International Journal of Advancements in Research & Technology, Volume 2, Issue 8, August-2013
ISSN 2278-7763
97
Design of 9-Shaped Metamaterial for Enhanced Negative
Refractive Index Bandwidth
Rahul Yadav, Amit Kumar Yadav
1,2
M.E Student, Dept. Of Electronics and Telecommunication, Thakur College of Engineering & Technology, Mumabi, India-400101
ryrahulyadav01@gmail.com
1
ABSTRACT
The paper presents design of 9-shaped metamaterial working in the range of 10-20 GHz. A Gil GML 1034 (lossy) substrate is
used for the design of metamaterial Structure. The electromagnetic excitation to the designed metamaterial is also varied to investigate its effect on metamaterail potential parameters. The extraction of metamaterial parameters is done using NicolsonRoss-Wier (NRW) approach. Computer Simulation Tool and Matlab R2009B is used for designing and extraction of parameters
respectively.
Keywords : 9-shaped Dual Split Ring Structure, NRW Approach, Negative Refractive Index Bandwidth.
1 INTRODUCTION
In recent years, metamaterial have dragged the attention in
microwave applications. Now days, these materials are being
used widely in antenna system since they provide gain and
bandwidth enhancement. Metamaterial were first introduced
by Veselago in 1967. Metamaterial are basically artificial materials which exhibits negative permittivity (- ε ), negative permeability (- µ ) and negative refractive index (NRI) in the microwave frequency range for isotropic medium, and which do
not occur naturally. Metamaterial are also called doubly negative material (DNG) and left handed materials (LHM). The
name LHM is used because the electric field, magnetic field
and the wave vector form a left-handed system [1].
investigate the effect on metamaterial parameters.
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In year 2002, Enoch et al. found that zero indexes metamaterial
(ZIMs) can be used to achieve directive emission on antenna
system [2]. Most existing ZIMLs are implemented either with
the help of single electrical resonator with approximately zero
permittivity, but in these the wave impedance of the ZIMs is
not able to match with that of air impedance and this effectively lowers the radiation efficiency of the antenna. Thus employing such ZIMLs completely depends on the application
boundaries. In 2009, Ma et al, it was theoretically stated that
an anisotropic ZIML with proper design had good impedance
matching with air, so that anisotropic ZIMLS can efficiently
enhance the antenna gain. Also Cheng et al. realized that
ZIMLS composed of split ring resonator (SRR) array helps to
achieve enhanced directivity for a line source [3]. However
there is constraint in the operating bandwidth.
In the proposed work, a 9-shaped split ring resonator structure is design to overcome the bandwidth constraints as in
case of conventional metamaterial (MTM). The work is mainly
focused to achieve wideband negative refractive index which
thus can be employed to ameliorate the antenna parameters
like reflection coefficient and drastically. The boundary conditions around the designed metamaterial are also altered to
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2 DESIGN OF METAMATERIAL SUPERSTRATE
A 9-shaped coupled structure is designed with substrate permittivity of 3.38. For this Gil GML 1034 (lossy) substrate of
thickness 1.6mm is used. A three-dimensional unit cell is initially defined with normal (ϵ=1, µ=1) background properties.
Geometry of the proposed MTM structure is shown in Fig 1.
As far as the boundary conditions are concerned, in the left
and right (x-axis) of the metamaterial structure perfect electric
conductor (Et) boundary condition, in the front and back (yaxis) perfect magnetic conductor (Ht) boundary condition and
in z-axis i.e. top and bottom are defined with open space. It is
important to assign necessary and appropriate boundary conditions to achieve a TEM mode. For the excitation of 9-shaped
split ring resonator (SRR), waveguide ports are defined on
positive and negative z-axis which is shown in Fig 2.
(a) Front View
(b) Perspective View
Fig. 1 9-shaped MTM structure
With the defined boundaries, it signifies that electric field of
incident wave will be polarized along X-axis and magnetic
field of incident wave will be polarized along Y-axis.
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International Journal of Advancements in Research & Technology, Volume 2, Issue 3, August-2013
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Fig. 4 Plot of phase of scattering coefficient for 9-shaped MTM
3.1 Retrieval & Characterization of 9-Shaped MTM
Fig. 2 MTM structure with boundaries
The parametric values of 9-shaped metamaterial (MTM) structure are shown in Table 1.
