Download Polarization-Independent Metamaterial Analog of

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 10, OCTOBER 2012
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Polarization-Independent Metamaterial Analog of
Electromagnetically Induced Transparency
for a Refractive-Index-Based Sensor
Fan-Yi Meng, Member, IEEE, Qun Wu, Senior Member, IEEE, Daniel Erni, Member, IEEE,
Ke Wu, Fellow, IEEE, and Jong-Chul Lee, Senior Member, IEEE
Abstract—A polarization-independent metamaterial analog of
electromagnetically induced transparency (EIT) at microwave
frequencies for normal incidence and linearly polarized waves is
experimentally and numerically demonstrated. The metamaterial
consists of coupled “bright” split-ring resonators (SRRs) and
“dark” spiral resonators (SRs) with virtually equal resonance
frequencies. Normally incident plane waves with linear polarization strongly couple to the SRR, but are weakly interacting with
the SR, regardless of the polarization state. A sharp transmission
peak (i.e., the transparency window) with narrow spectral width
and slow wave property is observed for the metamaterial at the
resonant frequency of both, the bright SRR and the dark SR.
The influence of the coupling strength between the SRR and SR
on the frequency, width, magnitude, and quality factor of the
metamaterial’s transparency window is theoretically predicted by
a two-particle model, and numerically validated using full-wave
electromagnetic simulation. In addition, it is numerically demonstrated that the EIT-like metamaterial can be employed as a
refractive-index-based sensor with a sensitivity of 77.25 mm/RIU,
which means that the resonance wavelength of the sensor shifts
77.25 mm per unit change of refractive index of the surrounding
medium.
Index Terms—Electromagnetically induced transparency (EIT),
metamaterial, polarization independent, refractive index, sensor.
I. INTRODUCTION
E
LECTROMAGNETICALLY induced transparency (EIT)
is a quantum interference effect that refers to the formation of a transmission window inside the absorption band of a
Manuscript received May 24, 2012; accepted July 05, 2012. Date of publication August 16, 2012; date of current version September 27, 2012. This work
was supported by the National Natural Science Foundation of China under Grant
60801015 and Grant 60971064, and by the Fundamental Research Funds for the
Central Universities under Grant HIT.IBRSEM.2009 and Grant HIT.IBRSEM.
201122.
F.-Y. Meng and Q. Wu are with the Department of Microwave Engineering, Harbin Institute of Technology, Harbin 150001, China (e-mail:
[email protected]; [email protected]).
D. Erni is with the Faculty of Engineering, Laboratory for General and Theoretical Electrical Engineering (ATE) and the CENIDE-Center for Nanointegration Duisburg–Essen, University of Duisburg–Essen, D-47048 Duisburg, Germany (e-mail: [email protected]).
K. Wu is with the Poly-Grames Research Center and the Department of
Electrical Engineering, Center for Radiofrequency Electronics Research of
Quebec, École Polytechnique de Montréal, Montréal, QC, Canada H3T 1J4
(e-mail: [email protected]).
J.-C. Lee is with the Department of Wireless Communication Engineering,
Kwangwoon University, Seoul 139-701, Korea (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMTT.2012.2209455
three-level atomic media. Recently, a lot of attention has been
paid to the fact that the EIT-like effect can occur in classical
oscillator systems, such as coupled optical micro-resonators
[1], mechanical spring-mass configurations [2], and optical
waveguides side coupled to a resonator [3], [4]. Particularly,
metamaterials can also be configured to induce the EIT-like
effect [5]–[10]. Such EIT-like metamaterials usually consist
of “bright” and “dark” resonant elements, which have almost
equal resonance frequencies and are coupled with each other.
The resonance of the bright element has a low quality factor and
is directly excited by the incident waves. On the contrary, the
dark element usually supports a sharper resonance profile and
hardly interacts with the incident waves. Similar to EIT in an
atomic system, the metamaterial-based EIT-like effect brings a
significant reduction of the group velocity of electromagnetic
waves. The slow-wave property has been widely applied in
the design of phase shifters [5]–[10], traveling-wave tubes
[11], [12], or optical buffers and storage [13]–[16]. Meanwhile,
EIT-like metamaterials are capable of integrating the dual
advantages of a narrow transmission window and a strong
field confinement, which is crucial for sensing applications
[17]–[19]. In addition, the excellent resonance quality factor,
and hence, the narrow resonant spectral band of EIT-like metamaterials, are also helpful for developing frequency-selective
surfaces [20], [21] and filters [22]–[25].
Several EIT-like metamaterials have been demonstrated at
frequencies in microwave [26]–[28], near-infrared [6]–[10],
terahertz [29]–[32], and visible [33]–[36] regimes. However, all
EIT-like metamaterials presented thus far are highly sensitive
to the polarization state of incident waves. Their characteristic
electromagnetic response is only supported for a predefined
linear polarization state. Compared to the polarization-sensitive metamaterials, polarization-insensitive ones are more
convenient for practical use because they can endure changes
in polarization states of the incident waves. Furthermore, for
many applications, such as most circular microwave waveguide
systems, frequency-selective surfaces, or fiber-optic systems,
it is necessary to work with elliptically polarized waves or
waves with varying linear polarization. For all these cases, the
implementation of EIT-like metamaterials requires polarization-independent design concepts.
