# design of 9-shaped metamaterial for enhanced negative refractive index bandwidth

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International Journal of Advancements in Research & Technology, Volume 2, Issue 8, August-2013 97 ISSN 2278-7763

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Design of 9-Shaped Metamaterial for Enhanced Negative Refractive Index Bandwidth

Rahul Yadav, Amit Kumar Yadav 1,2M.E Student, Dept. Of Electronics and Telecommunication, Thakur College of Engineering & Technology, Mumabi, India-400101 [email protected]

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 in-vestigate its effect on metamaterail potential parameters. The extraction of metamaterial parameters is done using Nicolson-Ross-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 mate-rials which exhibits negative permittivity (- ε ), negative per-meability (-µ ) and negative refractive index (NRI) in the mi-crowave frequency range for isotropic medium, and which do not occur naturally. Metamaterial are also called doubly nega-tive 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]. 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 effective-ly lowers the radiation efficiency of the antenna. Thus employ-ing 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 struc-ture 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 condi-tions around the designed metamaterial are also altered to

investigate the effect on metamaterial parameters.

2 DESIGN OF METAMATERIAL SUPERSTRATE A 9-shaped coupled structure is designed with substrate per-mittivity of 3.38. For this Gil GML 1034 (lossy) substrate of thickness 1.6mm is used. A three-dimensional unit cell is ini-tially 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 (y-axis) 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 con-ditions 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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Fig. 2 MTM structure with boundaries

The parametric values of 9-shaped metamaterial (MTM) struc-ture are shown in Table 1.

Table 1 Geometric dimensions of 9-Shaped (MTM)

Sr.no Parameter Dimension (mm) 1 Height of Substrate (h) 1.6 2 Length of Substrate (L) 4 3 Width of Substrate (W) 4 4 Thickness of Meta Strip (t) 0.44 5 Length of Metamaterial(L1) 3 6 Width of Metamaterial (W1) 3

3 RESPONSE VERIFICATION OF 9-SHAPED MTM The s-parameters i.e. (magnitude and phase) of proposed 9-shaped MTM are simulated for verification of metamaterial properties. Plot of reflection coefficient (S11) and transmission coefficient (S21) is shown in Fig.3 and argument of respective scattering coefficient is shown in Fig .4.

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 S11 and at 10.84 GHz and 13.7 GHz for S21.

Fig. 4 Plot of phase of scattering coefficient for 9-shaped MTM

3.1 Retrieval & Characterization of 9-Shaped MTM Extraction of potential parameters of proposed 9-shaped met-amaterial is done using Nicholson-Ross-Weir (NRW) ap-proach. 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 transmis-sion and reflection coefficient for normal incident waves on MTM, which is given by,

212

11 2 212

(1 )1

TST

− Γ=

−Γ (1)

212

21 2 212

(1 )1

TST

−Γ=

−Γ (2)

Where ‘T’ is the transmission propagation factor given by exp( )T j lβ= − (3) Solution of equation 1 and 2 yields,

11 21 12

11 21 12

( )1 ( )

S STS S+ −Γ

=− + Γ

(4)

2 2 2 221 11 21 11

2111 11

1 ( ) 1 ( )[ ] 12 2S S S S

S S− − − −

Γ = ± − (5)

2

21 1X XΓ = ± −

(6) Now since the mode of operation is microstrip, this yield in effective permittivity and effective permeability.

12

12

11

eff

eff

Xµ

ε+ Γ

= =−Γ

(7)

0 ln( )eff effcY j zdw

µ ε= = (8)

Where, Y is the propagation constant. Thus, the permittivity and permeability can be obtained as , , /eff eff real eff imgj Y Xε ε ε= − = (9)

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, ,eff eff real eff imgj YXµ µ µ= − = (10) The Snell-Decartes law implies that the refractive index can be defined as eff effn µ ε= (11) To retrieve the metamaterial parameters like negative permit-tivity, 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. 5 Extracted result of MTM unit cell for permittivity

Fig. 6 Extracted result of MTM unit cell for permeability

Fig. 7 Extracted result of MTM unit cell for negative refractive index

Fig. 8 Extracted result of MTM unit cell for effective wave impedance

From the extracted parameters of 9-shaped metamaterial, re-sult of permittivity exhibits a negative response in the fre-quency 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 dou-ble negative material (DNG).

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, ini-tially 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 respec-tively.

