dual-band electromagnetically induced transparency effect
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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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