Special Issue on Metamaterials LHM
Forward and backward leaky wave radiation
in split-ring-resonator-based metamaterials
I. Arnedo, J. Illescas, M. Flores, T. Lopetegi, M.A.G. Laso, F. Falcone, J. Bonache, J. Garcı́a-Garcı́a,
F. Martı́n, J.A. Marcotegui, R. Marqués and M. Sorolla
Abstract: The ability of planar left-handed metamaterials (LHMs) based on split-ring resonators
(SRRs) to radiate backwards in a certain frequency range, as predicted by theory, is demonstrated.
A comparison between an LHM and a negative permeability metamaterial in terms of the experimental backward and forward radiation cones (which are related to their dispersion diagrams)
is carried out. The results of this work open the possibility to use SRRs as miniaturised and flexible
radiating elements for antennas and arrays in wireless communication applications.
1
Introduction
Left-handed metamaterials (LHMs), characterised by
simultaneously exhibiting a negative value of dielectric permittivity, 1, and magnetic permeability, m, are originating
an intense research activity in the last years, verifying
Veselago’s [1] visionary predictions in the late 1960s.
Some of these theoretical predictions, like the reversal
of Snell’s law, Doppler effect and Cherenkov radiation,
caused by the simultaneous negative values of effective
permittivity and permeability, remained in the theoretical
speculation until year 2000 [2].
According to theory, LHMs are negative refractive index
media with antiparallel phase and group velocities. The
wavevector k forms a left-handed triplet with the vectors
E and H, the electric and magnetic field intensities, and
wave phase fronts travel towards the source, that is opposite
to the energy flow direction.
A key point for the practical development of the first
LHM [2] was the introduction of the split-ring-resonator
(SRR) [3]. Such particle, composed of two concentric metallic rings with slits etched in each ring at opposite sides,
exhibits a strong magnetic response when adequately
excited by an external time varying magnetic field in the
axial direction. Owing to the distributed capacitance
between concentric rings, SRRs behave as a resonant LC
tank which can be excited by a time varying magnetic field.
A periodic array of SRRs inhibits the propagation of a
properly polarised electromagnetic wave in the vicinity of
the SRR resonance frequency. This frequency selective
behaviour has also been interpreted as a consequence of
# The Institution of Engineering and Technology 2007
doi:10.1049/iet-map:20050320
Paper first received 30th November 2005 and in revised form 30th May 2006
I. Arnedo, M. Flores, T. Lopetegi, M.A.G. Laso, F. Falcone, and M. Sorolla are
with the Electrical Engineering Department, Public University of Navarre,
Campus Arrosadia, Pamplona E-31006, Spain
J. Illescas and J. A. Marcotegui are with CONATEL, S.L., Polı́gono Plazaola F,
Aizoáin, Navarra, 31195, Spain
J. Bonache, J. Garcı́a-Garcı́a and F. Martı́n are with the Department
d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra
(Barcelona) 08193, Spain
R. Marqués is with the Departamento de Electrónica y Electromagnetismo,
Universidad de Sevilla, Sevilla 41012, Spain
E-mail: mangel.gomez@unavarra.es
IET Microw. Antennas Propag., 2007, 1, (1), pp. 65– 68
the periodic structure properties that can be considered as
an effective medium with negative permeability in a
narrow band above SRR resonance.
By inserting these particles in a thin wire media (which
exhibits an effective negative permittivity below a frequency analogous to the plasma frequency), the stop band
is switched to a pass band with 2D backward wave propagation, and an LHM results [2].
Recently, backward leaky wave radiation has been
reported in dual planar transmission lines, consisting of a
coplanar waveguide (CPW) or a microstrip line periodically
loaded with series capacitors and shunt connected inductors
[4, 5]. This structure behaves as a 1D LHM and its leaky
wave radiation flows backward giving rise to a phenomenon
analogous to the reversal of Cherenkov radiation predicted
when a charged particle travels faster than the phase velocity of electromagnetic waves in an LHM.
In this letter, it is shown that an LHM based on SRRs and
wires also produces backward leaky wave radiation. The
LHM will be implemented in CPW technology, where the
set of SRRs is periodically etched on the back side of
the CPW host transmission line, while the set of wires is
placed connecting the central strip and the ground plane, just
above the SRRs (Fig. 1a). Using this configuration, the magnetic field of the fundamental CPW mode provides adequate
excitation to the SRRs, enabling the existence of a frequency
band with effective negative magnetic permeability. The negative permittivity is obtained from the shunt wires, which make
the structure to behave as a plasma below cutoff [6].
2
Leaky wave radiation in SRR-based CPWs
Leaky wave theory allows the study of the radiation characteristics of open periodic structures by means of an appropriate examination of their dispersion diagrams [7].
