Transmission properties of composite metamaterials in free space
Mehmet Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis
Citation: Appl. Phys. Lett. 81, 120 (2002); doi: 10.1063/1.1492009
View online: http://dx.doi.org/10.1063/1.1492009
View Table of Contents: http://aip.scitation.org/toc/apl/81/1
Published by the American Institute of Physics
Articles you may be interested in
Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial
Applied Physics Letters 78, 489 (2001); 10.1063/1.1343489
Electric-field-coupled resonators for negative permittivity metamaterials
Applied Physics Letters 88, 041109 (2006); 10.1063/1.2166681
High performance optical absorber based on a plasmonic metamaterial
Applied Physics Letters 96, 251104 (2010); 10.1063/1.3442904
Origin of dissipative losses in negative index of refraction materials
Applied Physics Letters 82, 2356 (2003); 10.1063/1.1563726
Direct calculation of permeability and permittivity for a left-handed metamaterial
Applied Physics Letters 77, 2246 (2000); 10.1063/1.1314884
Capacitor-loaded split ring resonators as tunable metamaterial components
Journal of Applied Physics 101, 024911 (2007); 10.1063/1.2427110
Transmission properties of composite metamaterials in free space
Mehmet Bayindir,
a)
K. Aydin, and E. Ozbay
Department of Physics, Bilkent University, Bilkent, 06533 Ankara, Turkey
P. Markos
ˇ
b)
and C. M. Soukoulis
c)
Ames Laboratory and Department of Physics, Iowa State University, Ames, Iowa 50011
共Received 31 January 2002; accepted for publication 13 May 2002兲
We propose and demonstrate a type of composite metamaterial which is constructed by combining
thin copper wires and split ring resonators 共SRRs兲 on the same board. The transmission
measurements performed in free space exhibit a passband within the stop bands of SRRs and thin
wire structures. The experimental results are in good agreement with the predictions of the transfer
matrix method simulations. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1492009兴
In recent years, the composite metamaterials 共CMMs兲
have inspired great interest due to their unique physical prop-
erties and novel applications of these materials.
1,2
Two im-
portant parameters, electrical permittivity
⑀
and magnetic
permeability
, determine the response of the material to the
electromagnetic radiation. Generally,
⑀
and
are both posi-
tive in ordinary materials. While
⑀
could be negative in or-
dinary materials 共for instance in metals兲, no natural materials
with negative
are known. However, for certain structures
which are called left-handed materials 共LHM兲, both the ef-
fective permittivity
⑀
eff
and permeability
eff
possess nega-
tive values. In such materials the index of refraction is less
than zero, and therefore, phase and group velocity of an elec-
tromagnetic 共EM兲 wave can propagate in opposite directions.
This behavior leads to a number of interesting properties.
3
The phenomena of negative index of refraction was first
theoretically proposed by Veselago in 1968.
4
Veselago also
investigated various interesting optical properties of the
negative index structures.
A negative permittivity medium can be obtained by ar-
ranging thin metallic wires periodically.
5–10
This structure
behaves like a high-pass filter which means that the effective
permittivity will take negative values below the plasma fre-
quency. On the other hand, a negative effective magnetic
permeability medium is difficult to obtain. In 1999, Pendry
et al. has suggested that an array of split ring resonators
共SRRs兲 might exhibit a negative effective magnetic perme-
ability for frequencies close to the resonance frequency of
these structures.
11
By combining these SRRs and thin wires,
Smith and his co-workers reported the experimental demon-
stration of left-handed metamaterials.
12
This was later fol-
lowed by direct measurement of negative index of
refraction,
13
and analytical formulation of the left-handed
medium.
14
Also, the negative permittivity and permeability
of CMM, as well as negative refraction index were calcu-
lated from the numerical data in Ref. 15. All of these mea-
surements were performed in a waveguide chamber which
limited one of the dimensions of the LHM structures to a
maximum of three cells.
16
Very recently, the fundamental
properties of the LHMs were verified by the transfer matrix
method 共TMM兲,
17
ab initio,
18
the finite-element method,
19
and finite-difference-time-domain
20
simulations.
In this letter, we propose and demonstrate a type of
CMM. The transmission spectra is obtained in free space
which allows us to use CMM structures without any restric-
tions on the size of the structures. The CMM structures ex-
hibit a passband within the stop bands of the SRRs and the
thin wire structures. An improved version of the TMM is
used to simulate our structures, and qualitative agreement
with the experimental results is obtained.
We first constructed a CMM that consists of periodical
arrangement of thin copper wires and SRRs. This configura-
tion has a geometry which is similar to a previously reported
structure.
12,17
The details of the SRR structure is shown in
Fig. 1共a兲. It consists of two rings separated by a gap, which is
similar to the SRR structures in Refs. 16 and 17. As seen in
Fig. 1共b兲, we first constructed the SRRs and the wires on
a兲
Author to whom correspondence should be addressed; electronic mail:
bayindir@fen.bilkent.edu.tr
b兲
Present address: Institute of Physics, Slovak Academy of Sciences, Brat-
islava, Slovakia.
c兲
Also at: Research Center of Crete, IESL-FORTH, Heraklion, Crete,
Greece.
