Numerical and experimental demonstration of a coordinate transformation-based azimuthal directive emission

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Numerical and experimental demonstration of a
coordinate transformation-based azimuthal
directive emission
ARTICLE · JANUARY 2012
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Paul-Henri Tichit
Université Paris-Sud 11
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Shah Nawaz Burokur
Université Paris Ouest Nanterre La Défense
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André de Lustrac
Université Paris-Sud 11
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Available from: Paul-Henri Tichit
Retrieved on: 19 December 2015

12. J. Asmussen and D.K. Reinhard, Diamond films handbook, Marcel
Dekker, New York, 2002.
13. H. Angus Macleod. Thin-film optical filter, 4th ed., CRC Press,
New York, 2010.
VC 2012 Wiley Periodicals, Inc.
NUMERICAL AND EXPERIMENTAL
DEMONSTRATION OF A COORDINATE
TRANSFORMATION-BASED AZIMUTHAL
DIRECTIVE EMISSION
Xinying Wu, Paul-Henri Tichit, Shah Nawaz Burokur, Souad
Kirouane, Alexandre Sellier, and Andre de Lustrac
IEF, Univ. Paris-Sud, CNRS, UMR 8622, 91405 Orsay Cedex,
France; Corresponding author: andre.de-lustrac@u-psud.fr
Received 22 January 2012
ABSTRACT: This article deals with the modeling, practical
implementation, and characterization of an azimuthal directive antenna
around 10 GHz. The design of the antenna is based on transformation
optics concept by transforming the radiation of a plane source into an
azimuthal radiation. This coordinate transformation procedure is
achieved by modifying the electromagnetic properties of the space
around the plane source. Metamaterials presenting electric and
magnetic resonances are used to produce the effective material
parameters necessary for the transformation. S11 parameter and direct
far-field measurements are performed on a fabricated prototype to
experimentally demonstrate the narrow beam profile and the beam
deflection. VC 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett
54:2536–2540, 2012; View this article online at wileyonlinelibrary.com.
DOI 10.1002/mop.27122
Key words: coordinate transformation; metamaterials; azimuthal;
directive emission
1. INTRODUCTION
Metamaterials are artificial materials typically fabricated via
suitable periodic arrangement of microstructured metallic or
dielectric inclusions. Because of their unusual electromagnetic
properties [1], these microstructured metamaterials have made
relevant a wide array of interesting applications. Metamaterials
have been proposed for the design of directive antennas [2–4].
In Ref. 2, Enoch et al. proposed to use the refractive properties
of a low optical index material interface to achieve the directive
emission. Burokur et al. [3] also studied numerically the pres-
ence of a left-handed medium with simultaneous negative per-
mittivity and permeability over a patch antenna where a gain
enhancement of about 3 dB has been observed. In Ref. 4, Ourir
et al. have shown the possibility of using a novel composite
metamaterial surface as reflector in a Fabry–Perot cavity system
to produce an ultrathin directive antenna. Recently, the concept
of transformation optics [5, 6] has revived the interests for man-
made metamaterials. As these pioneering works of Leonhardt
[5] and that of Pendry [6], transformation optics is an emerging
research field where Maxwell’s equations are invariant under a
coordinate transformation. It generates enormous interest as it
offers an unconventional strategy for the design of novel class
metamaterial devices. The most intriguing application conceived
remains the invisibility cloak [7–9]. Other interesting wave
manipulation applications such as waveguide transitions and
bends have also been proposed [10–14]. For antenna applica-
tions, an omnidirectional retroreflector [15] and a Luneberg lens
[16] have been experimentally demonstrated. New techniques of
source transformation have offered new opportunities for the
design of active devices with source distribution included in the
transformed space. This approach has led us to design an ultradir-
ective emission by stretching a source into an extended coherent
radiator [17–19] and also a quasi-isotropic emission from a direc-
tive source by space expansion [20]. A lens capable of converting
the radiation from an embedded isotropic source into multibeam
emission has also been experimentally demonstrated [21].
In this letter, we present the design, implementation, and
characterization of a metamaterial-based azimuthal directive
antenna at 10 GHz using coordinate transformation concept. The
latter concept is applied to transform the vertical radiation of a
plane source into a directive azimuthal one. The theoretical
analysis devoted to this coordinate transformation is presented
and numerical simulations are performed using finite element
method to confirm the proposed concept. A bulk metamaterial
respecting constitutive electric permittivity and magnetic perme-
ability parameters generated by the transformation is used to
produce the azimuthal emission. Full-wave numerical simula-
tions and experimental measurements are performed to show the
performances of the proposed device. Good quantitative and
qualitative agreements are found.
2. DESIGN CONCEPT
In our previous recent works, we have proposed a concept based
on coordinate transformation to realize a directive emission
from quasi-omnidirectional sources such as microstrip patch
antennas or monopoles [17–19]. In this study, our plan is to
show how these recent achievements can be extended to trans-
form a broad angular radiation into an azimuthal directive emis-
sion. We will start from the basic transformation media
approach. The schematic principle of the transformation illus-
trating the proposed method is presented in Figure 1.
Let us consider a source radiating in a rectangular space.
This radiation emitted from the latter source can be transformed
into an azimuthal one. The transformation procedure is noted
F(x0
,y0
) and consists in bending the emission. Figure 1 shows
the working principle of this rotational coordinate transforma-
tion. Mathematically, F(x0
,y0
) can be expressed as:
x0
¼ axcos byð Þ
y0
¼ axsin byð Þ
z0
¼ z
8