In this paper, we experimentally and numerically demonstrate
that a polarization-independent analog of EIT can be achieved in
a planar electromagnetic metamaterial. Moreover, the influence
of the physical parameters on EIT-like effects of the metamate-
0018-9480/$31.00 © 2012 IEEE
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 10, OCTOBER 2012
Fig. 1. (a) Schematics of the polarization-independent EIT-like metamaterial
cell consisting of the bright SRR and the dark SR separated by the distance .
(b) Expanded view of the layout of the dark SR.
rial is theoretically analyzed by a two-particle model and then
numerically validated. The numerical simulations also demonstrate the sensing ability of such metamaterial for refractiveindex changes of the surrounding medium.
II. STRUCTURE DESIGN
A schematic layout of the implemented unit cell of the
metamaterial, including all geometrical parameters, is shown
in Fig. 1. The topology consists of a metallic spiral resonator
(SR) enclosed within a much larger metallic split-ring resonator
(SRR) on a dielectric substrate. The SRR is square shaped and
leaves two equal gaps on its upper and left side arms, which
are furthest separated from the SR topology. The SR has a
square shape too and is made of a single metallic strip rolled
up to form a spiral. The SR and SRR are designed to have very
close resonance frequencies. The SR is positioned close to the
lower right corner of the SRR at the same separation distance
from the right and lower side arms of the SRR. The distance
determines the electromagnetic coupling strength between the
SRR and SR.
From [37], it is known that the SR acts as a magnetic resonator
and its fundamental mode supports a circular current flow that
has no direct contribution to an electric dipole moment. This
means that the SR’s resonance can be excited only by the magnetic field penetrating through its plane. Hence, the SR weakly
interacts with the normally incident plane wave (at any linear
polarization) shown in Fig. 1, and is thus designated as the “polarization-independent” dark element in this study.
In contrast to the SR, the SRR in Fig. 1 acts as an electric resonator. Due to the asymmetric alignment of the two gaps, the
current flow of the SRR’s fundamental mode has an asymmetrical distribution, where the current in the lower and right arms
of the SRR is much stronger than in the upper and left arms. This
causes a significant electric dipole moment in both the - and
-direction, and thus leads to strong coupling between the SRR
and the normally incident plane wave at any linear polarization
state. Obviously, the SRR behaves like an electrically coupled
resonator that is designated as the “polarization-independent”
bright element.
It is worth noting that the dark element, namely, the SR, supports a resonance with a significantly larger quality factor compared to the bright element (i.e., the SRR) at the same resonant frequency. Referring to the analyses in [38] for particles
or unit cells with sizes much smaller than the free-space wavelength, it has been shown that both the SRR and SR topology
operate still well below the quasi-static limit and are essentially
behaving as lumped
circuits. In the SR topology, the current lines are bridging the gap between adjacent rings in the
form of a displacement current. Hence, the equivalent capacitance
of the SR, which arises from the distributed capacitive coupling between the contiguous rings, is much larger
than the equivalent capacitance of the SRR arising from the slit
capacitance of the inline gaps [38]–[40]. This renders the resonance quality factor of the SR to be much larger than that of the
SRR with the same resonant frequency.
Due to its larger equivalent capacitance, the SR will also have
a smaller equivalent inductance than the SRR with the same resonant frequency
. Since the equivalent inductance is directly proportional to the strip length, the SR
will be constructed from a shorter strip, which leads the two-turn
topology to cover a much smaller area than the SRR. The huge
difference between the two footprints provides the SR sufficient
space for different positioning, and enhances the controllability
of the EIT-like effect in the metamaterial. This is advantageous
because the profile of the EIT-like transmission window can
be easily adjusted while altering the separation distance between the SR and SRR, and hence, the electromagnetic coupling
strength between the dark SR and bright SRR.
III. DEMONSTRATION OF EIT-LIKE EFFECTS
To demonstrate the polarization-independent EIT-like effects, numerical simulations with CST Microwave Studio
software package [38] are performed. The geometry of the
unit cell (Fig. 1) containing the coupled SRR and SR is designed as
mm,
mm,
mm,
mm,
mm, and
mm, where
the conducting strips consist of copper with a thickness of
0.018 mm. The substrate has a permittivity of
, a loss
tangent of 0.002, and a thickness of 0.54 mm. The coupled SRR
and SR are periodically arranged with a spacing of 38.2 mm in
both the - and -direction.
These geometric parameters are chosen to yield resonance
frequencies of the SR and SRR around 1.56 GHz, where the
corresponding quality factors are 99.8 for the SR and 8.8 for the
SRR. The resonant frequency and the quality factor of the SRR
(SR) are obtained from the simulated reflection spectrum of the
single SRR (SR) structure [41]. It is worth mentioning that, in
obtaining the resonance frequency and quality factor of the SR,
the SR plane is rotated to be perpendicular to the incident magnetic field because the SR weakly interacts with the normally
incident plane wave, which leads to an obscure profile of the
SR’s resonance curve. Although such excitation for the SR is
different from the case shown in Fig. 1, it is reasonable because
the quality factor of a highly resonant linear system is supposed
MENG et al.: POLARIZATION-INDEPENDENT METAMATERIAL ANALOG OF EIT FOR REFRACTIVE-INDEX-BASED SENSOR
Fig. 2. Simulated transmission spectra of only the SRR (dashed line), only
the SR (dashed–dotted line), and the overall metamaterial structure (solid line),
together with the analytically calculated transmission spectrum of the overall
metamaterial structure based on the two-particle model (circled line).
to be independent of the manner of excitation [5]. In the simulation, the analyzed structure is modeled by a single unit cell
(containing an SR and/or SRR), which is periodically continued
according to the corresponding periodic boundary conditions.