Fig. 9 9-Shaped MTM with waveguide port excitation at dist. (d1 )

Fig. 10 9-Shaped MTM with waveguide port excitation at dist. (d1 – n)

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Fig. 11 9-Shaped MTM with waveguide port excitation distance (d1 = 0)

For analysis purpose, let us assume that distance is varying in terms of variable (dn) 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;

( 1 / )X d v mE And ( 1 / )Z d A mH i.e. out of ‘K’ fields only ‘d1-W’ fields will be polarized with respect to the MTM. Here wave-guide port excitation covers only (h×L) area and therefore indicates that for practical realization the metamaterial struc-ture should be placed exactly on the top of the EM source. For distance ‘d1-n’ the electric fields and magnetic fields will be

polarized as ( 1 / )X d n v mE − and ( 1 / )Z d n A mH − . But in case of d1=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+∆h1 by L), therefore the metamaterial structure will be place exactly over EM source by an incremental gap of ‘∆h1’. Where ‘h1’ is the height above the EM source. To verity the effect, potential parameters for these configura-tions are extracted as shown in Fig. 12-20.

Fig. 12 Extracted Result of Permittivity with port distance (d1)

Fig. 13 Extracted result of permeability with port distance (d1)

Fig. 14 Extracted result of refractive index with port distance (d1)

Fig. 15 Extracted result of permittivity with port distance (d1-n)

Fig. 16 Extracted result of permeability with port distance (d1-n)

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Fig. 17 Extracted result of refractive index with port distance (d1-n)

Fig. 18 Extracted result of permittivity with port distance (d1=0)

Fig. 19 Extracted result of permeability with port distance (d1=0)

Fig. 20 Extracted result of refractive index with port distance (d1=0)

Form the extracted parameters for the variation in the bounda-ry 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 (d1), NRI is achieved in the frequency range (12-14.5) GHz and a notch at 19.5 GHz, for port excitation with distance (d1-n) NRI is achieved in the frequency range (10-11.3) GHz and for port excitation with no gap (d1=0) NRI is achieved in the frequency range (10.35-10.65) GHz and (11.6-13.3) GHz.

5 RESULT AND DISCUSSION After the analysis of variations in boundary condition around the proposed 9-shaped MTM structure, it is found that orien-tation 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.

Table 2 Parametric Results of (BC) Variation in 9-shaped MTM

Sr.no Boundary

Condition NRIBandwidth(GHz) Negativity

Strength of RI 1 x-Et,y-Ht,z-open

(Reference case)

4.3 -5

2 x-Et,Z-Ht, y-open, (d1)

1.25 -5

3 x-Et,Z-Ht, y-open,(d1-n)

1.4 -6

4 x-Et,Z-Ht, y-open, (d1=0)

2.2 -6

Also it is observed that the negative refractive index band-width increases as the waveguide port excitation distance de-creases in case of d1, d1-n and d1=0 configuration, thereby forming an inverse relation between NRI bandwidth and waveguide port distance.

6 CONCLUSION

A 9-Shaped MTM has been designed to achieve negative re-fractive 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 an-

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tenna parameters like gain and bandwidth. The future work aims to design metamaterial with improved negative refrac-tive index strength and integration of the proposed 9-shaped metamaterial structure over the antennas operating in the fre-quency band between 10 GHz to 20 GHz.

ACKNOWLEDGMENT The authors would like to thanks all the experts for their sup-port.

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[3] Ma, Y. G., P. Wang, X. Chen, and C. K. Ong, “Near-field plane-wave-like beam emitting antenna fabricated by anistropic metamaterial, ” Applied Physics Letters, vol.94, no.4, 2009.

[4] Pendry, J.B., A.J.Holden, D.J.Robin, and W.J.Stewart, “Low frequency Plasmon’s in thin-wire structures,” J.Physics-Condensed Matter, vol.10, pp. 4785-4809, 1998.

[5] V.Lucarini, J.J.Sarinen, K.E Peiponen, and E.M.Vartiainen, Kramers-Kronig Relation in Optical Materials Research, Berlin Germany, Springer-Verlag, 2005.

[6] D.K.Ghodgaonkar,V.V.Varadan,V.K.Varadan, Free-space Measure-ment of Complex Permittivity and complex permeability of Magnetic Materials at Microwave Frequencies, IEEE Transaction on Instrumen-tation and Measurements, vol.39, no.2, pp.387-394, 1990.

[7] Chen, Xudong, Grzegorczyk, Tomasz M., Wu, Bae-Ian, Pacheco Jr., Joe & Kong, Jin Au, “Robust method to Retrieve the Constitutive Ef-fective Parameters of Metamaterials,” Phy.Rev.E., 70, 016608, (2004).

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