2566 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 56, NO. 11, NOVEMBER 2008 Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial Fuli Zhang, Sylvain Potet, Jorge Carbonell, Member, IEEE, Eric Lheurette, Olivier Vanbésien, Xiaopeng Zhao, and Didier Lippens Abstract—Negative-zero-positive index refraction was demon- strated numerically on the basis of full-wave analysis of a microstructured omega-type array and experimentally via angle resolved transmission measurement of a prism-type prototype. The experimental results are interpreted in terms of characteristic impedance and refractive index retrieved by a Fresnel inversion technique. The possibility to balance the dispersion characteristics with a negative-zero-positive index is demonstrated over - and -bands. Index Terms—Composite right/left-handed metamaterial, nega- tive index materials, negative refraction, retrieval technique. I. INTRODUCTION N EGATIVE refraction in backward wave media was demonstrated at microwaves frequencies by using split ring resonator (SRR)/wire and omega-type arrays either by taking advantage of negative refraction in a metamaterial isotropic slab or in a prism-type microstructure [1]–[14]. Positive refraction was often used as a reference experiment by using a conventional homogenous material such as Plex- iglas, and the zero refraction was assessed by studying the collimating beam of a point source embedded in a zero index medium [15]–[17]. In this paper, we investigate the possibility to combine all the refractive situations, namely, negative, zero, and positive index Manuscript received March 10, 2008; revised June 12, 2008. First published October 24, 2008; current version published November 07, 2008. This work was supported by the Centre National d’Etudes Spatiales (CNES). This work was supported in part under Bilateral Project EGIDE/PICASSO-MEC (Spain). The work of F. Zhang was supported by the China Scholarship Council under a fellowship. F. Zhang is with the Institut d’Électronique de Microélectronique et Nan- otechnologies (IEMN), Unite Mixte de Recherche (UMR), Centre National de la Recherche Scientifique (CNRS) 8520, Université des Sciences et Technologies de Lille 1, 59652 Villeneuve d’Ascq, France, and also with the Department of Applied Physics, Northwestern Polytechnical University, 710072 Xi’an, China. S. Potet was with the Institut d’Électronique de Microélectronique et Nan- otechnologies (IEMN), Unite Mixte de Recherche (UMR), Centre National de la Recherche Scientifique (CNRS) 8520, Université des Sciences et Technolo- gies de Lille 1, 59652 Villeneuve d’Ascq, France. He is now with Temex, 10150 Pont Sainte Marie, France. J. Carbonell is with the Instituto de Telecomunicaciones y Aplicaciones Mul- timedia, Universidad Politécnica de Valencia, E-46022 Valencia, Spain. E. Lheurette, O. Vanbésien, and D. Lippens are with the Institute of Elec- tronics Microelectronics and Nanotechnologies, Unite Mixte de Recherche (UMR), Centre National de la Recherche Scientifique (CNRS) 8520, Université des Sciences et Technologies de Lille 1, 59652 Villeneuve d’Ascq, France (e-mail: didier.lippens@iemn.univ-lille1.fr). X. Zhao is with the Department of Applied Physics, Northwestern Polytech- nical University, Xi’an 710072, China. Color versions of one or more of the figures in this paper are available at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2008.2005891 refraction by using the same sample, which does not exhibit any forbidden gap between the left-handed dispersion branch and the right-handed one. The absence of a forbidden gap in the propagation of waves in a metamaterial-based structure was al- ready shown in the so-called balanced composite transmission lines [18]–[20]. However, to the best of our knowledge, this is the first time that such a property is demonstrated for a metama- terial based on an SRR and wire technology. The basic idea was first to replace the dual SRR and wire array by an inclusion that simultaneously exhibits an electric and magnetic dipole. This idea was developed in [8]. For this purpose, we chose an omega-type pattern whose magnetic and electric responses were already demonstrated in [8]–[14] and were experimentally characterized in a hollow waveguide in [21]. It can also be shown that an interconnected omega array in- trinsically possesses a relatively broad left-handed transmission branch due notably to the Drude-like response of the effective permittivity resulting from the transverse interconnections [14]. The necessary condition for a balanced composite dispersion characteristic is the equality of the electric and magnetic plasma frequencies. Let us recall that these characteristic frequencies govern the dispersion properties of the effective permittivity and permeability as the transition frequency between the nega- tive and positive values of the effective parameters in the upper part of the spectrum. This equality avoids facing the situation of a single negative medium between the double negative con- dition (left-handed branch) and the double positive one (right- handed branch). Any single negative medium corresponds to a forbidden gap, which we try here to avoid between the backward and forward wave transmission windows. With respect to the transmission line approach, the balance of the plasma frequen- cies would correspond to the equality between the resonance frequencies of the series and the shunt equivalent resonant cir- cuits. The second goal of the paper will be to demonstrate, by full wave modeling and by angle resolved vectorial analysis, that the design of a balanced composite current loop/wire array was successful. This fact will be confirmed by several methods in- cluding the derivation of the refractive index via a refractive ex- periment (numerical and real world) and by a Fresnel inversion retrieval technique. In this paper, Section II deals with the design rules, while we will consider the numerical and modeling experiments in Sections III and IV, respectively. Concluding remarks and prospects are considered in Section V. II. DESIGN RULES Fig. 1(a) shows a schematic of the basic cell, while Fig. 1(b) illustrates the interconnection arrangement along the -axis, 0018-9480/$25.00 © 2008 IEEE Authorized licensed use limited to: UNIVERSIDAD POLITECNICA DE VALENCIA. Downloaded on November 10, 2008 at 04:22 from IEEE Xplore. Restrictions apply.