Fig. 2 depicts the simulated transmission spectra of only the
SRR (dashed line), only the SR (dashed–dotted line), and the
spectral response of the overall metamaterial structure with
mm (solid line), illuminated by a normally incident plane
wave with vertical polarization (i.e.,
polarization). It can be
observed that the SRR alone yields a broad stopband centered at
1.56 GHz, which is caused by the coupling between the SRR and
the incident wave [5]. In contrast, the SR alone has a nearly perfect all-pass behavior—no stopband is visible at all—because its
interaction with the incident wave is very weak. An interesting
phenomenon occurs when the SRR and the SR are lumped together to form the metamaterial’s unit cell: a transmission peak
(i.e., a transparency window) emerges in the overlapping frequency region of the stopbands of the SR and SRR because of
the electromagnetic coupling between the SR and SRR. Such a
transparency window caused by the coupling between the dark
and bright elements is commonly regarded as an efficient metamaterial-based analog of the EIT effect. The transmission spectrum of the overall metamaterial structure excited by horizontally
and 45 off axis polarized (i.e.,
) impinging
plane waves is also simulated (the results are displayed and discussed in detail in Section V). It is shown that both the central
frequency and quality factor of the transparency window are independent on the polarization direction of the incident wave.
Fig. 3 shows the transmission spectra of the cross-polarized
waves generated by only the SRR and the overall metamaterial
structure. The transmission spectrum is calculated as the ratio of
the magnitude of the horizontal (or vertical) component of the
transmitted electric field through the metamaterial to the magnitude of the electric field excitation, which is set up to be polarized in the vertical (or horizontal) direction. By comparing
Figs. 3 and 2, one finds that the SRR alone causes a cross-polarized wave almost equivalent to the co-polarized wave at its resonant frequency of 1.56 GHz. This phenomenon can be easily
understood from the current distribution, as shown in Fig. 4(a).
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Fig. 3. Simulated transmission spectra of the cross-polarized waves generated
by only the SRR (dashed line) and the overall metamaterial structure (solid line).
It can be seen that the normally incident wave (either vertically
or horizontally polarized) will induce almost the same current
distribution on the left and the lower side arms of the SRR, and
thus excite a transmitted wave with the same electric field contribution from the vertical and horizontal direction. In contrast
to the single SRR structure, when the coupling between the SR
and SRR is introduced, the cross-polarized wave at 1.56 GHz
becomes quite weaker, which means that the resonance of the
SRR is effectively suppressed because of the electromagnetic
coupling between the SR and SRR, as depicted in Fig. 4(b)–(d).
To visualize the underlying mechanism of the metamaterial’s transparency window, the induced current distributions
at 1.56 GHz are simulated and compared for the uncoupled
SRR [see Fig. 4(a)] and the SRR coupled with the SR [see
Fig. 4(b)–(d)]. From Fig. 4(a), it is observed that without coupling to the dark SR, the SRR supports a large current flowing
on its right and lower side arms and a very low current flowing
in the left and the upper arms. From this point of view, the SRR
can be approximately considered as a pair of crossed metal
strips, whose resonance is excitable by a normally incident
plane wave polarized in the - or -direction. At the same time,
the resonance of the SRR blocks the electromagnetic wave
transmission and leads to the stopband in the transmission
spectrum because the re-radiated electric field by the resonant
SRR is considerably enhanced and has opposite phase with
respect to the incident electric field.
Fig. 4(b)–(d) shows the induced current distribution in the
integrated SRR and SR for three different separation distances
. It can be seen that, first, placing the SR close to the SRR
causes an increase of the suppressed induced currents in the
SRR because of the coupling (yielding a destructive interference) between resonantly interacting eigenmodes of the SR and
SRR [42]. To be specific: in this case, the induced current in
the SRR are excited through two pathways; one undergoes the
resonance that is directly excited by the incident wave, giving
rise to the induced currents in a counterclockwise direction. The
other pathway yields clockwise-induced currents caused by the
coupling from the SR. The two pathways introduce antiparallel
current in the SRR and consequently lead to a weakened overall
induced current at the corresponding resonance. Next, while
the distance
is closest at 2 mm, the coupling from the SR
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 10, OCTOBER 2012
Fig. 4. Simulated surface current distributions at 1.56 GHz for the bright SRR,
which is: (a) uncoupled and (b)–(d) coupled to the dark SR with different separation distances , and the surface current distributions at: (e) 1.67 GHz and
mm.
