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An Interdigitated Split Ring Resonator for Low Frequency

Metamaterials

Sung-Min Sohn, J. Thomas Vaughan*, and Anand Gopinath

Department of Electrical and Computer Science Engineering, University of Minnesota

200 Union Street SE, Minneapolis, Minnesota 55455, USA

Email: sohnx021@umn.edu

*Center for Magnetic Resonance, University of Minnesota,

2021 Sixth Street SE, Minneapolis, MN 55455

Abstract

An interdigitated split ring resonator (IR) has been proposed to obtain negative magnetic permeability ()

and also negative refractive index (n) by itself. Its electromagnetic properties have been characterized using anumerical simulator (HFSS). The experimental results show that the resonators exhibit a negative permeabil-ity and refractive index and may be used for planar metamaterial structures at low frequency ranges below afew GHz.

1. IntroductionA new design of a split ring resonator for generating metamaterials at low frequencies is discussed in

this paper. Metamaterials require simultaneously thin metallic strips for the negative permittivity ()

and ring resonators with a gap for a negative permeability [1],[2]. Resonances at RF low frequencies,

from a few tens of megahertz to a few gigahertz frequencies, require high capacitance and/or induc-

tance which determine resonant frequencies. The Ozbay group has proposed planar spirals as resona-

tors for low frequency metamaterials, because they provide a split ring resonator with high inductive

values [3]. These spiral resonators (SRs), however, require additional metallic strips behind the sub-strate for negative indices. When constraints such as size and operating bandwidth in RF regions are

defined, increasing capacitive and/or inductive values by changing the geometry should be carried out.

It, therefore, brings about the miniaturization of resonators for use at RF regions. However, the inci-

dent wave magnetic field must be oriented perpendicular to the plane of resonator, and the electric

field must be oriented parallel to the metallic strip [2],[4]. If small planar structures that resonate under

a few GHz range can be designed, the scope of metamaterial applications will be enormously enlarged,

and this paper provides a miniaturization technique.

2. Novel interdigitated split ring resonator structureAn interdigitated split ring resonator (IR) is proposed to miniaturize the structure for resonant opera-

tion at the desired RF frequency by increasing capacitance of the structure. Furthermore, the proposed

resonator is a planar structure and possesses negative refractive index without a metallic strip behindthe substrate. Fig. 1 (a): shows the proposed IR which is composed of pairs of fingers and a frame on a

substrate that has the thickness (h). This reso-

nator lines have width (w), thickness (t), and a

square frame length of a unit cell (l). Each

pair of fingers has spacing (s1) and overlapped

length (s2) creating capacitance between fin-

gers. The distance between pairs of fingers

(s3) depends on the number of pairs (n) and

the length of the frame. Comparing the pro-

posed structure with other planar resonators

[3], the primary difference is that there are

pairs of fingers which are evenly distributedinside the frame. It is possible to obtain reso-

(a) (b)Fig. 1: (a) Unit cell diagram of IR (b) A manufac-tured unit cell

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nant frequencies which have a more linear variation with changing design parameters. A time varying

magnetic field applied perpendicular to the plane of the IR will induce circulating currents. This circu-

lating current will result in a buildup of charge across the space between fingers with the energy stored

as a capacitance [5]. Thus this structure is similar to a simple LC circuit with a resonant frequency(fLC) due to the capacitance between the fingers and the inductance from the current path of the loop of

the resonator.

3. The properties of interdigitated split ring resonator structure

A. Resonance frequency

Fig. 2: shows that the resonant frequencies are inversely proportional to parameters of the size of the

unit cell and the number of finger pairs. Among several design parameters, the side of the square unit

cell (l) is the primary variable affecting the resonant frequency, as shown in Fig. 2 (a). The number of

fingers also affects the resonant frequency as shown in Fig. 2 (b), but the effect is smaller. The varia-

tion in resonant frequency is larger with a smaller number of finger pairs. As the number of finger

pairs increase, the response becomes linear. The resonant frequency of spiral resonator varies

sharply with a few turns, and then remains almost constant [3]. To design a resonator for a par-ticular frequency, the unit cell side is chosen first, followed by the number of pairs of fingers, and fi-

nally s1and s2are chosen.

B. Negative index

The metallic strip behind a split ring resonator behaves as a medium with negative effective permit-

tivity if the electromagnetic wave propagates with electric field, E, parallel to the strip. The proposed

IR has increased capacitance within the loop frame due to the added finger pairs which create negative

permittivity without the metallic strip on back side of substrate. When designing a metamaterial, the

proper characteristics are not obtained if a thick substrate is used, as the presence of the strip on the

back side of the thick substrate does not couple the negative permittivity to the negative permeability

of the split ring resonator. The proposed structure with a frame and fingers creates negative permittivi-

ty as well as negative permeability without the strip. This statement is supported by the results of thesimulation discussed above and experiment.

(a) (b)

Fig. 2: Properties of IR; (a) resonant frequency vs. the square unit cell side (l) as the number of pairs offingers (n=6, 10, 14, w=0.1mm); (b) resonant frequency vs. the number of pairs of fingers (n) for a fixed side of

unit cell (l=8, 10, 12mm, w=0.1mm) on Rogerss RT/duroid 5880 substrate (=2.2).

4. Experimental results

The fabricated IRs (w=0.2mm, n=2, t=18of copper foils on Rogerss RT/duroid 5880 substrate,

=2.2 ) are evaluated as shown in Fig. 3 (a). The measured amplitude of scattering parameters is plot-

ted in Fig. 3 (b), and Fig. 3 (c) plots the effective phase shifts calculated using a reference plane shift

from the antennas to the plane at the center of the resonator. The interdigitated split ring resonator hasindices of negative refraction, shown in Fig. 3 (d), without the need of a metallic strip. Parameters

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(a) (b)

(c) (d)

Fig. 3: (a) experimental setup (b) measured scattering parameters with single and array structure (c)the phase shift and (d) reflective index and permeability

including refractive index and permeability have been calculated from measured scattering parameters

by the equations in reference [6]. The negative index band is formed in the resonance frequency region

with the change in phase shift. These results correspond to the dip in the phase of S21, which indicates

the presence of a negative index band [6].

5. Conclusion

In conclusion, this paper has proposed the interdigitated split ring resonator (IR). Simulation results

show that resonant frequencies are linearly varied by increasing capacitance with increased number of

finger-pairs. Experimental results have shown that negative refractive indices have been obtained with

a planar structure without metal strip behind the substrate.

References

[1] D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Metamaterials and negative refractive index, Science.vol. 305, pp. 788-792, August 2004.

[2] P. Markos and C. M. Soukoulis, Wave propagation, New Jersey: J. Princeton University Press, 2008.[3] K. B. Alici, F. Bilotti, L. Vegni, and E. Ozbay, Miniaturized negative permeability materials,Appl.

Phys. Lett.,vol. 91, 071121, 2007.[4] M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, Left-

handed metamaterials: detailed numerical studies of the transmission properties,J. Opt. A.,S12,No2.,2005.

[5] D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Composite medium withsimultaneously negative permeability and permittivity, Phys. Rev. Lett., vol. 84, pp. 4184-4187, May

2000.[6] D.R. Smith, D. C. Vier, Th. Koschny,and C. M. Soukoulis, Electromagnetic parameter retrieval frominhomogeneous metamaterials, Phys. Rev. E.vol. 71, 036617, 2005.

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