Left-Handed Wave Propagation of a Coplanar Waveguide based on Split Ring Resonators
Due to the absence of 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 wth effectice permittivity and permeability is obtained. The famous concept of SRR is used here and is described in further detail in [1]. Various concepts are described and also 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 recantangular 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 left-handed material (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: Fig.4: S-Parameters for the LH SRR-CPW structure
Figure 5: Fig. 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: Fig.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 behaviour 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: LH- wave propagation in a CPW coupled to split ring resonators (SRR) 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
CST Article "Left-Handed Wave Propagation of a Coplanar Waveguide based on Split Ring Resonators"
last modified 15. Dec 2006 10:32
printed 6. Oct 2008 6:59, Article ID 246
URL:
All rights reserved.
Without prior written permission of CST, no part of this publication may be
reproduced by any method, be stored or transferred into an electronic data processing system, neither mechanical or by any other method.
Article ID: 246
Last modified: 15. Dec 2006 10:32
Other Articles
This example shows the simulation of a high voltage transformer bushing using CST EM STUDIO™'s Electrostatic solver.
Read full article..
This example shows the simulation of a conductor backed coplanar waveguide with a ground via fence for reducing EMI radiation. The excellent agreement between simulation and simulated results can be observed.
Read full article..
This article demonstrates the application of CST MICROWAVE STUDIO® (CST MWS) to the analysis of large reflector feed arrays. An array consisting of 19 elements was simulated but a larger array of more than 100 elements may also be simulated since the memory scaling with mesh cells in CST MWS is almost linear. The simultaneous excitation feature in CST MWS was applied to obtain farfield patterns in just a single simulation. A parameter sweep was also carried out to obtain the S-Parameters as a funtion of element feeding postion.
Read full article..
This article summarises the simulation study conducted with CST MICROWAVE STUDIO® (CST MWS) of thin-film silicon solar cells with nano-structured interfaces. The good agreement between the experimental data and solar cell simulations shows the reliability and versatility of the performed FIT simulations to
investigate nano-optics of thin-film solar cell devices in 3 dimensions.
This article is presented with the courtesy and permission of Hasse, C. and Stiebig, H. , Forschungszentrum Juelich who gave a presentation of their work at the CST European User group Meeting at Boppard, Germany, 9-10th March 2006.
Read full article..
Scott McMorrow, Steve Weir, Teraspeed Consulting Group LLC
Fabrizio Zanella, CST of America
Read full article..