(f) 1.48 GHz for the SRR coupled to the SR with
provides the strongest modulation of the SRR’s resonance condition, thus rendering the induced currents in the SRR to become considerably weak compared to the other two cases. On
the other hand, as the separation
extends from 2 to 5 mm,
the induced currents in the SRR increase due to the weakened
destructive interference between the eigenmodes of the SR and
the SRR, hence, leading to a reduced transparency peak that
tends toward transmission values of the sole SRR, as shown in
Fig. 2. To summarize, the induced transparency (window) of
the metamaterial is excited by the coupling (destructive interference) between the dark resonance mode of the SR and the
bright resonance mode of the SRR. In addition, the two dips
that confine the transparency window in the transmission spectrum (Fig. 2, solid line) of the overall metamaterial structure can
be interpreted by the concept of hybridization model [37]. The
distributions of the induced currents at 1.67 and 1.48 GHz are
simulated and depicted in Fig. 4(e) and (f). It has been observed
that, at 1.67 GHz, the SR and SRR possess opposite induced currents, which is tantamount to the bonding mode in a hybridized
Fig. 5. Simulated time evolution of a Gaussian pulse propagating normally
through: (a) an infinite monolayer of the metamaterial and (b) only through the
metamaterial’s substrate layer.
molecular system. In contrast, at 1.48 GHz, the induced currents
in the SR and SRR have the similar direction, which can be directly associated with the antibonding mode in the molecular
system.
Another characteristic feature of EIT-like metamaterials is
the support of “slow wave” propagation. To demonstrate this
property in our designed metamaterial, we simulate a Gaussianshaped pulse with a pulsewidth of 11 ns centered at 1.56 GHz
that is transmitted normally through the infinite monolayer of
the metamaterial with an overall thickness of 0.558 mm (adding
up 0.54 mm of the substrate thickness and 0.018 mm of the
metal strips). In the simulation, the distance between the reference planes of the incident and transmitted waves is set to
12 mm. From Fig. 5(a), it can be deduced that the peak of the
incident Gaussian pulse appears at 24.9 ns, whereas the peak of
the transmitted pulse emerges at 27.8 ns. The transmitted pulse
is thus delayed by 2.9 ns, which is 72.5 times longer than the
delay time (0.04 ns) of the pulse propagating the same distance
in free space. From Fig. 5(a), it is also found that the transmitted
pulse through the metamaterial becomes wider than the incident
pulse, which is caused by the dispersion characteristics of the
metamaterial.
MENG et al.: POLARIZATION-INDEPENDENT METAMATERIAL ANALOG OF EIT FOR REFRACTIVE-INDEX-BASED SENSOR
For a better comparison, Fig. 5(b) shows the transmitted
pulse through only the metamaterial substrate with the thickness
of 0.54 mm keeping the same distance between the reference
planes of the incident and transmitted waves as 12 mm. The
pulse peak appears at 24.942 ns, being thus delayed by 0.042 ns,
which is much shorter than the transmission delay through the
metamaterial.
IV. INFLUENCE OF THE COUPLING STRENGTH BETWEEN THE
SR AND SRR ON THE TRANSPARENCY WINDOW
The influence of the coupling strength between the SR and
SRR on the transparency window of the metamaterial can be
theoretically analyzed by introducing a two-particle model—a
particle (designated as “particle A”) represents the bright SRR,
which is driven by the incident electric field
, and
a particle (designated as “particle B”) represents the dark SR,
which hardly couples to the incident wave. The particles A and
B both are supposed to have the same resonant frequency .
Assuming that the coupling strength between the two particles
is , and the loss factors of the two particles is much less than
, then the displacements
and
of the particles A and B
with respect to their respective equilibrium positions satisfy the
following coupled differential equations:
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Here, is the proportionality factor. The weak coupling between the dark SR and the incident wave leads to a negligibly
small . Therefore, (6) can be approximated by
(7)
For the aforementioned weak coupling, the transmission of electromagnetic wave through the metamaterial slab with a thickness is given by (8), shown at the bottom of this page.
In order to validate the two-particle model, we fit the analytical expression of the transmission spectrum [according to
(7) and (8)] for a metamaterial with
mm to the corresponding simulation in Fig. 2 and present the analytical results by a red-circled curve (in the online version) in the same
figure for a direct comparison. It is evident that the fitted analytical model agrees perfectly well to the results obtained by the
corresponding full-wave simulation. For fitting the transmission
curve, first, we let
,
rad/s (1.56 GHz), and
mm, and then used
rad/s
(1.48 GHz) (or
rad/s (1.67 GHz)
to get
rad/s. Next, substituting the transmission
values for the metamaterial at ,
, and
into (8) leads to
(1)
(2)
Here,
,
, and
are the effective charge, effective mass, and loss factor of the particle A (B), respectively.
Solving (1) and (2), we obtain
(3)
(4)
The effective polarization of the metamaterial is then
(5)
Hence, the effective electric susceptibility of the metamaterial can be written as
(9)
Finally, combining and solving (7)–(9), we obtained
rad/s,
rad/s and
. Also
worth mentioning is that, in (7) and (8), we assume
,
which does not perfectly correspond to the actual case, as shown
in Fig. 2. This leads to a little difference between the simulated
results and the fitted results based on (7) and (8).