FIG. 1. 共a兲 A single SRR with parameters ᐉ⫽ 3 mm and d⫽t⫽w
⫽ 0.33 mm. 共b兲–共c兲 Schematic drawing of two different configurations of
the composite medium consisting of thin wires and SRRs.
APPLIED PHYSICS LETTERS VOLUME 81, NUMBER 1 1 JULY 2002
1200003-6951/2002/81(1)/120/3/$19.00 © 2002 American Institute of Physics
separate boards and stacked them in a periodical arrange-
ment.
We measured the transmission spectrum of a structure
which is made by using N
x
⫽ 25, N
y
⫽ 25, and N
z
⫽ 20 unit
cells. Each unit cell consists of a copper wire and a SRR, and
the dimensions of the unit cell are a
x
⫽ 5 mm, a
y
⫽ 3.63 mm, and a
z
⫽ 5 mm. The thickness and width of the
thin copper wires are 30
m and 0.5 mm. As shown in Fig.
1共a兲, we approximate the rings by squares of size ᐉ
⫽ 3 mm. The parameters of the SRR are d⫽ t⫽ w
⫽ 0.33 mm. The transmission measurements are performed
in free space by using an HP 8510C network analyzer and
microwave horn antennas. For all measurements, EM waves
propagate along the x direction. The electric field polariza-
tion is kept along the y axis, and magnetic field polarization
is kept along the z axis. The thickness and the dielectric
constant of the board are measured to be 0.45 mm and
⑀
b
⫽ 4.4, respectively.
Figure 2 shows the measured transmission spectra of
SRRs 共dotted line兲, thin wires 共dashed line兲, and the CMM
共solid line兲. The SRR medium displays a stop band extending
from 8.1 to 9.5 GHz which is in agreement with the TMM
simulations.
17
The thin wire structure has a plasma frequency
around 10 GHz. Although we were expecting the CMM
transmission band to be at the same frequencies with the
SRR stop band, we observed that the CMM transmission
band shifted to lower frequencies 共6.7–8.1 GHz兲. Such a
shift has also been reported in Ref. 16, and has been ex-
plained by the sensitivity of the mutual position of SRRs and
wires with respect to each other.
To overcome this alignment problem, we constructed a
second CMM structure 关Fig. 1共c兲兴. In this configuration, we
placed copper wires between the columns of the SRRs on the
same board. This configuration has no alignment problems
with the SRRs and thin wires, and can easily be fabricated at
smaller scales. We then measured the response of EM to the
CMM structure, which is made by N
x
⫽ 25, N
y
⫽ 25, and
N
z
⫽ 20 unit cells 关Fig. 1共c兲兴. Each unit cell consists of a
copper wire and a SRR, and the dimensions of the unit cell
are a
x
⫽ 5 mm, a
y
⫽ 3.63 mm, and a
z
⫽ 6 mm. As shown in
Fig. 3, this CMM allows propagation of EM waves between
8.7 and 9.9 GHz. The CMM passband exactly coincides with
the stop band of SRR. The wire structure also exhibits a stop
band that covers the observed CMM passband. The peak
transmission amplitude of the passband is ⫺ 16 dB, which is
higher than the ⫺ 24 dB peak amplitude reported in Ref. 16.
We also performed numerical calculations for the
CMMs. We used a modified version of the TMM code,
21
which is recently developed to investigate the transmission
and reflection properties of composite metamaterial
structures.
17
The main change from the standard algorithm
commonly used to study photonic band gap materials
22
is the
faster normalization of the transmitted electromagnetic
waves in the calculation of the transmission coefficient
through the composite structures.
In order to calculate the transmission spectrum, the total
volume of the system is divided into small cells and fields in
each cell are coupled to those in the neighboring cells. We
assume periodic boundary conditions in the directions paral-
lel to the interfaces. Both SRRs and wires are located on the
same dielectric board and the wire width is 0.66 mm. The
unit cell is a
x
⫻ a
y
⫻ a
z
⫽ 5⫻3.66⫻ 5 mm. Each unit cell is
discretized to N
x
⫻ N
y
⫻ N
z
⫽ 15⫻ 11⫻15 mesh points. Ten
unit cells are considered along the propagation direction, and
periodic boundaries are supposed in y and z directions.
Figure 4 presents the calculated transmission spectra of
the SRRs only 共dotted line兲 and the CMMs structure 共solid
lines兲 corresponding to Fig. 1共c兲. The SRRs exhibits a for-
bidden band between 8.4 and 9.2 GHz, which is in good
agreement with the measured results in Fig. 3. As the mesh
length 共0.33 mm in the present simulations兲 defines the lower
limit for the size of the components, we cannot simulate real
thickness of the SRR and wire 共which is only 0.03 mm兲.We
think that the resonance gap will shift slightly to higher fre-
quencies in simulations made with more mesh points.
