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,
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