For the ideal lossless structures with
, (7) is
further simplified to
(10)
Obviously, the two-particle system can support a transparency
where
with
window at
(11)
(6)
, which means that the
Hence, one obtains
transparency frequency
is very close to the resonant frequency . This conclusion is verified by the simulated results
shown in Fig. 2. It is worth noting that some special EIT-like
metamaterials, such as the cut-continuous strips metamaterial
(8)
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[20], [43] and the split-closed rings metamaterial [9], encompass a “quasi-dark” element, which couples to the incident wave
to a certain extent. For these metamaterials,
cannot be neglected anymore because the quantity is proportional to the
coupling strength between the quasi-dark element and the incident wave. In addition, (11) reveals that this residual coupling
renders the transparency frequency
of the metamaterial
with such a quasi-dark element to slightly red-shift below the
resonant frequency , where this detuning is weighted by the
coupling strength between the two particles.
The influence of the coupling strength on the spectral width
of the transparency window follows from further analyzing (7).
Here, the effective susceptibility approaches infinity as
. Hence, the metamaterial yields a stopband that
is defined by the two edge frequencies
and
, and the width of the transparency window is
then simply given by
Fig. 6. Simulated transmission spectra of the metamaterial with different separations between the SRR and SR.
(12)
The transparency window therefore narrows with decreasing
inter-particle coupling strength .
The effect of the coupling strength on the magnitude of the
transparency window of the metamaterial also follows from the
two-particle model. Substituting
and
into (6)
leads to
(13)
It can be seen that
increases as decreases. It deserves noting that, for much larger than and ,
gets very small and changes very slowly with . However, as
decreases to a value comparable to
and , the change of
over becomes remarkable. A bigger
will not only result in larger ohmic losses, but also a larger
impedance mismatch between the metamaterial and the surrounding lossless medium, both of which contributes to a lower
magnitude of the transparency window. Fig. 6 shows a fullwave simulation of the transmission spectrums for the metamaterial with different separation distance , which determines the
coupling strength . It can be observed that, with decreasing
coupling (i.e., increasing separation), the transparency window
narrows and becomes weaker, which is in perfect agreement
with the results derived from the two-particle model.
The influence of the coupling strength on the quality factor
of the transparency window needs to be discussed along two different cases. For
much larger than
and , (12) and (13)
imply that with decreasing , the transparency window narrows,
where the transmission magnitude remains approximately constant. In this case, the quality factor of the transparency window
increases as decreases. When is comparable to
and ,
according to (12) and (13), decreasing brings not only a narrower transparency window, but also a lower transmission magnitude, which has a negative impact on the quality factor of the
transparency window. Especially if
is large enough, there
will be an inflection point , from which the quality factor decreases with diminishing
.
Fig. 7. Simulated quality factor of the metamaterial’s transparency window as
a function of the separation distance between the SRR and SR.
Fig. 7 displays the simulated quality factor as a function of
the separation distance . It is shown that, for large coupling
strengths , an increase in the quality factor is observed for
larger distance (i.e., for decreasing ). This trend persists up
to
mm (corresponding to the inflection point ), where
the quality factor attains its maximum value of 175.4. When
mm
, the quality factor decreases with increasing (i.e., further decreasing ). It is worth mentioning that
the maximum quality factor (175.4) of the metamaterial’s transparency window is much larger than that (99.8) of the single
dark SR.
V. DESIGN, FABRICATION, AND TESTING OF METAMATERIAL
WORKING AT HIGHER FREQUENCY
In order to further demonstrate and verify the EIT-like effect
of the proposed metamaterial structure, a prototype sample
of the metamaterial operating at a higher frequency around
5.8 GHz was designed, fabricated, and tested. Especially worth
noting is that, in order to facilitate the fabrication process,
the structure of the dark SR is slightly modified, as shown in
Fig. 8(b). Referring to Figs. 1 and 8(b), the designed geometric
parameters of the metamaterial with higher resonant frequency
are as follows:
mm,
mm,
mm,
MENG et al.: POLARIZATION-INDEPENDENT METAMATERIAL ANALOG OF EIT FOR REFRACTIVE-INDEX-BASED SENSOR
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Fig. 8. (a) Photography of the fabricated prototype of the EIT-like metamaterial with higher resonant frequency. (b) Geometry of the modified SR used for
the fabricated metamaterial prototype.
Fig. 9. Experimental setup for measuring the transmission spectrum of the
metamaterial.
mm,
mm, and
mm, where
the conducting strips consist of copper with a thickness of
0.018 mm. The substrate has a permittivity of
, a loss
tangent of 0.002, and a thickness of 0.9 mm. The coupled SRR
and SR are periodically arranged with a spacing of 15 mm in
both the - and -direction. Simulated results show that, with
these geometric parameters, both the dark SR and bright SRR
resonates around 5.8 GHz, and the quality factors of the SR and
the SRR are 91 and 2, respectively.
The modified prototype of the metamaterial was fabricated as
displayed in Fig. 8. The physical dimensions of the overall metamaterial structure are 300 mm 300 mm (20 20 unit cells),
which correspond to electrical dimensions of
with
regard to the resonant frequencies of both the SR and SRR. The
metamaterial prototype was tested using the free-space measurement setup, as shown in Fig. 9, which consists of two standard horn antennas operating at the -band with the metamaterial prototype placed in between. The line of sight between the
two horns passes through the center of the metamaterial prototype and the horns are located about 800 mm apart from the
metamaterial prototype to ensure the formation of a uniform
plane wave impinging upon the metamaterial prototype.