For the CMMs, we performed simulations for two dif-
ferent values of dielectric permittivity, namely
⑀
CMM1
⫽ 1
⫹ 38 000i, and
⑀
CMM2
⫽⫺300 000⫹588 000i. It is observed
that the larger imaginary part of the metallic permittivity
gives higher transmission peak. When we take smaller
FIG. 2. Measured transmission spectra of thin wires, SRRs, and the com-
posite structure with the first type of metamaterial configuration 关Fig. 1共b兲兴.
The transmission passband is observed due to negative values of the permit-
tivity and the permeability.
FIG. 3. Measured transmission spectra of thin wires, SRRs, and the com-
posite structure with the second type of metamaterial configuration 关Fig.
1共c兲兴. A transmission band is observed within the stop bands of wire and
SRR structures.
121Appl. Phys. Lett., Vol. 81, No. 1, 1 July 2002 Bayindir
et al.
imaginary part 共lossy materials兲, the transmission peak dis-
appears. We also investigated how the number of unit cells
along the propagation direction affects the peak transmission
amplitude. As shown in the inset of Fig. 4, the peak disap-
pears when the number of unit cells is decreased.
Our experimental and theoretical results on the CMMs
clearly shows a transmission passband which is expected
from the left-handed metamaterials. However, we still refrain
from calling our CMM as a left-handed material. Further
investigations, such as negative index measurements, has to
be done with these structures for verification of the LHM
behavior.
In conclusion, we report the free-space experimental
measurement of composite metamaterials that consist of
SRR and thin wire arrays. One of the structure exhibits a
transmission passband, which indicates a possible left-
handed material property.
This work was supported by NATO Grant No.
SfP971970, National Science Foundation Grant No. INT-
9820646, DARPA, NATO Grant Nos. PST. CLG. 978088,
and NFS INT-0001236. P. M. thanks VEGA for partial finan-
cial support. Ames Laboratory is operated for the U.S. De-
partment of Energy by Iowa State University under Contract
No. W-7405-Eng-82.
1
J. B. Pendry, Phys. World 14,47共2001兲.
2
For a recent review, see articles in Photonic Crystal and Light Localiza-
tion in the 21st Century, edited by C. M. Soukoulis 共Kluwer, Dordrecht,
2001兲.
3
J. B. Pendry, Phys. Rev. Lett. 85, 3966 共2000兲.
4
V. G. Veselago, Sov. Phys. Usp. 10, 509 共1968兲.
5
D. R. Smith, S. Schultz, N. Kroll, M. M. Sigalas, K. M. Ho, and C. M.
Soukoulis, Appl. Phys. Lett. 65, 645 共1994兲.
6
D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, Phys. Rev. Lett.
76, 2480 共1996兲.
7
J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett.
76, 4773 共1996兲.
8
J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, J. Phys.:
Condens. Matter 10, 4785 共1998兲.
9
D. R. Smith, D. C. Vier, W. J. Padilla, S. C. Nemat-Nasser, and S. Schultz,
Appl. Phys. Lett. 75,1425共1999兲.
10
B. Temelkuran, M. Bayindir, E. Ozbay, J. P. Kavanaugh, M. M. Sigalas,
and G. Tuttle, Appl. Phys. Lett. 78,264共2001兲.
11
J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans.
Microwave Theory Tech. 47, 2075 共1999兲.
12
D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz,
Phys. Rev. Lett. 84, 4184 共2000兲.
13
R. A. Shelby, D. R. Smith, and S. Schultz, Science 292,77共2001兲.
14
D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 共2000兲.
15
D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65,
195104 共2002兲.
16
R. A. Shelby, D. R. Smith, and S. C. Nemat-Nasser, Appl. Phys. Lett. 78,
489 共2001兲.
17
P. Markos and C. M. Soukoulis, Phys. Rev. B 65, 033401 共2002兲; Phys.
Rev. E 65, 036622 共2002兲.
18
T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter,
D. R. Smith, D. C. Vier, and S. Schultz, J. Appl. Phys. 90,5419共2001兲.
19
C. Caloz, C. C. Chang, and T. Itoh, J. Appl. Phys. 90, 5483 共2001兲.
20
R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 056625 共2001兲.
21
J. B. Pendry, A. MacKinnon, and P. J. Roberts, Proc. R. Soc. London, Ser.
A 437,67共1992兲.
22
J. B. Pendry, J. Mod. Opt. 41, 209 共1994兲.
FIG. 4. Calculated transmission of electromagnetic waves through an array
of SSRs 共dotted line兲 and the composite metamaterials 共solid lines兲 are
shown in Fig. 1共c兲 for two different values of the metallic permittivity
(
⑀
CMM1
⫽ 1⫹ 38 000i, and
⑀
CMM2
⫽⫺300 000⫹588 000i). Inset: Variation
of the transmission spectra by increasing the number of unit cells along the
propagation direction.
122 Appl. Phys. Lett., Vol. 81, No. 1, 1 July 2002 Bayindir
et al.