Table 1 Geometric dimensions of 9-Shaped (MTM)
Sr.no
1
2
3
4
5
6
Parameter
Height of Substrate (h)
Length of Substrate (L)
Width of Substrate (W)
Thickness of Meta Strip (t)
Length of Metamaterial(L1)
Width of Metamaterial (W1)
Dimension (mm)
1.6
4
4
0.44
3
3
Extraction of potential parameters of proposed 9-shaped metamaterial is done using Nicholson-Ross-Weir (NRW) approach. Although there are other formulations available [5]-[7]
to retrieve the metamaterial parameters, but the presented
approach offers more simplified computational process. The
analytical procedure begins with the calculation of transmission and reflection coefficient for normal incident waves on
MTM, which is given by,
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S11 =
S 21 =
(1 − T 2 )Γ12
2
1 − Γ12
T2
(1)
2
(1 − Γ12
)T
2
1 − Γ12T 2
(2)
Where ‘T’ is the transmission propagation factor given by
3 RESPONSE VERIFICATION OF 9-SHAPED MTM
T exp(− j β l )
=
The s-parameters i.e. (magnitude and phase) of proposed 9shaped MTM are simulated for verification of metamaterial
properties. Plot of reflection coefficient (S 11 ) and transmission
coefficient (S 21 ) is shown in Fig.3 and argument of respective
scattering coefficient is shown in Fig .4.
(3)
Solution of equation 1 and 2 yields,
T=
=
Γ 21
(4)
( S11 + S 21 ) − Γ12
1 − ( S11 + S 21 )Γ12
(5)
2
2
1 − ( S 21
− S112 )
1 − ( S 21
− S112 )
± [
] −1
2 S11
2 S11
(6)
Γ 21 = X ± X 2 − 1
Now since the mode of operation is microstrip, this yield in
effective permittivity and effective permeability.
X
=
=
Y
Fig. 3 Plot of scattering coefficient for 9-shaped MTM
It is observed that dual band response is achieved at 10.45
GHz, 17.28 GHz for S 11 and at 10.84 GHz and 13.7 GHz for S 21 .
µeff
=
e eff
1 + Γ12
1 − Γ12
=
µeff e eff j
c0
ln( z )
dw
(8)
Where, Y is the propagation constant.
Thus, the permittivity and permeability can be obtained as
eee
eff = eff , real − j eff ,img =Y / X
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(7)
(9)
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International Journal of Advancements in Research & Technology, Volume 2, Issue 3, August-2013
ISSN XXXX-XXXX
mmm
eff = eff , real − j eff ,img =YX
99
(10)
The Snell-Decartes law implies that the refractive index can be
defined as
n = µeff e eff
(11)
To retrieve the metamaterial parameters like negative permittivity, negative permeability, phase, negative refractive index
(NRI) and the effective wave impedance, MATLAB R2009B
Tool is used. The results for the respective parameters of the
proposed metamaterial structure are shown in Fig. 5-8.
Fig. 8 Extracted result of MTM unit cell for effective wave impedance
From the extracted parameters of 9-shaped metamaterial, result of permittivity exhibits a negative response in the frequency range between (10-15) GHz and (17-20) GHz, result of
permeability shows a negative response in the frequency
range between (10-11) GHz and (17-20) GHz and this results
in dual negative refractive index (NRI) in the frequency range
between (10-13) GHz, (15.5-17.4) GHz and (19.6-20) GHz thus
providing a negative refraction bandwidth of 4.3 GHz. Since
ε<0 and µ<0, therefore proposed 9-shaped MTM acts as double negative material (DNG).
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Fig. 5 Extracted result of MTM unit cell for permittivity
4 BOUNDARY CONDITION VARIATIONS
This section describes that how by changing the practical
boundary condition, a metamaterial response can be achieved
in different frequency bands. To understand the problem, initially electromagnetic waveguide excitation for the proposed
9-shaped MTM is varied in terms of its strength i.e. (Incident
area of waveguide excitation on MTM) and distance between
waveguide excitation and MTM as shown in Fig.9-11 respectively.
Fig. 6 Extracted result of MTM unit cell for permeability
Fig. 9 9-Shaped MTM with waveguide port excitation at dist. (d 1 )
Fig. 7 Extracted result of MTM unit cell for negative refractive index
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Fig. 10 9-Shaped MTM with waveguide port excitation at dist. (d 1 – n)
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Fig. 11 9-Shaped MTM with waveguide port excitation distance (d 1 = 0)
For analysis purpose, let us assume that distance is varying in
terms of variable (d n ) and ‘n’ be the positive integer. Now
with the assumption that the electromagnetic field strength is
‘k’ V/m and the direction of wave propagation is towards
positive y-axis.