The experiments were performed in a microwave anechoic
chamber, which emulates the free-space environment. An Agilent 8510B vector network analyzer (VNA) is employed to measure the electromagnetic transmission through the metamaterial prototype. A thru calibration was performed to calibrate the
VNA within a frequency band of 4.5 GHz 7 GHz in the absence of the metamaterial prototype. Fig. 10(a) shows the measurement results of the transmission spectra of the metamaterial
Fig. 10. Measured and simulated transmission spectra of the metamaterial prototype for: (a) vertical polarized, (b) horizontal polarized, and (c) 45 off-axis
polarized incident waves for different angles of incidence (with respect to the
normal direction). The line with a circle, up-triangle, and square represents the
transmission spectrum for 0 , 15 , and 30 angle of incident, respectively. The
dashed line represents the simulated transmission spectra for 0 angle of incident.
prototype for vertically
polarized incident waves with incidence angle of 0 (normal direction), 15 , and 30 . One can
find a clear transparency window at 5.8 GHz nearly independent of the incidence angle. Fig. 10(a) also includes the corresponding full-wave simulation for the normally incident wave.
It can be seen that the simulated results are in a good agreement
with the measurement results. Fig. 10(b) shows the measurement results of the metamaterial prototype for horizontally
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 10, OCTOBER 2012
TABLE I
COMPARISON BETWEEN FOM VALUES OF DIFFERENT METHODS
(AND ASSOCIATED SENSOR TOPOLOGIES) FOR SENSING
REFRACTIVE INDEX CHANGES
Fig. 11. Simulated resonance shift of the EIT-like metamaterial with respect to
a change in the relative permittivity of the surrounding medium.
polarized incident waves with incidence angle of 0 , 15 , and
30 , together with the corresponding simulated results for the
normally incident wave. Fig. 10(c) shows the measurement results of the metamaterial prototype for 45 off axis
polarized incident waves for incidence angle of 0 , 15 , and 30
including the simulated results for the normally incident wave.
One can see that the metamaterial shows only a minor dependence of the frequency response against the angle of incidence.
By comparing Fig. 10(a)–(c), it can be concluded that the metamaterial prototype exhibits polarization-independent EIT-like
effects for normally incident plane waves with linear polarization, which is verified both experimentally and theoretically.
Moreover, the metamaterial prototype shows only a minor dependence of the frequency response with respect to the incidence angle for values below 30 .
VI. REFRACTIVE-INDEX-BASED SENSOR
Once the dark SR and bright SRR are strongly coupled, the
electromagnetic energy is predominantly localized inside the
unit cell of the EIT-like metamaterial. In this case, the metamaterial essentially behaves as a resonant cavity and can be
employed as a refractive-index-based sensor because its resonant frequency (i.e., the transparency frequency) substantially
depends on the dielectric condition of surrounding media [35].
In the following, we demonstrate the sensing ability of our prior
EIT-like metamaterial structure discussed in Section II by simulating the transmission spectrums of the single-layer metamaterial in the correspondingly lower frequency range. The metamaterial is introduced into middle of a 4-mm-thick dielectric slab
with a relative permittivity that stands for the different dielectric loading of the intended sensor structure. Fig. 11 depicts the
simulated results of the metamaterial’s generic sensor operation.
A clear shift of the transmission peak to lower frequency is visible when increasing the
of the metamaterial’s surrounding
medium from 1.2 to 1.6. The sensitivity of the metamaterial
sensor, which is defined as the shift in resonance wavelength
per unit change of refractive index, amounts to 77.25 mm/RIU.
The metamaterial sensor can be further evaluated by the figure
of merit (FOM), which is the ratio of the sensitivity value to the
full width at half maximum (FWHM) of the resonance [20]. In
case of Fig. 11, the FWHM of the transparency window is about
9.49 mm, which leads to a
.
Table I compares the corresponding FOM values from different methods of sensing refractive index according to sensor
structures with nanobars [21], nanotubes [44], nano-SRRs [45],
SRRs with an asymmetrically coupled resonance (ACR) [46],
planar EIT-like metamaterial [20], and our proposed EIT-like
metamaterial. It can be seen that the sensing performance of our
EIT-like metamaterial competes with the best ones and is just
slightly below the value of the nano-SRRs in [21]. It is worth
mentioning that the FOM of 8.14 obtained at
mm of our
proposed EIT-like metamaterial can be further maximized just
by increasing the separation distance because the quality factor
of the transparency window grows with up to
mm, as
already demonstrated in Fig. 7.
VII. CONCLUSION
We have investigated polarization-independent EIT-like effects achieved in a planar metamaterial consisting of coupled
SRs and SRRs. A sharp transparency window with narrow width
and slow wave property was observed both experimentally and
within full-wave simulations. The experimental and the simulated results are in good agreement with theoretical predictions.
A two-particle model is introduced to theoretically analyze the
influence of the coupling strength between the SR and SRR on
the center frequency, bandwidth, magnitude, and quality factor
of the transparency window. These analytical results are numerically validated using CST Microwave Studio full-wave electromagnetic simulation tools based on the finite integral time-domain method. Finally, a potential application of the EIT-like
metamaterials as refractive-index-based sensors has been numerically demonstrated. Results show that the transmission resonant frequency of the metamaterial is very sensitive to the refractive index changes of the surrounding medium. This provides a remarkable sensing technique for practical applications
in environmental, chemical, and biological diagnostics.
