J. D. Baena

Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines

In this paper, a new approach for the development of planar metamaterial structures is developed. For this purpose, split-ring resonators (SRRs) and complementary split-ring resonators (CSRRs) coupled to planar transmission lines are investigated. The electromagnetic behavior of these elements, as well as their coupling to the host transmission line, are studied, and analytical equivalent-circuit models are proposed for the isolated and coupled SRRs/CSRRs. From these models, the stopband/passband characteristics of the analyzed SRR/CSRR loaded transmission lines are derived. It is shown that, in the long wavelength limit, these stopbands/passbands can be interpreted as due to the presence of negative/positive values for the effective /spl epsiv/ and /spl mu/ of the line. The proposed analysis is of interest in the design of compact microwave devices based on the metamaterial concept.

Microwave filters with improved stopband based on sub-wavelength resonators

The main aim of this paper is to demonstrate the potentiality of sub-wavelength resonators, namely, split-ring resonators, complementary split-ring resonators, and related structures to the suppression of undesired spurious bands in microwave filters, a key aspect to improve their rejection bandwidths. The main relevant characteristics of the cited resonators are their dimensions (which can be much smaller than signal wavelength at resonance) and their high-Q factor. This allows us to design stopband structures with significant rejection levels, few stages, and small dimensions, which can be integrated within the filter active region. By this means, no extra area is added to the device, while the passband of interest is virtually unaltered. A wide variety of bandpass filters, implemented in both coplanar-waveguide and microstrip technologies, have been designed and fabricated by the authors. The characterization of these devices points out the efficiency of the proposed approach to improve filter responses with harmonic rejection levels near 40 dB in some cases. It is also important to highlight that the conventional design methodology for the filters holds. For certain configurations, the presence of the resonators slightly lowers the phase velocity at the frequencies of interest with the added advantage of some level of reduction in device dimensions.

On the resonances and polarizabilities of split ring resonators

In this paper, the behavior at resonance of split ring resonators (SRRs) and other related topologies, such as the nonbianisotropic SRR and the broadside-coupled SRR, are studied. It is shown that these structures exhibit a fundamental resonant mode (the quasistatic resonance) and other higher-order modes which are related to dynamic processes. The excitation of these modes by means of a properly polarized time varying magnetic and/or electric fields is discussed on the basis of resonator symmetries. To verify the electromagnetic properties of these resonators, simulations based on resonance excitation by nonuniform and uniform external fields have been performed. Inspection of the currents at resonances, inferred from particle symmetries and full-wave electromagnetic simulations, allows us to predict the first-order dipolar moments induced at the different resonators and to develop a classification of the resonances based on this concept. The experimental data, obtained in SRR-loaded waveguides, are in agreement with the theory and point out the rich phenomenology associated with these planar resonant structures.

Electroinductive waves in chains of complementary metamaterial elements

Electronductive waves supported by chains of resonators drilled on a metallic plate are presented. Propagation of energy comes as a consequence of the electric coupling between these resonators. Therefore, these waves are termed as electroinductive waves. They can be interpreted as the dual counterpart of the so-called magnetoinductive waves, which are due to the mutual inductances along chains of resonators. In order to show their existence, some electromagnetic simulations and experiments have been carried out, using as resonators the complementary particle of the split ring resonator. The reported result opens the way to a high variety of applications in one- and two-dimensional devices, such as transducers, delay lines, bends, power dividers, couplers, antennas, lenses, etc.

Bulk Metamaterials Made of Resonant Rings

In this brief review, we present the fundamentals of bulk resonant ring metamaterial (RRM) theory. Metamaterials made of resonant rings are discussed, and some basic design rules are provided. Homogenization (including spatial dispersion) of 3-D resonant ring latices is reviewed, with emphasis in isotropic designs. Edge effects in finite size metamaterial samples are discussed. Finally, possible applications and future trends are briefly reviewed.

Resonance and cross-polarization effects in conventional and complementary split ring resonators periodic screens

Frequency selective surfaces made of conventional and complementary split ring resonators (SRR and CSRR) are analyzed theoretically and experimentally. For the theoretical study a surface admittance approach is used, which holds for any arbitrary angle and polarization of a plane wave. This method is based on reported theories about the behavior of single SRR and CSRR. Experimental results in free space are provided in order to check the theory. Good qualitative agreement is observed between theory and experiment, although some quantitative disagreements still remain and need explanation. Application of these devices as frequency selective surfaces and polarization converters could be possible due to the high variety of the resonant and cross-polarization effects seen.

Self-Complementary Metasurface for Designing Narrow Band Pass/Stop Filters

A self-complementary metasurface is studied in this paper. The metasurface is a 2-D periodical arrangement of unit cells formed by a metallic printed split ring resonator and its complementary counterpart. It is demonstrated that this structure behaves like a very selective band-pass filter for a certain linear polarization while band-stop filtering is achieved for the orthogonal polarization over the same frequency range. This idea opens the door to a new class of frequency selective surfaces made of connected and unconnected elements, whose filtering properties are mechanically tunable from band-pass to band-stop by rotating the surface or the polarization.

Spatial Angular Filtering by FSSs Made of Chains of Interconnected SRRs and CSRRs

Two frequency selective surfaces (FSSs) made of an infinite set of parallel 1-D chains of interconnected split ring resonators (I-SRRs) and interconnected complementary split ring resonators (I-CSRRs) are studied. The main result was that the central frequencies of the stopband and passband can be strongly tuned by controlling the angle of incidence.

Direct Polarisability Extraction Method

The method of finding the polarisability of a particle under test is described in the paper. To this point the particle is placed inside the waveguide and its polarisability is calculated either from known field at the input and the output port or from scattering parameters. The method is verified by electromagnetic simulation in the case of particle with known polarisability

Metamaterial microstrip backward couplers for fully planar fabrication techniques

A novel approach to obtain metamaterials in microwave planar circuit technology compatible with fully planar fabrication techniques is described. Microstrip lines with dual split ring resonators (SRRs) etched on the ground plane along with series capacitive gaps in the upper conductor strip are considered. The occurrence of left-handed (metamaterial) wave propagation in such media is demonstrated. Then, a metamaterial coupler made of a regular microstrip line and a left-handed microstrip line is examined. Co-directional traveling waves result in contra-directional Poynting vectors on the lines thus leading to power being coupled backwards. Backward coupling much tighter than that achievable with traditional (also backward) /spl lambda//4-couplers of the same inter-line distance is reported.