Progress In Electromagnetics Research Symposium Proceedings, Marrakesh,Morocco, Mar. 20–23, 2011 315

A New Multi-ring SRR Type Metamaterial Design with MultipleMagnetic Resonances

O. Turkmen1, 2, E. Ekmekci1, 3, and G. Turhan-Sayan1

1Department of Electrical and Electronics EngineeringMiddle East Technical University, Ankara, Turkey

2Department of Electronics and Telecommunications EngineeringKocaeli University, Kocaeli, Turkey

3Department of Electronics and Communication EngineeringSuleyman Demirel University, Isparta, Turkey

Abstract— In this study, we propose a new SRR unit cell design for multi-band metamaterialapplications. The suggested unit cell structure consists of N number of concentric split ringsto obtain magnetic resonances at N distinct frequencies. The value of each distinct resonancefrequency can be adjusted by changing design parameters such as metal widths and gap distancesfor each ring as well as ring-to-ring separations. The suggested multi-band structure is simulatedusing CST Microwave Studio. Effective medium parameters of the resulting multi-ring SRR typemetamaterials are estimated by a retrieval algorithm.

1. INTRODUCTION

Metamaterials are specially designed periodic structures which can show unique properties such ashaving negative values of permeability and/or negative values of permittivity over finite frequencybands. Theoretical aspects and many important applications of metamaterials in microwave, ter-ahertz and optic regions have been investigated in detail in a vast amount of publications for thelast decade [1–6]. Split ring resonator (SRR) type magnetic resonators are among the most popu-lar metamaterial structures having negative permeability over narrow frequency bands. Althoughvarious forms of SRR structures have been found useful in narrowband applications, research onmetamaterials has also been focused recently on the design of multiband and/or frequency tunablemetamaterials.

In this study, a new N -ring SRR unit cell design is introduced for multi-band metamaterialapplications. For a given substrate material, design parameters are the side lengths and widthsof metal strips, gap distances for each ring, and the separation distances between the rings. As aproof of concept, several multi-band SRR arrays are designed and simulated in this paper for threedifferent cases (for N = 1, 2 and 3) by using CST Microwave Studio. Complex transmission andreflection characteristics (i.e., the complex S-parameters S21 and S11) of the proposed SRR arraysare obtained by CST, and then they are used to extract the effective medium parameters µeff andεeff of the designed metamaterials to verify the nature of resulting resonances. The basic retrievalprocedure given in [7] is used for parameters estimation.

2. DESIGN AND SIMULATIONS

The schematic view of the proposed multi-ring unit cell for the case of N = 3 is shown in Figure 1together with the excitation details where propagation direction is in the direction of x-axis, incident

Figure 1: Simulation setup and the excitation.

316 PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011

H field is perpendicular to the SRR plane (i.e., in the direction of z-axis) and the incident E fieldis perpendicular to the gap containing edges of the SRR rings (i.e., in the direction of y-axis). Acubic computational region with a side length of 7.5mm is used during the simulation procedureas shown in Figure 1. The PEC type boundary conditions are applied at the boundary surfacesperpendicular to the E field while the PMC type boundary conditions are applied at the boundarysurfaces perpendicular to the H field. Remaining boundaries are defined as the input and outputports. Using this setup, single-ring, two-ring and three-ring SRR arrays are designed and simulatedon a planar substrate with the relative permittivity of 4.4 and the loss tangent of 0.001. Metallicinclusions are made of copper with the thickness of 0.035mm and the conductivity of 5.8×107 S/m.Dimensions of the substrate in the x, y and z directions are 7.5 mm, 7.5 mm and 0.6mm respectively.

Each one of the SRR arrays simulated in the first step of this work are composed of only onetype of single-ring square-shaped unit cells shown in Figure 2 where the side lengths (L) of the SRRmetal rings are chosen to be 6mm, 5 mm and 4 mm for the SRR-A, SRR-B and SRR-C type unitcells, respectively. The same gap distance g = 0.25mm and the same metal strip width w = 0.2mmare used in these three different unit cells.