ACKNOWLEDGMENT
Author F.-Y. Meng would like to thank Prof. W. Hong,
Southeast University, Nanjing, China, for very fruitful discussions.
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 10, OCTOBER 2012
Fan-Yi Meng (S’07–M’09) received the B.S. degree, M.S., and Ph.D. degrees
in electromagnetics from the Harbin Institute of Technology, Harbin, China in
2002, 2004, and 2007, respectively.
Since August 2007, he has been with the Department of Microwave Engineering, Harbin Institute of Technology, where he is currently an Associate Professor. He has coauthored four books, 40 international refereed journal papers,
over 20 regional refereed journal papers, and 20 international conference papers. His current research interests include electromagnetic and optical metamaterials, plasmonics, and electromagnetic compatibility (EMC).
Dr. Meng was a recipient of several awards including the 2010 Award of
Science and Technology from the Heilongjiang Province Government of China,
the 2010 “Microsoft Cup” IEEE China Student Paper Contest Award, two Best
Paper Awards from the National Conference on Microwave and Millimeter
Wave in China (2009 and 2007, respectively), the 2008 University Excellent
Teacher Award of the National University of Singapore, the 2007 Excellent
Graduate Award of Heilongjiang Province of China, and the Outstanding
Doctor Degree Dissertation Award of the Harbin Institute of Technology.
Qun Wu (M’94–SM’05) received the B.Sc. degree in radio engineering,
M.Eng. degree in electromagnetic fields and microwave technology, and
Ph.D. degree in communication and information systems engineering from the
Harbin Institute of Technology (HIT), Harbin, China in 1977, 1988, and 1999,
respectively.
From 1998 to 1999, he was a Visiting Professor with Seoul National University (SNU), Seoul, Korea. From 1999 to 2000, he was a Visiting Professor
with the Pohang University of Science and Technology. Since 1990, he has been
with Department of Electronic and communication Engineering, HIT, where he
is currently a Professor. He has authored or coauthored over 50 international and
regional refereed journal papers. His recent research interests are mainly in microwave active circuits, electromagnetic compatibility, monolithic microwave
integrated circuits (MMICs), and millimeter-wave microelectromechanical systems (MEMS) devices.
Dr. Wu was the recipient of two Third-Class Prizes and one Second-Class
Prize of Scientific Progress Awards from the Ministry of Aerospace of China in
1989 and 1992, respectively.
Daniel Erni (S’88–M’93) received the Diploma degree in electrical engineering
from the University of Applied Sciences (HSR), Rapperswil, Switzerland, in
1986, the Diploma degree in electrical engineering and Ph.D. degree from ETH
Zürich, Zürich, Switzerland, in 1990 and 1996, respectively.
Since 1990, he has been with the Laboratory for Electromagnetic Fields and
Microwave Electronics, ETH Zürich. He was the founder, and from 1995 to
2006, the Head of the Communication Photonics Group, ETH Zürich. Since October 2006, he has been a Full Professor of general and theoretical electrical engineering at the University of Duisburg–Essen, Duisburg–Essen, Germany. His
current research includes advanced data transmission schemes (i.e. O-MIMO)
in board-level optical interconnects, optical on-chip interconnects, ultra-dense
integrated optics, nanophotonics, plasmonics, electromagnetic and optical metamaterials, and quantum optics. On the system level, he has pioneered the introduction of numerical structural optimization into dense integrated optics device design. He is a member of the Editorial Board of the Journal of Computational and Theoretical Nanoscience and edited the 2009 “Special Issue on Functional Nanophotonics and Nanoelectromagnetics.” He has authored or coauthored over 300 publications.
Dr. Erni is a Fellow of the Electromagnetics Academy. He is a member of the
Center for Nanointegration Duisburg–Essen (CeNIDE). He is also as a member
of the Swiss Physical Society (SPS), the German Physical Society (DPG), and
the Optical Society of America (OSA). He is an associated member of the Swiss
Electromagnetics Research Centre (SEREC).
Ke Wu (M’87–MS’92–F’01) is a Professor of electrical engineering and Tier-I
Canada Research Chair in RF and millimeter-wave engineering with the Ecole
Polytechnique (University of Montreal), Montreal, QC, Canada. He holds the
first Cheung Kong endowed chair professorship (visiting) with the Southeast
University and the first Sir Yue-Kong Pao chair professorship (visiting) with the
Ningbo University. He also holds an honorary professorship with the Nanjing
University of Science and Technology, Nanjing University of Post Telecommunication, and the City University of Hong Kong. He has been the Director of
the Poly-Grames Research Center, and the founding Director of the Center for
Radiofrequency Electronics Research of Quebec (Regroupement stratégique of
FRQNT). He has also held guest and visiting professorships with many universities around the world. He has authored or coauthored over 800 referred
papers and a number of books/book chapters. He holds numerous patents. His
current research interests involve substrate integrated circuits (SICs), antenna
arrays, advanced computer-aided design (CAD) and modeling techniques, wireless power transmission, and development of low-cost RF and millimeter-wave
transceivers and sensors for wireless systems and biomedical applications. He
is also interested in the modeling and design of microwave photonic circuits and
systems.
