorbs a particularlight is rendered transparent by shining another light having the same resonance frequency[12, 13]. The plasmonic analogue of this EIT effect is known as plasmon induced transparency(PIT) effect in metamaterials [11, 12, 14]. PIT usually occurs as a result of interference betweena bright and a dark mode. The bright mode strongly couples with the incident light while thedark mode couples weakly to the incident light [11, 15–18]. Both the modes should have similarresonant frequencies with a very little deviation. In such a situation, the destructive interferenceof these modes induce a narrow transparency region in the otherwise absorptive spectrum. Withinthis region all the incident radiation gets transmitted through the medium and the dispersiveproperties of the medium gets strongly modified.

The PIT effect has been realized in a variety of metamaterial configurations. The planarmetamaterial configurations such as metal strips and coupled split ring resonators have beenreported to exhibit PIT effect in gigahertz as well as terahertz regime [19–22]. Active control andtuning the transparency window as well as its slow slight properties have also been explored overthe recent years [19, 23–25]. The PIT study has also been extended to different materials andexploring their capability in producing such effect. The materials such as silicon and graphenehave been found to exhibit interesting PIT properties too [21,22,26–28]. The research activities inthis area are strongly motivated by the fact that it can lead to the development of sensing [29–33]and slow light devices at room temperature [34–37]. The experimental investigations in thisarea have been supported by the well-defined theories such as equivalent circuit [12, 38] andcoupled Lorentz oscillator models [11, 19, 23]. In exploring PIT, the studies largely have focusedto examine this effect for a specific polarization of the incident light for which the effect isprominent. As we switch to the different polarization, the effect becomes either weaker orcompletely vanishes. In this context, strategically designed structures in metamaterials havebeen recently examined that are found to exhibit polarization independent PIT response [39, 40].Further, the research in this area is motivated for the development of more simplistic designsexplaining the effect.

In this article, we analyze a coupled resonator comprising of two C-shaped (2C) resonatorsand a cut-wire (CW) like structure. The PIT in the proposed model occurs due to the destructiveinterference between the cut-wire (CW) and the two C-shaped resonators. Although, the displace-ment of the C-shaped resonators in the y-direction has been studied in earlier works [41, 42], thenovelty of our work stems from the investigation of the coupling mechanism in the x-directionwhich was earlier overlooked. When the C-shaped resonators are displaced in the y-direction,the dark mode excitation in the PIT metamaterial is achieved through both electric and magneticfields of the CW. As the C-shaped resonator pair is translated along the CW starting from thebottom, the coupling mechanism switches from being capacitive in nature via the electric field tobeing inductive via the magnetic field of the CW [41]. However, the dark mode is excited onlythrough the electric field of the CW as the C-shaped resonators are translated in the x-direction,resulting in a capacitive coupling between the C-shaped resonator pair and the CW. It is observed


that the transparency window can be broadened by increasing the coupling between the CW andthe two C resonators. A simple lumped element equivalent circuit model using coupled oscilla-tor theory is described to confirm the numerical observations. The PIT effect in the proposedgeometry occurs only when the incident polarization is parallel to the longitudinal direction ofthe CW. This may limit the use of PIT effect for development of sensing applications. In orderto overcome this, we introduce two C and a CW structure in the perpendicular orientation inour metamaterial geometry so that the new meta-molecule consists of a cross wire and four C(4C) resonators. In order to establish the polarization independent response, we examine PITeffect from this new meta-molecule for the x and y polarized incident radiation. This paper isorganized as follows: First we discuss the design and numerical simulations of the PIT withalternately placed C-shaped structures w.r.t. the cut wire. Next, we discuss theoretical modelthat is used to explain our numerical observations. The polarization independent response of theproposed metamaterial is examined in the subsequent section. The results are summarized in theconclusion section.

2. Plasmon induced transparency: Geometry and numerical simulations

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h

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g

a

wd

a

xy

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(a) (b)

Fig. 1. (a) Schematic diagram of the planar metamaterial geometry comprising of a cut-wireand two C shaped resonators. (b) Transmission Plot for CW, 2C and the PIT effect for they-polarized incident light.

