J. Appl. Phys. 124, 063106 (2018); https://doi.org/10.1063/1.5040734 124, 063106

© 2018 Author(s).

Dual-band electromagnetically inducedtransparency effect in a concentricallycoupled asymmetric terahertz metamaterialCite as: J. Appl. Phys. 124, 063106 (2018); https://doi.org/10.1063/1.5040734Submitted: 20 May 2018 . Accepted: 23 July 2018 . Published Online: 10 August 2018

Koijam Monika Devi , Dibakar Roy Chowdhury, Gagan Kumar, and Amarendra K. Sarma

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Dual-band electromagnetically induced transparency effectin a concentrically coupled asymmetric terahertz metamaterial

Koijam Monika Devi,1,a) Dibakar Roy Chowdhury,2 Gagan Kumar,1

and Amarendra K. Sarma1

1Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam, India2Mahindra �Ecole Centrale, Jeedimetla, Hyderabad 500043, Telangana, India

(Received 20 May 2018; accepted 23 July 2018; published online 10 August 2018)

We propose a scheme to achieve a dual-band electromagnetically induced transparency (EIT)

effect in a planar terahertz metamaterial (MM), comprising an inner circular split ring resonator

(CSRR) concentrically coupled to an outer asymmetric two-gap circular split ring resonator

(ASRR). The scheme is numerically and theoretically analyzed. The dual-band EIT effect occurs

as a result of the near field coupling between the resonant modes of the resonators comprising the

MM configuration. It is observed that the dual-band EIT effect in the MM structure could be modu-

lated with an in-plane rotation of the CSRR structure. The dual-band EIT effect is also examined

by varying the asymmetry of the ASRR and the size of the inner CSRR. A theoretical model based

upon the four-level tripod-system provides an intuitive explanation about the underlying coupling

mechanism responsible for the dual-band EIT effect in the proposed MM structure. Our study could

be significant in the development of multi-band slow light devices, narrowband absorbers, etc., in

the terahertz regime. Published by AIP Publishing. https://doi.org/10.1063/1.5040734

I. INTRODUCTION

Over the past decade, research in metamaterials (MMs)

has been gaining momentum owing to its ability in control-

ling electromagnetic waves through careful design at the

subwavelength scale.1,2 Numerous artificial structures have

been investigated3–9 extensively for the realization of nega-

tive refractive index, super lenses, optical cloaking, sensing,

etc. Recently, MM structures have also been found to mimic

the quantum phenomenon in the classical regime.10–14 One

such quantum phenomenon is the electromagnetically

induced transparency (EIT). In EIT, an atom that absorbs a

particular light signal is rendered transparent by shining

another light signal having nearly the same resonance fre-

quency.15,16 In MMs, the EIT effect usually occurs as a result

of destructive interference between a bright and a dark mode

resulting from the structural composition of the MM struc-

ture.10–12 The bright mode is directly excited by the incident

light and exhibits a much broader linewidth compared to the

dark mode which is excited either by the incident light

directly or via coupling to the bright mode.17–20 Recent stud-

ies have revealed that the EIT effect can occur not only

through electric coupling but also due to the magnetic cou-

pling21 between the bright and the dark mode in the MM

structure. Rigorous theoretical studies as well as experimen-

tal investigations have revealed its potential in various appli-

cations22–26 such as switches, sensors, slow light

modulations, etc. The EIT effect in MMs has been realized

in planar structures comprising metal strips, coupled split

ring resonators, etc. in the gigahertz27–32 as well as tera-

hertz33–37 regime. Several studies have also been reported on

the dynamic tuning of the EIT effect through the

incorporation of non-linear media or semiconductor materi-

als34–38 at the unit cell level of the MM structures. The EIT

effect has also been demonstrated by breaking the symmetry

of the resonant structures39 in the MM structures.

