gn of Metasurfaces and Metamaterials
,
1
J. D. Baena,
2
J. Bonache,
3
M. Beruete,
1
rtı
´n,
3
and M. Sorolla
1
Universidad Pu´blica de Navarra, 31006-Pamplona, Spain
ismo, Universidad de Sevilla, 41012-Sevilla, Spain
tat Auto´noma de Barcelona, 08193-Barcelona, Spain
; published 1 November 2004)
the Babinet principle are applied to the design of
particle, the complementary split rings resonator, is
frequency selectivity and planar metamaterials with
in the fields of frequency selective surfaces and
d filter design, can be envisaged. The tunability of
so
proach is the
the complem
first step in
ducting and
magnetic fie
scattered fie
produced by
0
c
: (3)
ibed by (1),
VOLUME 93, NUMBER 19
PHYSICAL REVIEW LETTERS
week ending
5 NOVEMBER 2004where!
0
is the frequency of resonance of the SRR and
0
is a geometrical factor. This approximation neglects
higher order multipolar fields [2,3]. It also neglects
cross-polarization effects [9,10] (these effects are consid-
ered later in this Letter). Let us now consider the behavior
of the CSRR when it is illuminated from z<0 by an
external electromagnetic field E
0
c
;B
0
c
[see Fig. 2(b)].
SRR
x
z
CSRR
ext
d
FIG. 1. Geometries of the SRR and the CSRR.197401-1complementary split ring resonator (CSRR),
entary screen of the SRR (see Fig. 1). As a
our analysis the behavior of a perfectly con-
infinitely thin SRR in an external electro-
ld E
0
;B
0
[see Fig. 2(a)] is considered. The
ld E
0
;B
0
is approximately given by the field
a resonant magnetic dipole [3]
m  
0
!
2
0
=!
2
 1
1
B
0
 z^ z^; (1)
E
c
 cB  E
0
c
; cB
c
 E  B
Assuming that the SRR scattered field is descr
y
c
ron the Babinet principle. The key element of this new ap-
fields E  cB
c
, B 1=cE
c
, then at the shadowed
side (z>0) the total fields must satisfy [11]Babinet Principle Applied to the Desi
F. Falcone,
1,
*
T. L o p e t e g i ,
1
M. A. G. Laso
R. Marque´s,
2
F. Ma
1
Departamento de Ingenierı´a Ele´ctrica y Electro´nica,
2
Departamento de Electro´nica y Electromagnet
3
Departament d’Enginyeria Electro´nica, Universi
(Received 16 February 2004
The electromagnetic theory of diffraction and
artificial metasurfaces and metamaterials. A new
proposed for the design of metasurfaces with high
a negative dielectric permittivity. Applications
polarizers, as well as in microwave antennas an
all these devices by an applied dc voltage is al
appropriate substrate.
DOI: 10.1103/PhysRevLett.93.197401
Artificial metamaterials and metasurfaces with special
electromagnetic properties have been a subject of grow-
ing interest in recent years [1,2]. Most proposed meta-
materials make use of split ring resonators (SRRs) [3], or
similar geometries, to achieve a negative effective per-
meability in a certain frequency range. The negative
permittivity has been commonly obtained from an array
of metallic wires or plates [2,4]. No particles acting as
point electric dipoles with negative polarizability have
been proposed to the date. In addition to these bulk
metamaterial designs, one- and two-dimensional planar
microwave circuits which show a left-handed behavior
have been recently proposed [5–7], some of them making
use of the SRR concept [7]. More recently, the applica-
tion of these concepts to the design of artificial surfaces
with special electromagnetic properties has been consid-
ered [8].
In this Letter we present a new approach for the design
of planar metamaterials and metasurfaces, which is based0031-9007=04=93(19)=197401(4)$22.50 achievable if these particles are etched on the
PACS numbers: 78.20.Ci, 41.20.Jb, 42.25.Fx, 84.40.–x
According to the electromagnetic theory of diffraction
[11], the field in the shadowed region (z>0) is the field
scattered by the CSRR,E
0
c
;B
0
c
.Forz<0, the total field is
given by [11]
E
c
 E
0
c
E
0;r
c
E
0
c
; B
c
 B
0
c
 B
0;r
c
 B
0
c
; (2)
where E
0;r
c
;B
0;r
c
is the field that would be reflected by the
metallic screen without the CSRRs etched on it. The
scattered fields, E
0
c
;B
0
c
andE
0
;B
0
, must fulfill some sym-
metries that arise from the fact that they are produced by
currents which are confined in the z  0 plane: the com-
ponents B
0
z
, E
0
x
,andE
0
y
must be even functions of z,while
E
0
z
, B
0
x
,andB
0
y
must be odd functions of the same vari-
able [11].
According to the Babinet principle, if a screen with
apertures (the CSRR) is illuminated from z<0 by an
incident field E
0
c
;B
0
c
and its complementary screen (the
SRR) is illuminated by some complementary incident
0 0 0 02004 The American Physical Society 197401-1

tation, the induced dipolar sheet also produces an elec-EEE+
0
′
∼
∼
EEE E
c
++
00, r
′ EE
c
′
cc c c
∼
VOLUME 93, NUMBER 19
PHYSICAL REVIEW LETTERS
week ending
5 NOVEMBER 2004it can be easily verified that in order to satisfy (3), the
fields scattered by the CSRR at z>0, E
0
c
;B
0
c
should be
those produced by an electric dipole p1=cm,or
p 
1
c
2