The meta-molecule of the proposed structure comprises of a CW and two C shaped resonatorsand is designed in a way that they can exhibit PIT effect with CW as the bright resonator. Theschematic diagram of the proposed metamaterial geometry is shown in Fig. 1(a). In the proposedgeometry, the quantity ′L′ represents the length of the CW, ′a′ represents the dimension ofeach of the C shaped resonator, ′w′ denotes the width of the CW as well as the C resonatorsand ′g′stands for the gap of the C shaped resonators. The periodicity of the meta-molecule isdenoted by ′p′ and is taken to be 140 µm in our simulations. For our simulations, we have takenL = 84 µm, a = 35 µm, w = 4 µm and g = 27 µm. The distance ′d′ between the CW and the 2Cstructures is varied in our numerical simulations to examine modulation response of PIT effect.The CW and the 2C are assumed to be made up of aluminium having thickness, t = 200 nmon a quartz substrate of thickness, h = 25 µm, with a relative permittivity ε r = 3.75. It may benoted that in the simulation model, we have considered dc conductivity to model aluminium.The numerical simulations are performed using the technique of finite element frequency domainsolver in CST Microwave Studio. The metamaterial geometry is simulated under the unit cell


boundary conditions in the x-y plane. We set open boundary conditions along the direction oflight propagation and chose a mesh size of the order of λ/10, where λ is the wavelength of theincident radiation. The simulation is performed for the y linearly polarized light under the normalincidence.

Max

Min

f = 1 THz f = 1 THzf = 1 THz

y

x

y

x

y

x

(b) (a) (c)

Fig. 2. Electric field profiles of (a) the CW structures, (b) the 2C structures and (c) theproposed PIT metamaterial. The green arrow signifies the direction of electric field ofincident polarization.

Figure 1(b) shows the terahertz transmission response through the proposed metamaterialconfiguration for the y- polarized incident terahertz radiation. The blue traces represent the brightmode while the red traces represent the dark mode. The green traces signify the PIT effect fromthe proposed terahertz metamaterial geometry. It may be noted that the array of CWs exhibit atypical localized surface plasmon resonance at f = 1.0 THz while the two C structures supportan LC resonance at the same frequency. It may be noted that the CWs couple directly to theincident light and has a deep transmission dip and broad spectral response. On the other hand, the2 C structures result in a weakly coupled response to the incident terahertz beam. The resonancesfrom the CWs and 2 C structures behave like a bright mode and dark mode respectively. Theinterference of these two modes induces a narrow transparency window in the transmissionspectrum represented by green traces in the figure. In order to further understand the brightand dark modes as well as the PIT effect, we observe the induced electric field profiles in thetransparency region i.e. at 1.0 THz. The results are shown in Fig. 2. We may note that the CWstructure gets directly excited by the incident light resulting in a bright mode (Fig. 2(a)), while

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Fig. 3. Transmission versus frequency for different distances ′d′ of the proposed terahertzmetamaterials geometry exhibiting PIT effect. A decrease in the distance ′d′ results in thebroadening of the transparency window.


the 2 C shaped resonators are excited indirectly via coupling of the CW resonance resulting indark mode (Fig. 2(b)). When these two modes are allowed to couple with each other, a narrowtransparency window is induced due to the destructive interference of the modes (Fig. 2(c)). Inthis transparency window, the imaginary part of the field becomes negligible and the structurebecomes highly dispersive. This results in the significant reduction of the velocity of the incidentlight [11].

Next, we examine the displacement of C-shaped resonators w.r.t. the CW which is responsiblefor a coupling between the resonator and hence a modulation of transparency window is possible.This modulation is done by varying distance ′d′ from 2 µm to 20 µm. The results of transmissionfor different values of ′d′ are shown in Fig. 3. The red traces represent the PIT effect ford = 2 µm of the PIT metamaterial geometry which causes strong coupling between the CW and2C resonators. The green, blue and cyan traces represent the PIT effect for d = 5 µm, d = 10 µmand d = 15 µm respectively. The orange traces represent the case of d = 20 µm and contributeto the weakest coupling. It is evident that the PIT window gets narrower as we increase distance′d′. The narrowing of the PIT window occurs due to a reduction in the coupling of CW with theC-shaped resonators. Such a behavior indicates that the PIT effect can be modulated efficientlyby varying the coupling between the bright and the dark modes.

3. Semi-analytical model elaborating PIT effect

L

C1

L2

C 2C c

V(t) ~

1

R1 R 2

Fig. 4. An equivalent circuit model for the proposed PIT metamaterial shown in Fig. 1(a).

