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88 OPTICS LETTERS / Vol. 34, No. 1 / January 1, 2009the material is opaque [2]. On the other hand, con-
structing a negative  medium is difficult because of
the absence of a magnetic charge. Pendry et al. [3]
proposed in 1999 that split-ring resonator (SRR)
structures exhibit negative . Thereafter, composite
metamaterials (CMMs) with simultaneously nega-
tive  and  were constructed with a combination of
wire and SRR structures [4]. Since then many experi-
mental and theoretical works that have been re-
ported were conducted for novel applications, such as
negative refraction [5], subwavelength focusing [6],
cloaking [7], and reverse Doppler shift [8].
In addition to the negative index of refraction,
metamaterials have another important property: The
unit cells of metamaterials are much smaller than
the operating wavelength. This property can also
lead to different novel applications, such as the local-
ization of the field into a subwavelength region. Re-
cently, the localization of the field has attained great
interest from the scientific community, since it is the
key issue of several applications. One method for ob-
region.
The SRR structure that we used for the present
study was a one-dimensional periodic arrangement of
square rings. The CMM structure was obtained by
the combination of the SRR structure and wire
stripes. The structures were printed on a Teflon sub-
strate with =2.17, in which the thickness of the sub-
strate was 1 mm. The wire stripes were on the back
of the substrate, and the square SRRs were on the
front faces. The thickness of the copper was 0.05 mm.
The width of the wire stripes was 1.6 mm. The lattice
constant along the x direction (propagation direction)
was 4.95 mm. There were five layers along the propa-
gation direction, in which the height of the structure
was 40 layers. Thirty layers of structures were
stacked with a 2 mm period along the z direction.
The E field was in the y direction. The details regard-
ing the unit cell of the metamaterial structures are
shown in Figs. 1(a) and 1(b). The experimental setup
consisted of an HP 8510C network analyzer and two
standard gain horn antennae in order to measure theExperimental observa
localization using meta
Humeyra Caglayan,1,* Irfan Bulu
1Nanotechnology Research Center-NANOTAM, Depart
Engineering, Bilkent Universi
2School of Engineering and Applied Sciences,
Massachuse
*Corresponding author:
Received August 5, 2008; revised Novem
posted December 3, 2008 (Doc. ID
We report subwavelength localization of electromagn
ity resonances are observed in the transmission spe
terials cavity structures. These cavity resonances a
cells of metamaterials are much smaller than the op
sible within these metamaterial cavity structures. I
field is localized into a region of 
 /8, where 
 is the
America
OCIS codes: 350.4010, 160.3918.
The response of any material to electromagnetic
(EM) waves is determined by two parameters: dielec-
tric permittivity () and magnetic permeability 
.
Generally,  of naturally occurring materials is posi-
tive. Four decades ago, Veselago [1] proposed that ar-
tificially constructed materials can enable the nega-
tive values of  and , since there are no restrictions
with the laws of electromagnetism. In this pioneering
study, Veselago predicted that via artificially con-
structed materials, along with simultaneously nega-
tive  and , difficulty in obtaining negative refrac-
tion, reverse Doppler shift, and backward Cherenkov
radiation can all be overcome. However, obtaining a
simultaneously negative  and  and, therefore, a
negative index of refraction is a significant challenge.
Metallic thin wires arranged periodically are good
candidates for a negative  medium, because thistaining a localized field is to make a deformation in a
0146-9592/09/010088-3/$15.00 ©on of subwavelength
aterial-based cavities
arko Loncar,2 and Ekmel Ozbay1
t of Physics, Department of Electrical and Electronics
ilkent, 06800 Ankara, Turkey
ard University, 33 Oxford Street, Cambridge,
2138, USA
yan@fen.bilkent.edu.tr
11, 2008; accepted November 23, 2008;
3); published December 24, 2008
fields within cavities based on metamaterials. Cav-
m of a split-ring resonator and composite metama-
own to exhibit high-quality factors. Since the unit
ion wavelength, subwavelength localization is pos-
e present Letter, we show that the electromagnetic
ty resonance wavelength. © 2008 Optical Society of
unit cell of the periodic structure. This phenomenon
has been investigated experimentally and theoreti-
cally in photonic crystal structures [9–11]. Photonic
crystal defects have many important applications
such as thresholdless semiconductor lasers [12] and
single-mode light-emitting diodes [13]. However, de-
fect structures in metamaterials are investigated
only for periodically arranged single negative materi-
als [14]. In the present Letter, we investigate cavity
formation in SRR and CMM structures. We first
present the transmission results for SRR and CMM
structures. Subsequently, we introduce the cavity
structure and present the transmission of the SRR
cavity and CMM cavity structures. Our results show
that the modification of a unit cell of the metamate-
rial can exhibit a cavity resonance. Finally, we show
that the cavity formation in the metamaterials leadstransmission amplitude. The calculations throughout
2009 Optical Society of America
January 1, 2009 / Vol. 34, No. 1 / OPTICS LETTERS 89the Letter were performed by the commercial soft-
ware program CST Microwave Studio.