Recently, considerable interest has also been given to

realize the dual-band EIT effect in MMs, in which two trans-

parency windows are induced, through the careful arrange-

ments of the resonators. In MMs, the dual-band EIT effect

occurs as a result of the net coupling between the bright-

dark-dark modes or bright-bright-dark modes of the MM

structures.40–42 Due to its double tunable transparency win-

dows, the dual-band EIT phenomenon in MMs has the poten-

tial to realize multiband slow light systems, narrowband

absorbers, etc. In-spite of the significant interest, only limited

amount of work has been reported to investigate and explore

the applications of this effect. So far, very few MM configu-

rations40–45 comprising metal strips, split ring resonators

(SRR), hybrid structures, etc., have been investigated for the

realization of this effect. In the terahertz regime, the dual-

band EIT effect has been investigated in MM comprising a

central metal strip coupled to a split ring resonator (SRR)

and a two-gap SRR.40 The dual-band EIT effect and slow

light behavior have also been studied in a MM structure

comprising three coupled meta-atoms,41 for a wide range of

oblique incident angles, wherein the effect has been achieved

through the simultaneous interactions of the bright mode,

dark mode, and quasi-dark mode. In another recent study,

Xu et al.42 have demonstrated the dual-band EIT effect

through symmetry breaking in a terahertz MM structure

comprising two concentric square SRRs with their gaps

aligned parallel to each other. However, none of these previ-

ous studies have investigated the dual-band EIT effect using

asymmetric circular split ring resonators (CSRRs). As such,

there is ample scope to explore the dual-band EIT effect ina)Electronic mail: koijam@iitg.ernet.in

0021-8979/2018/124(6)/063106/7/$30.00 Published by AIP Publishing.124, 063106-1

JOURNAL OF APPLIED PHYSICS 124, 063106 (2018)

MMs, in order to achieve an effective modulation of the

transparency windows as well as to thoroughly understand

the underlying physical mechanisms causing the effect.

Therefore, more rigorous and detailed analysis using a sim-

plistic design is required to effectively control and tune the

dual-band EIT effect in MMs for the realization of its poten-

tial applications.

In this article, we examine the dual-band EIT effect in a

simple terahertz MM geometry comprising an inner CSRR

concentrically coupled to an outer asymmetric two-gap cir-

cular split ring resonator (ASRR). The dual-band EIT effect

in the proposed MM configuration occurs due to the coupling

of the resonant mode of the CSRR structure to the EIT

response of the ASRR structure. It may be noted that the

effect in the proposed MM occurs due to the coupling of two

meta-atoms (i.e., the CSRR and the ASRR), as opposed to

earlier studies41 where the effect occurs as a result of the

coupling between three meta-atoms. Although the dual-band

EIT effect has been studied earlier, the novelty of our work

lies in the modulation of the transparency windows through

the rotation of the CSRR in the proposed MM structure. The

circular structure of our proposed MM configuration pro-

vides an extra degree of freedom in controlling the dual-

band EIT effect arising in the structure. Here, we investigate

the modulation of the dual-band EIT effect by rotating the

inner CSRR in the x-y plane, in our proposed MM structure.

The dual-band EIT effect diminishes with an increase in the

rotation angle of the CSRR and finally vanishes with an

orthogonal rotation of the CSRR. The modulation of the

effect is further achieved by varying the asymmetry in the

ASRR and the size of the CSRR in the proposed metamate-

rial. A theoretical model based on a Four Level Tripod

(FLT) system clearly elucidates the coupling mechanism in

the MM structure. The design, numerical results, and the the-

oretical model are discussed in Secs. II, III and IV, respec-

tively, followed by a brief conclusion in Sec. V.

II. DESIGN OF THE METAMATERIAL STRUCTURE

The schematic diagram of the proposed asymmetric tera-

hertz MM structure is illustrated in Fig. 1. The meta-molecule

of the MM structure comprises an outer ASRR placed concen-

trically with respect to an inner CSRR. The ASRR and CSRR

structures, made of aluminium metal having a thickness of

200 nm, are placed on a silicon substrate of thickness

h¼ 10 lm, with a dielectric permittivity of 11.9. The periodic-

ity of the MM structure is taken as p¼ 80 lm. The outer

radius of the CSRR and the ASRR is denoted by r1 and r2,

respectively. “g” represents the split gaps of the ASRR and

the CSRR, while “w” represents the width of both resonators.

“h” denotes the rotation angle of the CSRR with respect to the

incident polarization, while “d” is the asymmetry parameter

of the ASRR. The parameters r2 ¼ 29 lm, g¼ 3 lm, and

w¼ 5 lm are fixed for all the numerical simulations. The

numerical simulations have been performed using the finite

difference frequency domain solver in CST Microwave

Studio. The MM structure is simulated under unit cell bound-

ary conditions in the x-y plane. An adaptive mesh size of the

order of k/10, where k is the wavelength of the incident radia-

tion, is employed. Open boundary conditions were set along

the direction of light propagation. The simulations are per-

formed for the y-polarized incident terahertz wave.