For distance ‘d1’, the electric fields and magnetic fields will be
polarized as;
EX (d1 v/ m)
And
H Z ( d 1 A/ m )
Fig. 13 Extracted result of permeability with port distance (d 1 )
i.e. out of ‘K’ fields only ‘d 1 -W’
fields will be polarized with respect to the MTM. Here waveguide port excitation covers only (h × L) area and therefore
indicates that for practical realization the metamaterial structure should be placed exactly on the top of the EM source. For
distance ‘d 1 -n’ the electric fields and magnetic fields will be
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polarized as E X ( d 1− n v / m ) and H Z ( d 1− n A / m ) .
But in case of d 1 =0, all the ‘K’ fields will get polarized thereby
indicating a maximum waveguide excitation around the MTM
structure. Since the waveguide port area here is (h+∆h 1 by L),
therefore the metamaterial structure will be place exactly over
EM source by an incremental gap of ‘∆h 1 ’.
Where ‘h 1 ’ is the height above the EM source.
Fig. 14 Extracted result of refractive index with port distance (d 1 )
To verity the effect, potential parameters for these configurations are extracted as shown in Fig. 12-20.
Fig. 15 Extracted result of permittivity with port distance (d 1 -n)
Fig. 12 Extracted Result of Permittivity with port distance (d 1 )
Fig. 16 Extracted result of permeability with port distance (d 1 -n)
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International Journal of Advancements in Research & Technology, Volume 2, Issue 3, August-2013
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Form the extracted parameters for the variation in the boundary conditions, it is observed that proposed 9-shaped structure
is still behaving as DNG (ε<, μ<0) with subsequent change in
the negative refraction bandwidth. For port excitation with
distance (d 1 ), NRI is achieved in the frequency range (12-14.5)
GHz and a notch at 19.5 GHz, for port excitation with distance
(d 1 -n) NRI is achieved in the frequency range (10-11.3) GHz
and for port excitation with no gap (d 1 =0) NRI is achieved in
the frequency range (10.35-10.65) GHz and (11.6-13.3) GHz.
Fig. 17 Extracted result of refractive index with port distance (d 1 -n)
5 RESULT AND DISCUSSION
After the analysis of variations in boundary condition around
the proposed 9-shaped MTM structure, it is found that orientation of structure with respect to the electromagnetic source
(say antenna) plays important role in obtaining the negative
refractive index in different ranges of frequency. Moreover
there is need to investigate the strength of negative refractive
index on the antenna parameters like gain and bandwidth. A
comparative analysis of results obtained for 9-shaped MTM
with different port excitation is shown in Table 2.
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Table 2 Parametric Results of (BC) Variation in 9-shaped MTM
Fig. 18 Extracted result of permittivity with port distance (d 1 =0)
Sr.no
1
Fig. 19 Extracted result of permeability with port distance (d 1 =0)
Boundary
Condition
x-Et,y-Ht,z-open
(Reference case)
NRIBandwidth(GHz)
4.3
Negativity
Strength of RI
-5
2
x-Et,Z-Ht,
y-open, (d 1 )
1.25
-5
3
x-Et,Z-Ht,
y-open,(d 1 -n)
1.4
-6
4
x-Et,Z-Ht,
y-open, (d 1 =0)
2.2
-6
Also it is observed that the negative refractive index bandwidth increases as the waveguide port excitation distance decreases in case of d 1 , d 1 -n and d 1 =0 configuration, thereby
forming an inverse relation between NRI bandwidth and
waveguide port distance.
6 CONCLUSION
Fig. 20 Extracted result of refractive index with port distance (d 1 =0)
Copyright © 2013 SciResPub.
A 9-Shaped MTM has been designed to achieve negative refractive index in the wider range of frequency band. The effect
of variation in the practical boundary conditions defined
around the metamaterial is studied. It is noted that there is
need to improve the negative refractive index in terms of its
negativity which will eventually allow ameliorating the anIJOART
International Journal of Advancements in Research & Technology, Volume 2, Issue 3, August-2013
ISSN XXXX-XXXX
102
tenna parameters like gain and bandwidth. The future work
aims to design metamaterial with improved negative refractive index strength and integration of the proposed 9-shaped
metamaterial structure over the antennas operating in the frequency band between 10 GHz to 20 GHz.
ACKNOWLEDGMENT
The authors would like to thanks all the experts for their support.
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