:
(1)
where x0
, y0
, and z0
are the coordinates in the bent space, and x,
y, and z are those in the initial rectangular space. In the initial
space, we assume free space with isotropic permittivity and per-
meability tensors e0 and l0. L2–L1 and L are, respectively, the
width and the length of the rectangular space. The rotational
transformation of Figure 1 is defined by parameter a considered
as an ‘‘expansion’’ parameter and parameter b which controls
the rotation angle of the transformation F(x0
,y0
).
The new material can then be described by permeability and
permittivity tensors:
e ¼ we0 and l ¼ wl0 with wi0
j0
¼
Ji0
i Jj0
j dij
detðJÞ
(2)
where Ja0
a ¼ @x0a
@xa represents the Jacobian transformation matrix of
the transformations of Eq. (1) and dij
is the Kronecker symbol.
Both electromagnetic parameters e and l have the same behav-
ior, allowing an impedance matching with vacuum outside the
2536 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 11, November 2012 DOI 10.1002/mop

transformed space. The inverse transformation is obtained from
the initial transformation of Eq. (1) and derived by a substitution
method, enabling the metamaterial design which leads generally
to anisotropic permittivity and permeability tensors.
By substituting the new coordinate system in the tensor com-
ponents, and after some simplifications, the material parameters
are derived. Calculations lead to permeability and permittivity
tensors given in the diagonal base by:
W ¼
Wxx Wxy 0
Wyx Wyy 0
0 0 Wzz
8
:
9
; with
Wxx ¼
a2
x02
þ b2
y02
r2
abr3
Wxy ¼ Wyx ¼
x0
y0
a2
À b2
r2
ð Þ
abr3
Wyy ¼
a2
y02
þ b2
x02
r2
abr3
Wzz ¼
1
abr
8

:
(3)
Figure 2 shows the variation of the different components of
the permeability and the permittivity tensor of the metamaterial
structure. The geometrical dimensions are as follows: the width
of the source is taken to be 5 cm, and the internal and external
radius of the metamaterial structure is 5 and 10 cm, respectively.
The working frequency is set to 10 GHz.
After diagonalization, we obtain a more simplified form the
tensors:
e ¼
Wrr 0 0
0 Whh 0
0 0 Wzz
8
:
9
;
e0 l
¼
Wrr 0 0
0 Whh 0
0 0 Wzz
8
:
9
;
l0 with
Wrr ¼ a
br
Whh ¼ a
b r
Wzz ¼ 1
abr
8