The terahertz transmission response of the CSRR struc-

ture, ASRR structure, and the coupled MM structure for the

y-polarized incident terahertz waves is shown in Figs.

2(a)–2(c). Figure 2(a) represents the transmission of the

CSRR structure at h ¼ 0� and r1 ¼ 13 lm. It is evident from

the figure that the CSRR gets excited by the linearly polar-

ized terahertz beam and has a narrow resonance dip at a fre-

quency, f¼ 0.82 THz. On the other hand, the ASRR structure

exhibits an EIT-like transmission profile having a transpar-

ency window from 0.6 THz to 0.81 THz with a transmission

FIG. 1. Schematic diagram of the concentrically coupled asymmetric tera-

hertz MM structure.

FIG. 2. Terahertz transmission profile vs. frequency for (a) CSRR with h¼ 0� and r1 ¼ 13 lm, (b) ASRR with d¼ 12 lm, and (c) the coupled MM

configuration for fixed values of h ¼ 0�, d¼ 12 lm and r1 ¼ 13 lm. Electric

field profiles of (d) the CSRR structures at the resonance frequency, (e) the

ASRR structures at the transmission peak, and (f) the dual-band EIT MM

structure at the transmission dip D2. The green arrow signifies the direction

of incident polarization.

063106-2 Devi et al. J. Appl. Phys. 124, 063106 (2018)

peak frequency, f¼ 0.62 THz. The transmission profile for the

ASRR structures with d¼ 12 lm is shown in Fig. 2(b). When

the CSRR is placed concentrically to the ASRR structure, the

single transparency window of the ASRR structure splits into

two transparency windows with the first transparency window

ranging from 0.59 THz to 0.75 THz and the second transpar-

ency window ranging from 0.82 THz to 0.93 THz. This

dual-band EIT effect occurs due to the coupling of the CSRR

resonances to the EIT effect of the ASRR structures in the

coupled MM structure. The terahertz transmission response of

the MM for h ¼ 0�, d¼ 12lm and r1 ¼ 13 lm is represented

by the green solid line in Fig. 2(c). To further understand the

coupling behavior leading to the dual-band EIT effect, we

also observe the electric field profiles of the structural compo-

nents of the MM structure. Figures 2(d)–2(f) represent the

electric field profiles of the CSRR, the ASRR, and the coupled

MM structure, respectively. Figure 2(d) describes the electric

field profile for the CSRR structures, at the resonance fre-

quency, when its gap is parallel to the direction of the incident

polarization. We may note from the figure that the electric

field in the CSRR structure is strongly confined to its gap for

this configuration, which indicates the excitation of an LC res-

onance in the CSRR structure. The ASRR structure exhibits a

single transparency EIT-like effect due to the coupling of the

resonances arising from the two arms of the ASRR.39 The

electric field profile of the ASRR structures at the transmission

peak is shown in Fig. 2(e). When the resonant mode of the

CSRR is made to couple with the EIT effect of the ASRR, a

transmission dip D2 arises within the transparency window.

Hence, a dual-band EIT effect is achieved in the coupled MM

structure. The electric field profile for the corresponding struc-

ture at the transmission dip D2 (i.e., f¼ 0.79 THz) is shown in

Fig. 2(f).

III. MODULATING THE DUAL-BAND EIT EFFECT

The transmission characteristics of the proposed MM

are studied for different rotation angles of the CSRR with

respect to the incident polarization. Figure 3(a) represents

the dual-band EIT of the proposed MM for a fixed

r1¼ 13 lm and d¼ 12 lm by varying h from 0� to 90�. The

red solid line represents the transmission of the MM struc-

ture when h ¼ 0�. The green line represents transmission for

h¼ 20�, while the blue traces signify the transmission for

h¼ 40�. The cyan and the orange traces represent the trans-

mission of the MM structure for h ¼ 60� and h ¼ 90�,respectively. It is clearly evident from the figure that the

dual-band EIT effect is most prominent for h ¼ 0�. The dual-

band EIT effect diminishes as the inner CSRR is rotated with

respect to incident polarization. When h ¼ 90�, the dual-

band EIT effect vanishes in the MM structure. Hence, one

can switch the dual-band EIT effect to a single EIT effect in

the coupled MM structure. Modulation of the effect is further

achieved by gradually varying the asymmetry of the ASRR,

“d” from 0 lm to 16 lm in the MM structure. The transmis-

sion characteristics of the MM structure for different values

of “d” with a fixed h ¼ 0� and r1 ¼ 13 lm are shown in Fig.