The SRR structure that was used in this work has
a bandgap between 5 and 7 GHz. However, the
closed-ring resonator (CRR) structure, which was ob-
tained by closing the splits in the rings, transmitted
EM waves at these frequencies [Fig. 2(a)]. Therefore,
this gap is due to the magnetic resonance [15], in
which the SRR structure exhibits a negative  me-
dium. When the electromagnetic field passes through
the ring, an induced current is created, and the gen-
erated field is perpendicular to the magnetic field of
the light. The magnetic resonance results in a nega-
tive . EM waves cannot propagate in the negative 
medium and possess a bandgap in the spectrum. On
the other hand, the CMM structure transmits EM
waves at the bandgap frequency of the SRR [Fig.
2(b)], since it has negative  and () at this range [4].
To break the symmetry of these periodic left-
handed metamaterials, we changed the center unit
cell of the structures by a closed-ring structure,
which was placed on both sides of the board and pos-
sessed positive  and  [Fig. 1(c)]. This deformation
in the SRR and CMM structures resulted in a cavity
structure with a cavity resonance in the transmission
spectrum. In Figs. 3(a) and 3(b) the transmission
from the SRR cavity and CMM cavity structures are
shown, respectively. The calculations agreed well
with the experiments. We observed a cavity reso-
nance with the Q factor (quality factor, defined as the
center frequency, divided by the FWHM) of 192 at
Fig. 1. (a) Unit cell of the SRR structure: a=4.95 mm, b
=0.25 mm. (b) Unit cell of the CMM structure: c=1.6 mm.
(c) Cavity structure: d=5.4 mm, e=1 mm. The unit cells of
metamaterials are much smaller than the operating
wavelength.
Fig. 2. (Color online) (a) The SRR structure has a bandgap
between 5 and 7 GHz. However, the CRR structure trans-
mits EM waves (black curve). Hence, the SRR structure ex-
hibits 0 medium at these frequencies. (b) The CMM
structure transmits EM waves, because it has 0 and
0 at this range.6.7 GHz 
44.7 mm by the SRR cavity structure. The
cavity resonance of the CMM structure was obtained
at 7.5 GHz 
40 mm with a Q factor of 108.
The reflection of the SRR (CMM) structure is very
high in the negative 
 frequency range, and, there-
fore, the SRR (CMM) structures on both sides of the
cavity behave like frequency-specific mirrors [16,17].
Any propagating light that is trapped between them
will bounce back and forth between these two mir-
rors. Since the mirrors localize light within a finite
region, the modes are quantized into discrete fre-
quencies, just as in Fabry–Perot resonances. The cav-
ity resonance frequency depends on the geometry and
size of the defects, as well as the geometry of the SRR
and CMM. This mechanism is investigated in [18].
The calculated electric-field distributions for the
cavity structures show that the EM waves at the cav-
ity resonance are trapped at the positive index region
(Fig. 4). The length of the cavity is only 
 /8, where 

is the cavity resonance wavelength. Hence, the field
at the cavity resonance is enhanced at the subwave-
length cavity region. Such a structure with enhanced
electromagnetic fields can be used for several appli-
cations, including nonlinear optics. Although it is
possible to localize light into a subwavelength region
with a regular Fabry–Perot cavity, this localization is
not smaller than 
 /2n, where n is the refractive in-
dex of the dielectric gap. However, the phase disper-
sion properties of metamaterial-based cavity systems
can be used to confine light into even smaller sub-
wavelength dimensions.
