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...
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