In order to elucidate our numerical findings on plasmon induced transparency as observed inthis work, we use an equivalent RLC circuit model which is shown in Fig. 4. In the model, theleft hand loop consisting of R1, L1, C1 and the right hand loop consisting of R2, L2, C2 forms aresonant circuit having resonance at f = 1.0 THz. The left hand loop represents the bright modeor the CW resonator, while the dark or 2 C resonator is represented by the right hand loop. Thecapacitance Cc in the circuit accounts for the coupling between the bright and the dark modes.The incident terahertz field is represented by V (t) in the model. The bright mode is directlyexcited by the incident terahertz radiation while the dark mode is excited through coupling withthe bright mode. For currents, say i1 and i2 flowing through the left and the right hand loop, thenfollowing the standard circuit analysis [2, 38], one may write(

i1i2

)=

− jωL1 + R1 + 1− jωC1

1− jωCc

1− jωCc

− jωL2 + R2 + 1− jωC2

−1 (V0

). (1)

Equation (1) can be transformed into the transmission parameter t(ω) using the standardparameters conversion formula [43]. This gives the transmission coefficient t(ω) ,

t(ω) =2Z21√

R01R02

(Z11 + Z01)(Z22 + Z02) − Z12 Z21, (2)


where Z01 and Z02 are the source and the load impedances of a general two port system. R01 andR02 are the real parts of Z01 and Z02.

Using this semi analytical approach, we calculate transmission results corresponding to aspecific set of parameters that we used in our numerical simulations of the PIT effect. Thetransmission is calculated for different values of ′d′ which causes a varying coupling betweenthe CW and the two C-shaped resonators as discussed above. The results are depicted in Fig. 5. Itis worthwhile to mention that the provided circuit model uses a capacitive coupling, representedby Cc , to explain the PIT response in the proposed metamaterial structure. This coupling couldbe modulated by varying the value of the capacitance Cc used in the model. As such, this modelcan be used to predict the near field coupling in metamaterial systems where capacitive couplingis dominant. Hence, we may observe the modulation of the transparency window by varyingthe value of Cc (Fig. 5). It is evident that the results from semi-analytical approach are in goodagreement with the numerical observations of Fig. 3.

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2 �m

20 �m15 �m

5 �m10 �m

Fig. 5. Transmission plot for the proposed metamaterial structure obtained using the semi-analytical model.

4. Polarization independent plasmon induced transparency

In the metamaterials configuration proposed above, the PIT effect occurs only when the incidentpolarization is parallel to the longitudinal direction of the CW. However, for certain applica-tions, a polarization independent response may be desirable. In order to achieve a polarizationindependent PIT effect, we introduce two more C and one CW structure in the above designin perpendicular orientation. The schematic of this new meta-molecule now comprising of across and four C resonators is shown in Fig. 6 along with the transmission results. We studytransmission through this new design for the x and y linearly polarized lights so as to elucidateour impression of polarization independent response. We observe that the design exhibits equallystrong PIT effect for both the polarizations which is explained through several steps in Figs.6(a)-(f). In the figure, green arrow indicates the direction of incident polarization. The red tracessignify the transmission for x-polarized light while the blue traces represent the transmissionfor the y-polarized light. The transmission for the cross structure is shown in Figs. 6(a) and 6(b)while the transmission for the four C structures is represented by Figs. 6(c) and 6(d). The crossstructures show a typical localized surface plasmon resonance at f = 1.0 THz while the 4Csupports an LC resonance at the same frequency i.e. f = 1.0 THz. It is clearly observed fromthe Figs. 6(a)-(d) that the cross structure has a broader and deeper transmission dip than that


of the 4C structures. The resonance from the cross structure is believed to be a bright mode,however the resonance from the C shaped structures is called a dark mode. When these twomodes are allowed to couple with each other, a narrow transparency window is induced dueto the destructive interference of the modes. Fig. 6(e) and 6(f) represents the PIT effect of theproposed geometry for both the x and y-linearly polarized lights. We notice an equally strongPIT effect for both the incident polarizations which indicates a polarization independent responseof the proposed geometry.

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on

(a)

Fig. 6. Terahertz transmission through CW structure for the (a) x-polarized and (b) y-polarized incident terahertz. The green arrow indicates the direction of electric field polar-ization of incident light. (c) and (d) represent the terahertz transmission for the 4C structurefor the two polarizations. (e) and (f) correspond to the PIT effect for both the polarizations.The inset in the figures show the corresponding metamaterials geometry.

Further, we examine the induced electric field profiles for the cross structure, the 4C structureand the PIT metamaterial independently (Fig. 7). The incident polarization is parallel to thedirection of the green arrow in the figure. Figure 7(a) and 7(b) represent the electric field profilesof the cross structure at f = 1.0 THz, for x and y linearly polarized incident light respectively.Figure 7(c) and 7(d) represent the electric field profiles of the 4C structure at f = 1.0 THz, forthe x and y linearly polarized incident lights respectively. It may be noted that for each of theincident polarizations, only the cut wire of the cross structure that is parallel to the incidentlight is excited, while for the C-shaped resonators whose gap is perpendicular to the incidentpolarization direction does not get excited in case of 4C structure. When the modes from theseexcitations are allowed to couple with each other, a narrow transparency window is induceddue to the destructive interference of the modes. Figure 7(e) and 7(f) represent the electric fieldprofiles of the PIT effect corresponding to this metamaterial geometry at the PIT transmissionpeak frequency of f = 1.0 THz.