3(b). The orange solid line represents the transmission for

d¼ 0 lm. The cyan traces signify the transmission for

d¼ 4 lm. The blue and the green traces represent the trans-

mission of the MM structure for d¼ 8 lm and d¼ 12 lm,

respectively. The red line represents the transmission of the

MM structure when d¼ 16 lm. It is clearly observed from

the figure that a single EIT effect occurs when the asymme-

try parameter, d¼ 0 lm. However, the single EIT effect in

the MM structure evolves into a dual-band EIT effect with

the introduction of asymmetry (i.e., d> 0 lm). The dual-

band EIT effect is further tuned by increasing the asymmetry

of the ASRR in the proposed MM structure.

In order to get insight into the dual-band EIT effect in

the MM structure, we study the electric field profiles for vari-

ous rotation angles and asymmetry parameters. Figures

4(a)–4(c) represent the electric field profiles of the MM

geometry at the transmission peak P2 of the second transpar-

ency window for h ¼ 0�, 40�, and 90�, with r1 ¼ 13 lm and

d¼ 12 lm fixed. It is evident from Fig. 4(a) that the CSRR is

excited by the incident terahertz radiation when h ¼ 0�. In

this case, the gap of the CSRR is parallel to the direction of

the incident polarization resulting in an LC resonance dip at

f¼ 0.82 THz [see Fig. 2(a)]. The coupled MM structure

exhibits a dual-band EIT effect for this configuration, due to

the coupling of the resonant modes of the CSRR and the

ASRR structures. However, as we rotate the CSRR with

respect to incident polarization, the near field coupling

behavior of the MM structure is modified. The electric field

FIG. 3. Terahertz transmission vs. frequency for (a) different values of rota-

tion angle h and (b) different values of the asymmetry parameter d of the

proposed MM geometry.

063106-3 Devi et al. J. Appl. Phys. 124, 063106 (2018)

profile for h ¼ 40� is shown in Fig. 4(b). The CSRR is

weakly excited by the incident terahertz radiation which

results in the diminishing of the dual-band EIT effect in the

MM structure. Finally, for h¼ 90�, i.e., when the gap of the

CSRR is perpendicular to the incident polarization, the LC

resonance in the CSRR is no longer excited. With this right-

angled rotation, an on-to-off resonance of the CSRR is

created in the MM structure. For this configuration, the dual-

band EIT effect reduces to a single EIT effect in the coupled

MM structure. The electric field profile for the corresponding

MM configuration is shown in Fig. 4(c). Hence, an efficient

tuning of the dual band EIT effect is achieved as a result of

this on-to-off resonance of the CSRR. Figures 4(d)–4(f) rep-

resent the electric field profiles of the MM structure at the

transmission peak P1 of the first transparency window for

d¼ 0 lm, 8 lm, and 16 lm with a fixed value of r1¼ 13 lm

and h¼ 0�. The electric field profile, at P1, corresponding to

d¼ 0 lm is shown in Fig. 4(d). For d¼ 0 lm, the outer

ASRR is a symmetric two-gap split ring resonator (SRR). It

is evident from the figure that the symmetric two-gap SRR is

excited by the incident electric field. The symmetric two-gap

SRR has broad dipolar resonance39 at a frequency close to

that of the CSRR. This dipolar resonance of the symmetric

two-gap SRR, when coupled to the LC resonance of the

CSRR, generates a transparency window leading to a single

transparency EIT effect in the coupled MM structure. By

introducing an asymmetry into the symmetric two-gap SRR,

which then becomes the ASRR, the dual-band EIT effect can

be realized in the coupled MM structure. The symmetry

breaking in the MM structure causes a difference in the reso-

nance frequencies of the two metallic arms giving rise to an

EIT response for the ASRR structures. Figure 4(e) represents

the electric field profile corresponding to d¼ 8 lm. In this

case, the ASRR structures exhibit an EIT like response due

to the breaking of symmetry in the resonant mode.

Consequently, the coupling of the ASRR with the CSRR

structure leads to the realization of a dual-band EIT effect in

the coupled MM structure. The effect can be further tuned

by increasing the asymmetry of the ASRR structure. The

electric field profile corresponding to d¼ 16 lm is shown in

Fig. 4(f). It is observed that the dual-band EIT effect in the

coupled MM structure is most pronounced for this configura-

tion. Therefore, an effective tuning of the dual-band EIT

effect is achieved in the MM structure.