:
ð4Þ
3. NUMERICAL SIMULATIONS
The transformation formulation is implemented using finite-ele-
ment method (FEM)-based commercial solver Comsol Multiphy-
sics. Figure 3 shows the comparison of two-dimensional (2D)
simulations between a plane source made of current lines in yz
plane above a limited metallic ground plane [Fig. 3(a)] and the
same source surrounded by a metamaterial defined by Eq. (4)
[Fig. 3(b)]. Figures 3(c) and 3(d) show respectively the far field
patterns of the plane source without and with the metamaterial
structure. A finer lobe is observed when the current lines interact
with the metamaterial. The left shift of the peak corresponds to
a rotation of 76
of the emitted radiation. We shall note that this
angular rotation is different from 90
due to the spatial shift of
the radiated beam from the symmetry axis.
To have an idea of the expected results from a physically
fabricated prototype, we first need to simplify the calculated ma-
terial parameters through a parameter reduction procedure. We
therefore fix a polarization of the electromagnetic field so that
we suppose having the magnetic field along the z-direction. In
this case, the relevant electromagnetic parameters are lzz, ehh,
and err. Thus, we decide to maintain ehh and lzz constant. Conse-
quently, the new set of coordinates is:
err ¼
1
br
8
:
9
;
2
Ä1:7
ehh ¼ 2:8
lzz ¼ 1:7
8

:
(5)
The values of err and lzz have been chosen so that they can
be easily achieved from metamaterials. ehh is produced by a host
medium, which is a commercially available resin. Physical pa-
rameter b allows an optimization of the material parameter err.
Figure 4(a) presents the profile of the different material parame-
ters resulting from an optimization for b ¼ 6. Figures 4(b) and
4(c) show, respectively, the calculated normalized electric field
distribution and the far field pattern where rotation of the beam
can be observed.
The previous material obeying Eq. (5) presents a continuous
variation in the radial permittivity. As it is not possible to
achieve such continuity in practice, we propose to perform a
discrete variation of err. Meta-atoms producing electric resonan-
ces are designed on the 0.787-mm thick low loss (tand ¼
0.0013) RO3003TM
dielectric substrate to provide the material
parameters. A realization of our proposed structure uses a lamel-
lar composite material, as illustrated in Figure 5(a). The pro-
posed structure is then composed of 30 identical layers where
Figure 1 Schematic principle of the 2D rotational coordinate transformation. The emission in a rectangular space is transformed into an azimuthal
one. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com]
DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 11, November 2012 2537

each layer [Fig. 5(b)] is divided in 10 unit cells. Because of con-
straints of the layout, we choose a rectangular unit cell with
dimensions 5 mm for both resonators. We are able to obtain the
desired ezz and lyy by tuning the resonators’ geometric parame-
ters. The 10 cells presented in Figure 5(c) are designed to con-
stitute the discrete variation of err. Table 1 summarizes the cor-
responding electromagnetic parameters of the cells. The discrete
metamaterial antenna simulated with HFSS from Ansys is pre-
sented in Figure 6(a).
For the numerical verification, a patch antenna presenting a
quasi-omnidirectional radiation is used as the feeding source of
the metamaterial antenna. Figure 6(b) shows the calculated mag-
netic field distribution. We shall note that the metamaterial
structure first transforms the quasi-omnidirectional radiation of
the patch source into a directive one.
4. EXPERIMENTAL MEASUREMENTS
Figure 7(a) shows a photograph of the fabricated prototype. A
microstrip square patch antenna printed on a 1-mm thick epoxy
dielectric substrate (er ¼ 3.9 and tand ¼ 0.02) is used as radiat-
ing source. A surrounding material made of alternating metama-
terial layers transforms the omnidirectional emission of the
patch antenna into a directive one steered in an off-normal
direction. The metamaterial is a discrete structure composed of
10 different regions where permittivity and permeability vary
according to Eq. (5) and to the profile of Figure 6(a). The bulk
metamaterial is assembled using 30 layers of RO3003TM
dielec-
tric boards on which subwavelength resonant structures are
printed. The layers are mounted 1 Â 1 in a molded matrix with
a constant angle of 3
between each. A commercially available
liquid resin is then flowed into the mold. This resin constitutes
the host medium and is an important design parameter which is
closely linked to ehh. Its measured permittivity has been found
to be close to 2.8. The mold is removed after solidification of
the resin.
To validate the directive emission device performances, S11
parameter measurements are first performed on the fabricated
prototype. The measured S11 parameter of the metamaterial
Figure 2 Variation of the permeability and permittivity tensor compo-
nents: (a) lxx, (b) lxy, (c) lyy, (d) ezz. [Color figure can be viewed in the
online issue, which is available at wileyonlinelibrary.com]
Figure 3 Calculated emission of a plane current source above a lim-
ited metallic ground plane (a) without and (b) with the metamaterial
structure. Calculated normalized far field of the antenna (c) without and
(d) with metamaterial. A 76
rotation of the radiation is clearly
observed. [Color figure can be viewed in the online issue, which is
available at wileyonlinelibrary.com]
Figure 4 (a) Profile of the different material parameters (err, ehh, lzz).
(b) Calculated emission of the plane source associated with the metama-
terial defined by the reduced parameters of Eq. (5) for a working fre-
quency of 10 GHz. (c) Calculated far field pattern of the metamaterial
antenna. [Color figure can be viewed in the online issue, which is avail-
able at wileyonlinelibrary.com]