0
!
2
0
=!
2
 1
1
E
0
c
 z^ z^ : (4)
In the nonshadowed region (z<0) the sign of this dipole
must change, in order to produce the aforementioned
symmetry properties of the scattered fields. Thus, for
z<0 we finally obtain
p  
0;c
!
2
0
=!
2
 1
1
E
0
c
 z^ z^; 
0;c
1=c
2

0
;
(5)
where c is the velocity of light in vacuum. For lossy and/
or thick screens, as well as in conventional circuit boards,
the previous equations should be considered only as an
approximation. Since E
0
c
E
0;r
c
 2E
0
c
 z^ z^ at z  0

,it
may be convenient, for some applications, to substitute (5)
by
p  
0
!
2
0
=!
2
 1
1
E
ext
; (6)
where 
0
 
0;c
=2 and E
ext
 E
0
c
E
0;r
c
is the total ex-
ternal field produced by the sources and the metallic
screen without the CSRR.
The aforementioned results can be directly applied to
the design of artificial metasurfaces. In fact, the results
BBB+
0
′
∼
m
z < 0 z > 0
p
-p
BBB B
c
++
00, r
′ BB
c
′
z < 0 z > 0
(a) (b)
p
m
-m
cc c c
∼ ∼
FIG. 2. Illustration of the behavior of a SRR (a) and a
CSRR (b) when they are illuminated by an external field
coming from z<0. Big arrows account for the main excitation
mechanism [3] given by (1) and (5). Small arrows stands for the
cross-polarization effect [9,10].for a single CSRR can be extended to a system of many
CSRRs with a density of N CSRRs per square meter.
Since the CSRRs are electrically small [3], the distance
between them can be made much smaller than the inci-
dent radiation wavelength. Thus we are in the long wave-
length limit, and the considered metallic surface can be
seen—from the source side—as an electric dipolar sheet
of magnitude P
s

1
2
Np on top of a flat metallic screen.
From the opposite side, a dipolar sheet of the same
intensity but of opposite sign is seen [see Fig. 2(b)]. Let
us consider the incidence of a plane wave on a CSRR
metasurface. Assuming that the angle of incidence and
the polarization of this wave allows for the CSRRs exci-
197401-2tromagnetic wave which interferes with the plane wave
reflected at the metallic screen. The effect of this inter-
ference can be dramatic near the resonance !
0
.Inpar-
ticular, the CSRRs screen could be potentially tailored in
order to destroy the reflected wave. At this frequency all
the electromagnetic power will be transmitted through
the screen. This behavior is just the dual of that expected
for a surface of N SRRs per square meter, illuminated by
the complementary wave. In this case, a magnetic dipolar
sheet is produced which, eventually, cancels the trans-
mitted wave, thus reflecting all the incident power.
Up to now, the cross-polarization effects in the SRR
[9,10] have been neglected. In the frame of such an
approximation, the aforementioned effects in a multiple
CSRR (SRR) screen would appear only if there is a
normal component of the electric (magnetic) incident
field, because only in this case the CSRRs (SRRs) are
excited. This fact would prevent the excitation of a mul-
tiple SRR (CSRR) metasurface by a normally incident
plane wave, thus limiting its usefulness as frequency
selective surfaces. However, when cross-polarization ef-
fects are considered [9,10], it becomes apparent that a
similar excitation can be observed for incident fields with
a nonvanishing component of the electric field along the
y axis of the SRRs (see Fig. 1). From duality, a similar
behavior is expected for CSRRs illuminated by an exter-
nal magnetic field polarized along the same axis.
Electromagnetic simulations (using the CST Microwave
Studio electromagnetic solver) have confirmed this hy-
pothesis. An experimental setup has been also designed
and built up to prove such effects. The experimental
device consists of a pair of CSRRs and SRRs metasurfa-
ces which were illuminated from one side by a normally
incident plane wave. The transmitted field was measured
at the opposite side (two horn antennas were used for
these purposes). Both metasurfaces were etched on a
commercial low loss microwave substrate (Arlon 250
LX-0193-43-11, whose parameters are shown in the cap-
tion of Fig. 3). The measured transmission coefficients for
the appropriate polarization of the incident wave —mag-
netic (electric) field along the y axis for the CSRR (SRR)
metasurface —are shown in Fig. 3. A sharp transmission
peak can be observed for the CSRR metasurface at the
resonance, whereas a sharp null can be also observed in
the SRR metasurface at a similar frequency. These results
confirm the proposed theory (the frequency of resonance
of the SRRs predicted by the model reported in [12] is
!
0
’ 24:41 10
9
s
1
). The shift between the fre-
quency of resonance of the SRR and the CSRR metasur-
faces can be mainly attributed to the effect of the
dielectric substrate, which affects in a different way the
frequency of resonance of the SRRs and the CSRRs. The
limited height of the transmission peak for the CSRR
metasurface can be attributed to the presence of the
197401-2