Comparison between the phase constants of the spatial harmonics of the Bloch mode, b, and the free-space wave
number, k0 , can be used to predict the frequency bands
where an open periodic structure can radiate. Specifically,
if jbj k0 , then radiation occurs at that frequency and the
angle, u, between the radiation beam and the propagation
axis can be calculated as
cos u ¼
b
k0
ð1Þ
65
giving rise to the following expression for the complex
propagation constant (b0 ) of the Bloch mode [9]
cosðb0 dÞ ¼
A11 þ A22
2
ð3Þ
However, as it has been noted in the work of Grbic and
Eleftheriades [10], the analysis of a single unit cell is inaccurate for the determination of the attenuation constant (imaginary part of the complex propagation constant) of leaky
periodic structures, due to mutual coupling and edge effects.
Nevertheless, as the number of unit cells employed in the
analysis increases, the spurious effects are less important
and the parameters obtained for the dispersion diagram are
more accurate. In this paper, the dispersion diagrams will be
extracted from the electromagnetic simulation of the whole
structures under analysis (the three-period devices). The
analytical procedure is identical to that described before,
but taking b0 . 3d as the argument of the cosine in (3).
The dispersion diagrams obtained for both structures
(depicted in Fig. 1) are shown in Fig. 2. The attenuation
constant (imaginary part of the propagation constant) is
a
7.5
Fig. 1
Layouts of the studied prototypes
a CPW-LHM structure
b CPW negative m structure
Grey parts indicate metal on the upper plane, and the black parts indicate metal on the lower plane
By using this theoretical framework, the radiation properties
of the metamaterial structures presented in Fig. 1 will be analysed. They include an LHM structure (Fig. 1a), obtained as
explained in the previous section, and a negative permeability
media (Fig. 1b), obtained by removing the wires. The SRR
dimensions have been tuned to achieve a resonant frequency
around 6.5 GHz following the method proposed by Baena
et al. [8] (ring widths: 0.2 mm, air gap between rings:
0.2 mm and external radius: 2.2 mm), whereas the separation
between the centres of adjacent rings (period of the structure)
is d ¼ 5 mm. Each prototype has three periods (total
length ¼ 3d ). The width of the wires is 0.2 mm. Finally,
the host CPW has been designed to have a 50 V characteristic
impedance (strip width w ¼ 5.4 mm, slot width s ¼ 0.3 mm)
on an Arlon 250-LX-0193-43-11 substrate (1r ¼ 2.43, thickness h ¼ 0.49 mm), using AgilentTM LineCalc.
The dispersion diagrams for both structures could be
calculated, as a first approximation, from the electromagnetic simulation of their unit cells. Specifically, the
S-parameters from the two-port unit cell are calculated
using CST Microwave StudioTM, and then converted to
wave-amplitude transmission matrix [Aij] parameters.
2
Finally, the wave amplitudes at the input (aþ
1 , a1 ) and
þ
2
output (a2 , a2 ) ports of the unit cell are enforced to
satisfy the propagation conditions of the forward traveling
Bloch wave, namely
0
þ
jb d
aþ
2 ¼ a1 e
0
jb d
a
2 ¼ a1 e
66
ð2Þ
6.5
6
5.5
−π
−π/2
0
β·d, α·d
π/2
π
π/2
π
a
7
6.8
Frequency (GHz)
b
Frequency (GHz)
7
6.6
6.4
6.2
6
−π
−π/2
0
β·d, α·d
b
Fig. 2 Dispersion diagram of the studied structures
a CPW-LHM
b CPW negative m media
Radiation region is shown with dotted lines
Only the frequency range of interest and the first Brillouin zone are
shown
Attenuation constant is also given in thin lines
IET Microw. Antennas Propag., Vol. 1, No. 1, February 2007
also given in thin line. The boundaries of the radiation
region have been also indicated with dotted lines. The spectral gap that customarily appears between the bound mode
region and the leaky mode region [11] is not detected in
our dispersion diagrams. However, the spectral gap bandwidth is usually extremely narrow and therefore it is difficult to notice in the dispersion diagrams having no
practical relevance for our study.
In Fig. 2a, the existence of a left-handed band for the
structure shown in Fig. 1a is verified. It corresponds to
the zone of the dispersion diagram where the slope is negative (shaded in the figure) and therefore the group and phase
velocities are anti-parallel. The attenuation constant is small
in most of this region. The upper part of such band is contained within the radiation region (jbj , k0), hence predicting the existence of a frequency range where the Bloch
mode becomes leaky. The left-handed behaviour of the
structure will result in a reversal of the direction predicted
for the leaky wave radiation. Actually, the phase matching
condition along the interface between the LHM and the
medium where the energy is radiated (free space, and therefore a right-handed medium) implies that the radiated
energy will necessarily have to propagate in the opposite
direction. This could also be explained by means of (1).
The phase and group velocities being antiparallel in an
LHM actually means that b is negative for the wave propagating energy from the source to the load, and therefore u
will be included in the second quadrant, that is from broadside (u ¼ 908) to backfire (u ¼ 1808) direction. This
phenomenon can be seen as analogous to the reversal of
Cherenkov radiation in LHMs predicted by Veselago [1].