Dr. Wu is a member of the Electromagnetics Academy, Sigma Xi, and URSI.
He is a Fellow of the Canadian Academy of Engineering (CAE) and the Royal
Society of Canada (The Canadian Academy of the Sciences and Humanities).
He has held key positions in and has served on various panels and international
committees including the chair of Technical Program Committees, international
Steering Committees, and international conferences/symposia. In particular, he
will be the general chair of the 2012 IEEE Microwave Theory and Techniques
Society (IEEE MTT-S) International Microwave Symposium (IMS). He has
served on the editorial/review boards of many technical journals, transactions,
and letters, as well as scientific encyclopedia including having been an editor
and guest editor. He is currently the chair of the joint IEEE chapters of the IEEE
MTT-S/AP-S/LEOS in Montreal, QC, Canada. He is an elected IEEE MTT-S
Administrative Committee (AdCom) member for 2006–2015. He has served as
chair of the IEEE MTT-S Member and Geographic Activities (MGA) Committee. He was an IEEE MTT-S Distinguished Microwave Lecturer (January
2009–December 2011). He was the recipient of many awards and prizes including the first IEEE MTT-S Outstanding Young Engineer Award, the 2004
Fessenden Medal of IEEE Canada, and the 2009 Thomas W. Eadie Medal of
the Royal Society of Canada.
Jong-Chul Lee (S’91–M’96–SM’07) received the B.S. and M.S. degrees in
electronic engineering from Hanyang University, Seoul, Korea, in 1983 and
1985, respectively. He received the M.S. degree from Arizona State University,
Tempe, in 1989 and the Ph.D. degree from Texas A&M University, College Station, in 1994, all in electrical engineering.
From June 1994 to February 1996, he was a Senior Researcher with the Photonic Devices Laboratory, System Integrated Circuit (IC) Research and Development Laboratory, Hyundai Electronics Industrial Company Ltd., where he
was involved in the development of several high-speed laser diodes and photodiodes and transmitter/receiver modules. He then joined the Department of
Radio Science and Engineering, Kwangwoon University, Seoul, Korea, where
he is currently a Professor. He also serves as Project Director of the ITRC
RFIC Center, Kwangwoon University, which, since Aug. 2000, is funded by
the Ministry of Information and Telecommunication. Since December 2001, he
has been a Guest Professor with the Department of Electronics and Communication, Harbin Institute of Technology. He is a Visiting Scholar with the Department of Electrical and Computer Engineering, University of California at
San Diego, La Jolla. He has authored or coauthored over 50 papers in international conference and journals. He currently participates in several government
projects related to millimeter-wave devices. His research interests include optoelectronics, RF photonics, RF MEMS, RF applications for ferroelectric materials, millimeter-wave passive and active devices, MMICs, and OEMIC.
Dr. Lee is a member of the Korea Electromagnetic Engineering Society
(KEES) and the Korean Institute of Electrical, Electronic, and Materials
Engineers (KIEEME).
-­‐ PRESS RELEASE -­‐
CST University Publication Award 2013: Winners Announced
December 19th, 2013 – Computer Simulation Technology (CST), Darmstadt, announces winners of
the CST University Publication Award 2013, an annual grant to university institutes and researchers
for published papers related to 3D electromagnetic field simulation applications.
The CST University Publication Award acknowledges the importance of work from university researchers and
academics by granting winners extensions and upgrades to their CST STUDIO SUITE® installations. 2013 marks
the 10th anniversary of the Award, showcasing support in further research and innovation within universities.
The selection committee place three conditions for participation: the papers must be authored or co-­authored
by university researchers, they must have been published either in scientific journals or conference
proceedings, and the numerical results must be entirely or in part obtained through simulations using CST
software products.
Submissions were evaluated on a number of criteria, including originality of application and theory, clarity of
presentation, and the skilful use of CST software. There is also a special award given for short papers of four
pages or less, to acknowledge the importance of short conference papers in promoting practical applications
of simulation.
“The quality of the publications submitted was outstanding and this emphasizes why we continue to support
university institutions and their research through the CST University Publication Award,” said Dr. Martin Timm,
Director of Global Marketing, CST. “Even after 10 years of granting the award, selecting a winner is never easy.
Learning about the vast range of interesting and novel areas of application is a privilege and I’d like to thank
everyone who has continued to support this initiative by contributing their papers.”
The following papers have been selected to receive the CST University Publication Award 2013:
x
"Polarization-­Independent Metamaterial Analog of Electromagnetically Induced Transparency for a
Refractive-­Index-­Based Sensor";; Fan-­Yi Meng, Qun Wu, Daniel Erni, Ke Wu, and Jong-­Chul Lee. IEEE
Transactions on Microwave Theory and Techniques, Vol. 60, No. 10, October 2012
https://www.cst.com/Products/Publications/ReferenceDetails/Polarization-­Independent-­
Metamaterial-­Analog-­Of-­Electromagnetically-­Induced-­Transparency-­For-­A-­Refractive-­Index-­Based-­
Sensor
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