antenna is compared with the simulated one using HFSS in Fig-
ure 7(b). A good agreement can be observed and return losses
reaching 18 dB is observed experimentally at 10.3 GHz com-
pared to 15 dB calculated. This quantity is further compared
with that of the feeding patch antenna alone. A better matching
can be clearly observed for the metamaterial antenna. The far-
field radiation patterns of the antenna have also been measured
in a full anechoic chamber to show the beam steering perform-
ances. The fabricated prototype is used as emitter and a wide-
band (2–18 GHz) dual polarized horn antenna is used as the re-
ceiver to measure the radiated power level of the emitter.
Measurements are performed for computer-controlled elevation
angle varying from À90
to þ90
. The microwave source is a
vector network analyzer (Agilent 8722 ES) that we also use for
detection. The simulated and measured far-field radiation pat-
terns in the E-plane (plane containing E and k vectors) are pre-
sented in Figure 7(c) for a frequency of 10 and 10.3 GHz,
respectively. A directive main beam and low parasitic secondary
lobes, around À10 dB are observed experimentally at an angle
of 66
. The main lobe presents 18
half-power beamwidth in the
E-plane. From the experimental results, we can clearly observe
the transformation of the omnidirectional far-field radiation of
the patch antenna into a directive one which is further bent at
an angle of 66
. The difference in bending angle is due to the
fabrication tolerances of the meta-atoms providing the gradient
radial permittivity and to the positioning of the patch source.
We shall also note that simulations using HFSS [Fig. 7(c)] show
90
beam steering as no spatial shift is considered in the calcu-
lation of the far-field pattern.
Figure 5 (a) Proposed structure using a lamellar composite material.
(b) Single metamaterial layer composed of 10 unit cells providing the
material parameters necessary for the coordinate transformation. (c)
Front and rear view of the metamaterial cells. [Color figure can be
viewed in the online issue, which is available at wileyonlinelibrary.com]
TABLE 1 Electromagnetic Parameters lzz, and err for the 10
Cells of the Metamaterial Layers
Layer ri (mm) Lhi (mm) lzz err
1 52.5 2.75 1.7 5.8
2 57.5 3.01 1.7 4.842
3 62.5 3.27 1.7 4.096
4 67.5 3.53 1.7 3.504
5 72.5 3.8 1.7 3.04
6 77.5 4.06 1.7 2.664
7 82.5 4.32 1.7 2.35
8 87.5 4.58 1.7 2.09
9 92.5 4.84 1.7 1.87
10 97.5 5.1 1.7 1.68
The length Lh of each cell is given as a function of its position along
the layer.
Figure 6 (a) Simulated design consisting of 30 metamaterial layers
each composed of 10 cells. (b) Calculated energy distribution at 10
GHz. [Color figure can be viewed in the online issue, which is available
at wileyonlinelibrary.com]
DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 11, November 2012 2539

5. CONCLUSIONS
We have designed and measured a device which was able to
transform an omnidirectional radiation into a directive one bent
at an angle as much as 66
using the coordinate transformation
concept. Metamaterials providing gradient radial permittivity
satisfying the transformation are used to fabricate the device.
Direct far field measurements have been performed to experi-
mentally demonstrate the directive azimuthal emission, making
the proposed device interesting for aeronautical applications.
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VC 2012 Wiley Periodicals, Inc.
Figure 7 (a) Photography of the fabricated prototype consisting of 30
metamaterial layers each composed of 10 cells. (b) Comparison between
simulations and measurements of the S11 parameter of the patch source
alone and the metamaterial antenna. (c) Far-field E-plane radiation pat-
terns of the patch source alone and of the metamaterial antenna. [Color
figure can be viewed in the online issue, which is available at
wileyonlinelibrary.com]

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