The electromagnetic theory of diffraction and the Babinet principle are applied to the design of artificial metasurfaces and metamaterials. A new particle, the complementary split rings resonator, is proposed for the design of metasurfaces with high frequency selectivity and planar metamaterials with a negative dielectric permittivity. Applications in the fields of frequency selective surfaces and polarizers, as well as in microwave antennas and filter design, can be envisaged. The tunability of all these devices by an applied dc voltage is also achievable if these particles are etched on the appropriate substrate. DOI: 10.1103/PhysRevLett.93.197401 PACS numbers: 78.20.Ci, 41.20.Jb, 42.25.Fx, 84.40.-x Artificial metamaterials and metasurfaces with special electromagnetic properties have been a subject of growing interest in recent years [1,2]. Most proposed metamaterials make use of split ring resonators (SRRs) [3], or similar geometries, to achieve a negative effective permeability in a certain frequency range. The negative permittivity has been commonly obtained from an array of metallic wires or plates [2,4]. No particles acting as point electric dipoles with negative polarizability have been proposed to the date. In addition to these bulk metamaterial designs, one-and two-dimensional planar microwave circuits which show a left-handed behavior have been recently proposed [5][6][7], some of them making use of the SRR concept [7]. More recently, the application of these concepts to the design of artificial surfaces with special electromagnetic properties has been considered [8].In this Letter we present a new approach for the design of planar metamaterials and metasurfaces, which is based on the Babinet principle. The key element of this new approach is the complementary split ring resonator (CSRR), the complementary screen of the SRR (see Fig. 1). As a first step in our analysis the behavior of a perfectly conducting and infinitely thin SRR in an external electromagnetic field E 0 ; B 0 [see Fig. 2(a)] is considered. The scattered field E 0 ; B 0 is approximately given by the field produced by a resonant magnetic dipole [3]where ! 0 is the frequency of resonance of the SRR and 0 is a geometrical factor. This approximation neglects higher order multipolar fields [2,3]. It also neglects cross-polarization effects [9,10] (these effects are considered later in this Letter). Let us now consider the behavior of the CSRR when it is illuminated from z < 0 by an external electromagnetic field E 0 c ; B 0 c [see Fig. 2(b)].According to the electromagnetic theory of diffraction [11], the field in the shadowed region (z > 0) is the field scattered by the CSRR, E 0 c ; B 0 c . For z < 0, the total field is given by [11]where E 0;r c ; B 0;r c is the field that would be reflected by the metallic screen without the CSRRs etched on it. The scattered fields, E 0 c ; B 0 c and E 0 ; B 0 , must fulfill some symmetries that arise from the fact that they are produced by currents which are confined in the z 0 plane: the compone...

