CST – Computer Simulation Technology

Left-Handed Wave Propagation of a Coplanar Waveguide based on Split Ring Resonators

Due to the absence of left-handed materials (LHMs) in nature, a LHM medium has to be artificially fabricated. This can be achieved by micro-structuring a material in a length scale shorter than a wavelength, so that a continuous medium with effective permittivity and permeability is obtained. The famous concept of the Split Ring Resonater (SRR) is used here and is described in further detail in [1]. Various concepts are described, as well as the measurement setups to operate in desired frequency bands. The measurement setup is modeled and simulated by CST MICROWAVE STUDIO® (CST MWS) : The model consists of a single SRR placed inside a circular aperture made in a metallic screen placed in a piece of rectangular waveguide as shown in Fig.1.



Figure 1: Model setup for simulating the SRRs magnetic polarizabilities...

An edge-coupled SRR design was used in this simulation model and Fig. 2 presents a typical simulation result with a peak of S21 at the SRRs resonance.



Figure 2: A typical response of the S-parameters

The proposed implementation of a left-handed structure [2] is depicted in Fig.3: It consists of a host ordinary coplanar waveguide (CPW). SRRs are symmetrically placed in the back side of the substrate. Thin wires connect the signal-line to the grounded sidelines of the CPW at coincident positions with the SRR's centers, shown in Fig. 3.



Figure 3: CST-MWS Model of the SRR-based LH - CPW

The dispersion relation given for a lumped element circuit model described in [2] forms a narrow pass band just above the resonant frequency of the rings. Since the wave propagation constant beta decreases with frequency, phase and group velocity are antiparallel. Therefore negative wave propagation occurs and the structure behaves as a narrow band LHM. Fig. 4 shows the S-parameter response. In Figs. 5 and 6 an animated plot is shown for the magnetic fields at the center of the passband and outside of the passband, respectively.



Figure 4: S-Parameters for the LH SRR-CPW structure


Figure 5: Propagation H-Field at the passband center. The port excitation incidents a propagating wave at the left side of the picture. Note the reversed propagation in the vicinity of the SRRs


Figure 6: H-Field at a vertical cutplane for a frequency above the passband

The current density of the SRRs can be seen in Fig. 7.



Figure 7: Animated Current density plot. The phase propagation can nicely be seen travelling from right to left

If connecting wires are removed, effective permittivity is no longer negative and the passband behavior is expected to change to a stop band. The pertinent CST MWS model and the S-parameters are shown in Figs. 8 and 9.



Figure 8: CPW Structure with wires removed


Figure 9: Simulated S-parameters for the model without connecting wires

Conclusion: left-handed wave propagation in a CPW coupled to SRRs and periodically loaded with signal-to-ground wires of the CPW acting as inductors has been shown. Since negative permeabiltiy and permittivity coexist only in the vicinity of the resonant frequency of the rings, signal propagation is limited to a narrow frequency band. The models were simulated with CST MWS and results agree very well with data given in [2].

References

[1] R. Marques, F. Mesa, J. Martel,F. Medina: "Comparative Analysis of Edge- and Broadside coupled SRRs for meta material design - Theory and experiments", IEEE Trans. on Ant. and Prop. , Vol 51, No. 10, Oct 2003

[2] F. Martin, J. Bonache, F. Falcone, M. Sorolla, R. Marques: "Split-Ring Resonator-based left-handed coplanar waveguide", Applied Physics Letters, Vol. 83, No. 22, 1 Dec 2003

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