2306 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 12, DECEMBER 2003
Tailoring Double-Negative Metamaterial Responses
to Achieve Anomalous Propagation Effects
Along Microstrip Transmission Lines
Ching-Ying Cheng, Member, IEEE, and Richard W. Ziolkowski, Fellow, IEEE
Abstract—The design of a double-negative metamaterial
loaded microstrip transmission line (DNG MTM-TL) to tailor
the propagation characteristics at - and -band frequencies is
presented. Guided-wave propagation along this DNG MTM-TL
was studied numerically. The scattering parameters of the DNG
MTM-TL were obtained with Ansoft’s High Frequency Structure
Simulator. A two-port network realization of the DNG MTM-TL
is established. The effective permittivity and permeability for the
DNG MTM-TL is extracted using this two-port network represen-
tation. It is shown that both a negative permittivity and a negative
permeability and, hence, a negative index of refraction exist in the
design frequency range. These material parameters are dispersive
and conform to a two-time derivative Lorentz material model type
of resonance behavior. This form of the index of refraction may be
very suitable for applications dealing with phase and dispersion
compensation along a microstrip transmission line.
Index Terms—Artificial dielectrics, backward waves, dispersion,
metamaterials (MTMs), propagation, transmission lines.
I. INTRODUCTION
I N RECENT years, there has been a renewed interest inusing sub-wavelength structures to develop materials that
mimic known material responses or that qualitatively have new
response functions that do not occur in nature. These efforts
include the realization of double-negative (DNG) materials,
i.e., materials with both negative permittivity and negative
permeability [1]–[4]. The transmission properties in such
metamaterials (MTMs) have been studied by several groups,
e.g., [5]–[10]. These MTMs are typically realized artificially
as composite structures that are constructed from arrays of
metallic inclusions in dielectric substrates. As discussed, e.g., in
[11] and [12], they exhibit unusual scattering and propagation
properties within a particular frequency range. For instance,
in contrast to a double-positive (DPS) medium, i.e., a normal
medium that has both positive permittivity and permeability,
the wavenumber in a DNG material is opposite to, rather
that parallel to, the Poynting’s vector associated with a plane
wave propagating in it. Thus, the Poynting’s vector is parallel
to, and the wavenumber is antiparallel to, the direction of
causal power flow [5]. Fig. 1(a) shows the “right-handed” wave
Manuscript received March 28, 2003. This work was supported in part by the
Intel Corporation.
The authors are with the Department of Electrical and Computer
Engineering, University of Arizona, Tucson, AZ 85721-0104 USA (e-mail:
ccheng@ece.arizona.edu; ziolkowski@ece.arizona.edu).
Digital Object Identifier 10.1109/TMTT.2003.819193
(a)
(b)
Fig. 1. Wave properties in: (a) DPS and (b) DNG mediums.
propagation behavior in a DPS medium and Fig. 1(b) shows the
so-called “left-handed” wave propagation behavior in a DNG
medium. Several experimental verifications of the existence of
the DNG MTMs have been reported [13]–[15].
In this paper, we describe our study of the performance
of microstrip transmission lines loaded with DNG MTMs
formed by embedding capacitively loaded strips (CLSs) and
capacitively loaded loops (CLLs) in the substrate region. It has
been demonstrated numerically that a suitable arrangement of
these components in Roger’s 5880 Duroid produces
a negative index of refraction in both the -band (2–4 GHz)
and -band (4–8 GHz). This double-negative MTM loaded
microstrip transmission line (DNG MTM-TL) problem will be
reviewed in detail. Simulations of this complex guided-wave
environment were performed with Ansoft’s High Frequency
Structure Simulator (HFSS). These results were used to char-
acterize the -parameter performance of this DNG MTM-TL
configuration. It will be shown that a matched MTM can be
obtained that yields complete transmission in both the - and
-bands. Furthermore, it will be shown that a two-port network
model can be used to extract the effective permittivity and
permeability in that regime. Extracted values will be shown
that yield DNG values in the matching region and, hence, that
produce a negative index of refraction there. The corresponding
group and phase velocities are also obtained. The property of
interest to the microstrip transmission-line application involves
the possibility that the wave impedance in the DNG MTM
could be matched to the intrinsic impedance of the transmission
line and, due to their dispersive nature, can then be used
to achieve nonstandard propagation characteristics along it.
0018-9480/03$17.00 © 2003 IEEE