Finally, we explore the possibility of modulating the PIT window through this proposedterahertz metamaterial configuration. For doing so, we examine the polarization independent PITresponse for different values of ′d′ for both x and y-linearly polarized incident terahertz light. Achange in the value of ′d′ results in the diagonal shifting of C-shaped resonators w.r.t. the crosswire. The results are shown in Fig. 8. Figure 8(a) represents the transmission for the x-polarizedincident light while the transmission response for the y-polarized light is shown in Fig. 8(b).It is evident from the figure that the PIT effect is equally strong for both the x- and y-incident


y y

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f = 1.0 THz f = 1.0 THzf = 1.0 THz

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f = 1.0 THz f = 1.0 THz f = 1.0 THz

y

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y

x

Fig. 7. Absolute value of electric field profile for cross structure for (a) x-polarized and(b) y-polarized light at the resonance frequency f = 1.0 THz. Electric field profile for 4Cstructure for (c) x-polarized and (d) y-polarized light at the resonance frequency f = 1.0THz. Electric field profile for the PIT metamaterial structure at the PIT dip for the x-polarizedand y-polarized light are depicted in (e) and (f). The incident electric field is parallel to thedirection of the green arrow.

polarizations. It may be further observed that the transparency window can be modulated bychanging the coupling between the cross wire and the C shaped structure through the variation of′d′ . The traces in different colors in the figure represent the transmission response for differentvalues of ′d′ as labeled in the figure itself. The red traces for d = 2 µm show the widest, whileorange trances for d = 20 µm depict the narrowest transparency window. A reduction in thetransparency window observed is due to the decrease in coupling as ′d′ increases. The efficientmodulation of the PIT window suggests the prospect of developing devices operating withinthe broad transparency region in terahertz domain. Also, the polarization independent behaviorcould be significant in the improvement of sensing devices.

0.0

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sion

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(a) (b)

2 �m

20 �m15 �m

5 �m10 �m

2 �m

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5 �m10 �m

Fig. 8. Transmission for a metamaterial comprising of a cross and 4C resonators: (a) x-polarized light and (b) y-polarized light for different values of ′d′.


5. Conclusions

We have numerically and theoretically analyzed coupled terahertz metamaterials comprising oftwo C-shaped resonators and a cut-wire (CW) structure. The PIT in the proposed configurationoccurs due to the destructive interference of the resonances from the cut-wire (CW) and thetwo C-shaped resonators. It is observed that the transparency window can be broadened byincreasing the coupling between the CW and 2C structures. A simple equivalent circuit modelusing coupled oscillator theory is described to validate our numerical observations. We extendour analysis to the terahertz metamaterials configuration that comprises of a cross wire andfour C-shaped (4C) resonators in order to achieve polarization independent response. ThereforePIT response of this geometry is examined for the two orthogonal polarizations of the incidentterahertz beam. The identical transmission response indicates a polarization independent PITbehavior. In this geometry, the transparency window is modulated by displacing the C-shapedresonators diagonally w.r.t. the cross-wire. As the resonators are displaced away from the crosswire, the transparency window gets narrower due to a decrease in the coupling strength. Theproposed study could be significant in the realization of terahertz devices such as tunable switches,modulators and slow light systems.

Funding

SERB,Department of Science and Technology, India (SB/FTP/PS-051/2014); SERB, Departmentof Science and Technology, India (EMR/2015/001339); DST,Government of India (Grant No.SB/FTP/PS-047/2013); CSIR, India [03(1252)/12/EMR-II].

Acknowledgments

The author, GK gratefully acknowledges the financial support from the SERB, Departmentof Science and Technology, India (SB/FTP/PS-051/2014). Author DRC gratefully acknowl-edges the financial support from the SERB, Department of Science and Technology, India(EMR/2015/001339). Author AKS would like to acknowledge the financial support fromDST,Government of India (Grant No. SB/FTP/PS-047/2013) and CSIR, India [03(1252)/12/EMR-II]. Author KMD would like to thank MHRD, Government of India for a research fellowship.


plasmon induced transparency effect through alternately

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