In the next step, a two-ring SRR unit cell is designed by combining the SRR-A and SRR-B unitcell topologies which are aligned in the gap-to-gap configuration as shown in Figure 3(a). Similarly,

(a) SRR-A (b) SRR-B (c) SRR-C

Figure 2: Front view of the single-ring square-shaped SRR unit cells with different parameters.

(a) (b)

Figure 3: Multi-ring SRR unit cell structures with two and three-rings.

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Progress In Electromagnetics Research Symposium Proceedings, Marrakesh,Morocco, Mar. 20–23, 2011 317

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Figure 4: Transmission and reflection spectra of the single-ring SRR arrays shown in Figure 2. (a) Magnitudeof S21. (b) Phase angle of S21. (c) Magnitude of S11. (d) Phase angle of S11.

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Figure 5: Transmission and reflection spectra, and the effective medium parameters for the two-ring SRRarray. (a) Magnitudes of S21 and S11. (b) Phase angles of S21 and S11. (c) Real and imaginary parts ofεeff . (d) Real and imaginary parts of µeff .

a three-ring SRR unit cell is also designed by combining all three types of unit cells SRR-A, SRR-Band SRR-C as given in Figure (3b). In both of these configurations, the distance between the rings

318 PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011

is chosen to be s = 0.3mm.

3. RESULTS

Complex S-parameters S21 and S11 computed for the single-ring array topologies SRR-A, SRR-Band SRR-C revealed magnetic resonance frequencies at 4.24GHz, 5.34 GHz, and 6.77GHz, respec-tively. The magnitude and phase plots for these transmission and reflection spectra are shownin Figure 4(a) through 4(d). Increase in the side length (and hence in the overall length) of themetal ring results in an increase of the self inductance [8] leading to a decrease in the LC resonancefrequency of the resonator, as expected.

Next, the magnitude and phase spectra of the S21 and S11 parameters are computed for thetwo-ring SRR topology of Figure 3(a). Resulting plots are given in Figure 5 together with the plotsfor the real and imaginary parts of the retrieved parameters, effective permittivity and effectivepermeability. As seen in Figure 5, the two-ring SRR array structure has three distinct resonancesover the range from 1GHz to 10 GHz. Two of those frequencies at 4.01 GHz and 5.19 GHz aremagnetic resonances and the last one at 8.96 GHz is an electric resonance.

As shown in Figure 6, on the other hand, the three-ring SRR array has four distinct reso-nances. Three of them (at 4.1 GHz, 5.05 GHz and 6.53 GHz) are magnetic resonances and the oneat 8.95 GHz is an electric resonance. These results demonstrate that a desired number of magneticresonances can be realized by selecting the number of SRR rings within the limits of geometricalconstraints. It is also worth mentioning that resonance frequencies can also be adjusted by changingthe design parameters g, w and s.

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Figure 6: Transmission and reflection spectra, and the effective medium parameters for the three-ring SRRarray. (a) Magnitudes of S21 and S11. (b) Phase angles of S21 and S11. (c) Real and imaginary parts ofεeff . (d) Real and imaginary parts of µeff .

Progress In Electromagnetics Research Symposium Proceedings, Marrakesh,Morocco, Mar. 20–23, 2011 319

4. CONCLUSIONS

The possibility of multiple magnetic resonances with negative permeability bands are demonstratedfor the suggested multi-ring SRR topologies, where the number of resonances is determined bythe number of concentric rings. Also, this topology has the flexibility of adjusting the resonancefrequencies by changing the design parameters such as the gap width, metal width and inter-ringdistances. It should be noted that this multi-ring SRR structure is also capable of displayingmultiple electrical resonances under proper excitation conditions. It is believed that the proposedmulti-ring SRR design will provide an electrically small and easy-to-fabricate alternative to thepresent multi-band metamaterial structures [9, 10]. As a future work, proposed SRR structures willbe fabricated and the simulation results will be verified by experimental results. Equivalent circuitmodel of the multi-ring SRR array structure will also be investigated.

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9. Ekmekci, E., K. Topalli, T. Akin, and G. Turhan-Sayan, “A tunable multi-band metamaterialdesign using micro-split SRR structures,” Opt. Express, Vol. 17, No. 18, 16046–16058, 2009.

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