Further modulation of the dual-band EIT effect in the

proposed MM structure is achieved by varying the size of

the inner CSRR, “r1” from 12.5 lm to 14 lm. The terahertz

transmission profile for different values of r1 with a fixed

h¼ 0� and d¼ 12 lm is shown in Fig. 5. The cyan solid line

represents the transmission of the MM structure when

r1¼ 12.5 lm. The blue line represents transmission for

r1¼ 13 lm, while the green traces signify the transmission

for r1¼ 13.5 lm. The red traces represent the transmission of

the MM structure when r1¼ 14 lm. When r1¼ 12.5 lm, the

resonance dip of the individual CSRR structure occurs at

f¼ 0.85 THz. As r1 is increased gradually, the resonance fre-

quency of the inner CSRR decreases steadily reaching a

value of 0.76 THz when r1¼ 14 lm. Hence, the dip D2 in the

dual-band EIT effect experiences a red shift with the increase

in r1 in the MM configuration, resulting in the red shifting of

the second transparency region as well. This further adds

another degree of freedom to the tuning capability of the

dual-band EIT effect in the proposed MM structure.

IV. ANALYTICAL MODEL BASED ON THEFOUR-LEVEL TRIPOD (FLT) SYSTEM

In order to validate our numerical findings and to better

understand the dual-band EIT effect in the MM structure, a

FIG. 4. Electric field profile of the MM structure at P2 for different rotation

parameters, i.e., (a) h ¼ 0�, (b) h ¼ 40�, and (d) h ¼ 90� for a fixed value of

r1 ¼ 13 lm and d¼ 12 lm. Electric field profile of the MM structure at P1

for different asymmetry parameters i.e., (d) d¼ 0 lm, (e) d¼ 8 lm, and (f)

d¼ 16 lm for a fixed value of r1 ¼ 13 lm and h ¼ 0�. The incident electric

field is along the direction of the green arrow.

FIG. 5. Terahertz transmission vs. frequency for different values of r1 with a

fixed h ¼ 0� and d¼ 12 lm.

063106-4 Devi et al. J. Appl. Phys. 124, 063106 (2018)

four-level tripod (FLT)-system is employed.42,46 The energy

level diagram for the FLT-system is illustrated in Fig. 6. In

the system, the transition between j1i ! j4i, driven by the

Rabi frequency, Xp is termed as the probe/dark transition,

while the transition between j2i ! j4i, driven by the Rabi

frequency, Xc is termed as the coupling/bright transition.

The levels j1i; j2i, and j4i constitute a K-system exhibiting

an EIT effect as a result of the destructive interference

between the excitation pathways j1i ! j4i and

j1i ! j4i ! j2i ! j4i. With the introduction of another

dark/control state j3i, this K-system evolves into an FLT-

system, exhibiting a dual-band EIT effect. This is because

the destructive interference has changed into a constructive

interference between the EIT effect of the K-system and the

dark/control state. In our proposed MM structure, the outer

symmetric two-gap SRR (corresponding to d¼ 0 lm)

behaves as the bright state with a broad dipolar resonance.

One dark state is introduced by breaking the symmetry in the

outer symmetric SRR (corresponding to d> 0 lm), as a

result of which, the outer ASRR represents a K-system.

Another dark state is introduced by placing the inner CSRR

concentrically to the ASRR in the MM structure. The cou-

pling between the ASRR and the CSRR structure leads to the

evolution of the proposed MM structure into an analog of the

FLT-system.

The equation of motion of the FLT-system could be

expressed as follows:

dq21

dt¼ � c21 � iðdp � dcÞ

� �q21 þ

i

2X�cq41;

dq31

dt¼ � c31 � iðdp � dc0 Þ

� �q31 þ

i

2X�c0q41;

dq41

dt¼ � c41 � idp½ �q41 þ

i

2ðXp þ Xcq21 þ Xc0q31Þ;