In this letter, a planar left-handed propagating medium consisting of a coplanar waveguide ͑CPW͒ inductively coupled to split ring resonators ͑SRR͒ and periodically loaded with narrow metallic wires is proposed. The wires make the structure behave as a microwave plasma with a negative effective permittivity which covers a broad frequency range. The negative permeability required to achieve left-handed wave propagation is provided by the rings in the vicinity of their resonant frequency. The result is a structure which allows negative wave propagation in a narrow frequency band. The transmission coefficient measured in a fabricated prototype device exhibits very low insertion losses in the pass band and high-frequency selectivity. Since rings are much smaller than signal wavelength at resonance and can be easily tuned, SRR-CPW-based structures are of interest for the design of very compact microwave circuits based on left handedness. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1631392͔The development of artificial materials ͑metamaterials͒ with simultaneously negative permeability and permittivity, or left-handed materials ͑LHMs͒, has been a subject of growing interest in recent years. Apart from its exotic electrodynamic properties ͑such as the reversal of Snell's law, Doppler effect, and Cherenkov radiation͒, pointed out by Veselago more than 30 years ago, 1 key to this interest is the potential applicability of these metamaterials to the fabrication of radio frequency ͑rf͒ and microwave components based on left handedness. Due to negative values of effective permittivity and permeability, LHMs are negative refractive index media with antiparallel phase and group velocities. 2,3 Namely, the wavevector k forms a left-handed triplet with the vectors E and H ͑the electric and magnetic field intensity͒ and wave fronts for propagating electromagnetic ͑EM͒ waves travel toward the source, i.e., opposite to the direction of energy flow.Due to the absence of transparent LHMs in nature, a LHM medium has to be artificially fabricated. This can be achieved by microstructuring a material in a length scale much shorter than the wavelength of EM radiation, so that a continuous medium with effective electromagnetic properties ͑permittivity and permeability͒ is obtained. An artificial LHM operating in the microwave region was reported by Smith et al. 4 The structure was fabricated by combining a periodic array of metal posts with an array of nonmagnetic split ring resonators ͑SRRs͒. Originally proposed by Pendry, 5 SRRs provide a negative effective permeability in the vicinity of the resonant frequency, while metallic wires behave like a two-dimensional ͑2D͒ plasma with negative permittivity up to the plasma frequency. Left-handed wave propagation has been also demonstrated in a one-dimensional ͑1D͒ configuration consisting of a hollow metallic waveguide periodic loaded with SRRs. 6 For EM propagation in the axial direction, the metallic waveguide emulates a lossless plasma whose dielectric permittivity is negative be...

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The symmetry properties of split ring resonators (SRRs) are exploited for the implementation of novel sensing devices. The proposed structure consists of a coplanar waveguide (CPW) loaded with movable SRRs on the back substrate side. It is shown that if the SRRs are placed with the slits aligned with the symmetry plane of the CPW, the structure is transparent to signal propagation. However, if the symmetry is broken, a net axial magnetic field can be induced in the inner region of the SRRs, and signal propagation is inhibited at resonance. The proposed structures can be useful as alignment sensors, position sensors and angle sensors. This novel sensing principle is validated through experiment.

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In this paper, the behavior at resonance of split ring resonators ͑SRRs͒ 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 resonance͒ 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.

In this paper compact alignment and position sensors based on coplanar waveguide (CPW) transmission lines loaded with split ring resonators (SRRs) are proposed. The structure consists of a folded CPW loaded with two SRRs tuned at different frequencies to detect both the lack of alignment and the two-dimensional linear displacement magnitude. Two additional resonators (also tuned at different frequencies) are used to detect the displacement direction. The working principle for this type of sensor is explained in detail, and a prototype device to illustrate the potential of the approach has been designed and fabricated.

In this paper, angular displacement and angular velocity sensors based on coplanar waveguide (CPW) transmission lines and S-shaped split ring resonators (S-SRRs) are presented. The sensor consists of two parts, namely a CPW and an S-SRR, both lying on parallel planes. By this means, line-to-resonator magnetic coupling arises, the coupling level being dependent on the line-to-resonator relative angular orientation. The line-to-resonator coupling level is the key parameter responsible for modulating the amplitude of the frequency response seen between the CPW ports in the vicinity of the S-SRR fundamental resonance frequency. Specifically, an amplitude notch that can be visualized in the transmission coefficient is changed by the coupling strength, and it is characterized as the sensing variable. Thus, the relative angular orientation between the two parts is measured, when the S-SRR is attached to a rotating object. It follows that the rotation angle and speed can be inferred either by measuring the frequency response of the S-SRR-loaded line, or the response amplitude at a fixed frequency in the vicinity of resonance. It is in addition shown that the angular velocity can be accurately determined from the time-domain response of a carrier time-harmonic signal tuned at the S-SRR resonance frequency. The main advantage of the proposed device is its small size directly related to the small electrical size of the S-SRR, which allows for the design of compact angular displacement and velocity sensors at low frequencies. Despite the small size of the fabricated proof-of-concept prototype (electrically small structures do not usually reject signals efficiently), it exhibits good linearity (on a logarithmic scale), sensitivity and dynamic range.