Although the field is highly localized at the cavity
region, the quality factors are not that high. The cal-
culated transmissions for an SRR cavity structure
Fig. 3. (Color online) A cavity structure is introduced by
replacing the center unit cell with a positive-index me-
dium. The cavity resonance is observed at 6.7 GHz

44.7 mm and 7.5 GHz 
40 mm by the (a) SRR cavity
structure and (b) the CMM cavity structure, respectively.
Fig. 4. (Color online) The calculated electric field is highly
localized at the cavity region for (a) SRR cavity and (b)
CMM cavity structures. Hence, the field at the cavity reso-
nance is enhanced at the subwavelength 

 /8 cavity re-
gion. (Red indicates the maximum, and blue indicates the
minimum.)
without loss, with loss on a board only, and loss on
metal only showed that the transmission at the cav-
ity resonance is decreased because of the loss of the
board and metal (Cu). The calculated Q factor for the
SRR cavity resonance without loss is 3290, whereas
for the CMM cavity it is 1420. Therefore, one can ob-
tain metamaterial cavities with higher Q factors by
using different designs and materials.
In conclusion, we report what we believe to be the
first experimental observation of cavity formation in
metamaterials. Our results showed that it is possible
to obtain a cavity structure by the deformation of a
unit cell of metamaterials. We presented the Q fac-
tors of the cavity resonances as 192 for an SRR-based
cavity and 108 for a CMM-based cavity. Furthermore,
it is possible to obtain a Q factor as high as 3290 us-
ing loss-free materials. We subsequently showed that
the field is localized into a subwavelength 

 /8 re-
gion at the cavity resonance frequency. The proposed
cavity structures can be extended to optical frequen-
cies and can be used in several applications such as
nonlinear optics [19] and high-density data storage.
This work is supported by the European Union
(EU) under the projects EU-METAMORPHOSE,
EU-PHOREMOST, EU-PHOME, EU-ECONAM, and
4. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-
Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184
(2000).
5. E. Ozbay, I. Bulu, and H. Caglayan, Phys. Status
Solidi B 244, 1202 (2007).
6. I. Bulu, H. Caglayan, and E. Ozbay, Opt. Lett. 31, 814
(2006).
7. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J.
B. Pendry, A. F. Starr, and D. R. Smith, Science 314,
977 (2006).
8. A. M. Belyantsev and A. B. Kozyrev, Tech. Phys. 47,
1477 (2002).
9. J. D. Joannopoulos, R. D. Meade, and J. N. Winn,
Photonic Crystal: Molding the Flow of Light (Princeton
U. Press, 1995).
10. M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev.
Lett. 84, 2140 (2000).
11. P. A. Postigo, A. R. Alija, L. J. Martínez, M. L. Dotor, D.
Golmayo, J. Sánchez-Dehesa, C. Seassal, P.
Viktorovitch, M. Galli, A. Politi, M. Patrini, and L. C.
Andreani, Photonics Nanostruct. Fundam. Appl. 5, 79
(2007).
12. P. R. Villenevue, S. Fan, and J. D. Joannopoulos, K.-Y.
Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif,
Appl. Phys. Lett. 67, 167 (1995).
13. P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M.
Brennan, and B. E. Hammons, Appl. Phys. Lett. 64,
687 (1994).
90 OPTICS LETTERS / Vol. 34, No. 1 / January 1, 2009TUBITAK under projects 105E066, 105A005,
106E198, 106A017. E. Ozbay also acknowledges par-
tial support from the Turkish Academy of Sciences.
References
1. V. G. Veselago, Sov. Phys. Usp. 10, 504 (1968).
2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J.
Stewart, J. Phys. Condens. Matter 10, 4785 (1998).
3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J.
Stewart, IEEE Trans. Microwave Theory Tech. 47,
2075 (1999).14. Y. H. Chen, J. W. Dong, and H. Z. Wang, Appl. Phys.
Lett. 89, 141101 (2006).
15. K. Guven, K. Aydin, and E. Ozbay, Photonics
Nanostruct. Fundam. Appl. 3, 75 (2005).
16. K. Aydin and E. Ozbay, IEE Proc. Microwaves,
Antennas Propag. 1, 89 (2007).
17. E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir,
IEEE Trans. Antennas Propag. 51, 2592 (2003).
18. H. Caglayan, I. Bulu, M. Loncar, and E. Ozbay, Opt.
Express 16, 11132 (2008).
19. A. Yariv and P. Yeh, Photonics: Optical Electronics in
Modern Communications (Oxford U. Press, 2007).