On the other hand, in Fig. 2b, the dispersion diagram for
the CPW structure loaded only with SRRs (Fig. 1b) is
shown. In this case, there is a frequency band where
strong rejection occurs due to the negative value exhibited
by the magnetic permeability. This strong rejection band
is predicted by the dispersion diagram because in that
region (shaded in the figure), the attenuation constant is
much larger than the phase constant [12]. Both the rejection
band and the lower part of the second pass band are included
in the radiation region (jbj , k0). However, the high attenuation constant present in the stop band prevents the structure
from radiating, since it operates at the reactive-mode region
at these frequencies, and not at the antenna region [12]. On
the other hand, at the lower part of the second pass band, the
structure radiates (small attenuation constant), and since it is
right-handed (positive slope), the radiation beam will be
contained in the first quadrant, from broadside to endfire
direction (positive value for b and hence, from (1), u
from 0 to 908).
It is also important to notice that in the frequency band
just above the radiation region the attenuation constant
has also a significant value. This behaviour suggests that
in this frequency band, the Bloch mode becomes again
leaky, but this time towards the surface wave mode supported by the surrounding substrate. Further 3D electromagnetic simulations have been done and the results obtained
clearly demonstrate this fact.
3
Fig. 3 Simulated radiation patterns for the prototypes
a CPW-LHM, calculated at the frequency corresponding to backfire
radiation (6.85 GHz)
b CPW negative m structure, calculated at the frequency corresponding
to endfire radiation (6.45 GHz), respectively
around 18% for the first prototype and 29% for the second
prototype.
The inversion of the radiation in the LHM structure is
clearly seen. These results have been experimentally verified with the aid of our Agilent 8722 vector network analyser and a horn antenna, which was conveniently oriented
following the polarisation of the electromagnetic fields
radiated by the magnetic dipoles associated to the SRRs.
(H-field in the vertical x – z plane).
Maintaining the value f ¼ 08, a scanning of u has been
performed and the value of the S21 parameter has been processed for the different angular steps. In this way, the y –z
horizontal plane (E-plane) has been measured. The same
procedure has been followed on the x – z vertical plane
(H-plane), maintaining u ¼ 08 and scanning f.
The measurements are depicted together with the simulated data in Fig. 4 for the CPW-LHM, and in Fig. 5 for
the CPW loaded only with SRRs (in both cases for the frequency that corresponds to backfire and endfire radiation,
respectively). The E-plane and the H-plane are given. As
it can be seen in Fig. 4, the CPW-LHM has a clear trend
to radiate backwards (with a 14 dB gain in the backward
direction with respect to the forward direction in measurements). On the other hand, in the SRR loaded CPW
(shown in Fig. 5), the radiation produced by the Bloch
mode when it enters the fast wave zone and becomes
leaky is, as predicted by the dispersion diagram, undoubtedly in the forward direction.
Simulation and measurement
In order to validate the predictions obtained from the dispersion diagrams, full wave electromagnetic simulations,
using CST Microwave StudioTM, and measurements have
been performed. With the aid of the simulator, radiation patterns have been calculated for both prototypes, for the frequencies corresponding to backfire and endfire radiation,
respectively (Fig. 3). The amount of radiated power is
IET Microw. Antennas Propag., Vol. 1, No. 1, February 2007
Fig. 4 Simulated (continuous lines) and measured (dotted lines)
radiation patterns for the prototype depicted in Fig. 1a
(CPW-LHM) at the frequency corresponding to backfire radiation
(6.85 GHz in simulation and 7.21 GHz in measured prototype)
E-plane (thin lines) and H-plane (thick lines)
67
planar structures for antennas and arrays in wireless applications has been shown.
5
Acknowledgments
This work has been supported by the Spanish CICYT under
project TEC2005-06923-C03-01.
6
Fig. 5 Simulated (continuous lines) and measured (dotted lines)
radiation patterns for the prototype depicted in Fig. 1b (CPW
negative m structure) at the frequency corresponding to endfire
radiation (6.45 GHz in simulation and 6.8 GHz in measured
prototype)
E-plane (thin lines) and H-plane (thick lines)
Finally, as frequency changes, and while within the radiation region, the angle of the radiation beam evolves going
upwards as predicted by (1) and the dispersion diagrams of
Fig. 2.
4
Conclusion
In this paper, it has been demonstrated that an array of SRRs
coupled to a CPW is able to produce forward leaky wave
radiation, as predicted from the classical dispersion
diagram method. If a set of periodically distributed wires
(short circuits between line and ground) are also introduced
along the CPW, backward leaky wave radiation is
measured. As it can be seen in the dispersion diagram, the
resulting LHM supports a backward-wave fundamental
spatial harmonic that becomes leaky at the radiation frequencies. To the authors’ knowledge, this is the first time
that backward leaky wave radiation is demonstrated in an
SRR and wire-based LHM. The potential of these fully
68
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