(1)

where qj1 is the off-diagonal density matrix element for the

transition jji ! j1i ðjji ¼ j2i; j3i; j4iÞ and cj1 (j¼ 2, 3, 4) is

the decay rates for the transition from jji ! j1i. The corre-

sponding frequency detunings are defined as dp¼xp � x41,

dc¼xc � x21, and dc0 ¼ xc0 � x31, where x21, x31, and x41

denote the energy-level transition frequencies. x is the inci-

dent frequency and xp, xc, and xc0 are, respectively, the res-

onant frequencies of the probe, the coupling, and the control

fields. For a steady state, Eq. (1) reduces to

q21 ¼iX�cq41

2 c21 � iðdp � dcÞ� � ;

q31 ¼iX�c0q41

2 c31 � iðdp � dc0 Þ� � ;

q41 ¼iðXp þ Xcq21 þ Xc0q31Þ

2 c41 � idp½ �:

(2)

Then from Eq. (2), one can obtain the exact solution of

q41 as

q41 ¼�Xp

2iðc41 � idpÞ �jXcj2

2ðic21 þ dp � dcÞ� jXc0 j2

2ðic31 þ dp � dc0 Þ

" # : (3)

The transmission amplitude for the FLT-system is given by the expression, t(x)¼ 1 � Im(q41) as

tðxÞ ¼ 1� ImXp

jXcj2

2 ic21 þ dp � dc½ �þ jXc0 j2

2 ic31 þ dp � dc0½ �� 2iðc41 � idpÞ

0B@

1CA: (4)

Using the expression given by Eq. (4) and through care-

fully tuning the Rabi frequencies and the decay rates of each

transition, we can obtain a theoretical fit of the numerically

simulated transmission. The theoretically fitted transmission

for the FLT-system, shown in Fig. 7, is in good agreement

with our numerical results represented in Fig. 3. When

d> 0 lm, the ASRR structure behaves as an analog of a K-

system. In this case, the rotation of the CSRR structure acts

as the dark/control field giving rise to the dual-band EIT

effect in the FLT-system. This control field evolves due to

the in-plane rotation of the CSRR in the MM structure which

in turn modifies the coupling behavior in the FLT-system.

This results in the diminishing of the dual-band EIT-like

effect in the MM structure. Finally, for an orthogonal rota-

tion of the CSRR, the dual-band EIT effect reduces into a

single EIT effect [as represented by the orange line in Fig. 7(a)]

FIG. 6. Energy level diagram of the FLT-system driven by three light fields

Xp, Xc, and Xc0 with the corresponding frequency detunings dp, dc, and dc0 ,

respectively.

063106-5 Devi et al. J. Appl. Phys. 124, 063106 (2018)

in our proposed MM. For this configuration, the FLT-system

behaves as if the dark/control state is absent, reducing to a K-

system. On the other hand, the K-system evolves into a FLT-

system when the asymmetry in the ASRR is varied. The asym-

metry parameter, in this case, acts as the dark/control state of

the FLT-system. Figure 7(b) represents the transmission for dif-

ferent values of the asymmetry parameter with fixed values of

h and r1. When d¼ 0 lm, the ASRR coupled to the CSRR

structure acts as the K-system. When the asymmetry is intro-

duced into the ASRR structure, this K-system evolves into the

FLT-system. With the help of these two control parameters, an

effective tuning of the dual-band EIT effect is achieved in the

proposed MM structure.

V. CONCLUSION

The dual-band EIT effect in a terahertz metamaterial

(MM) comprising an inner circular split ring resonator

(CSRR) concentrically coupled to an outer asymmetric

two-gap split ring resonator (ASRR) is numerically and

theoretically analyzed. The proposed MM structure exhib-

its the effect as a result of coupling between the resonant

mode of the CSRR and the EIT response of the ASRR.

The coupling behavior in the MM is modified through an

in-plane rotation of the CSRR structures. A gradual

orthogonal rotation of the CSRR leads to the vanishing of

the dual-band EIT effect in the MM. Modulation of the

effect is further achieved by gradually varying the asym-

metry of the outer ASRR as well as the size of the inner

CSRR. A theoretical model based on a Four Level Tripod

system intuitively explains the coupling behavior in the

proposed MM geometry. Our study may be significant in

realizing multi-band slow light devices, narrowband

absorbers, switches, etc. in the terahertz regime.

ACKNOWLEDGMENTS

G.K. gratefully acknowledges the financial support from

the Board of Research in Nuclear Sciences (BRNS), India

(No. 34/20/17/2015/BRNS). D.R.C. gratefully acknowledges

the financial support from the SERB, Department of Science

and Technology, India (No. EMR/2015/001339). K.M.D.

would like to thank MHRD, Government of India for a

research fellowship.

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