Subwavelength resolution with a negative-index metamaterial superlens
Koray Aydin, Irfan Bulu, and Ekmel Ozbay
Citation: Appl. Phys. Lett. 90, 254102 (2007); doi: 10.1063/1.2750393
View online: http://dx.doi.org/10.1063/1.2750393
View Table of Contents: http://aip.scitation.org/toc/apl/90/25
Published by the American Institute of Physics
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Subwavelength resolution with a negative-index metamaterial superlens
Koray Aydin,
a兲
Irfan Bulu, and Ekmel Ozbay
Nanotechnology Research Center-NANOTAM, Bilkent University, Bilkent, 06800 Ankara, Turkey;
Department of Physics, Bilkent University, Bilkent, 06800 Ankara, Turkey; and Department of Electrical
and Electronics Engineering, Bilkent University, Bilkent, 06800 Ankara, Turkey
共Received 8 March 2007; accepted 26 May 2007; published online 19 June 2007兲
Negative-index metamaterials are candidates for imaging objects with sizes smaller than a
half-wavelength. The authors report an impedance-matched, low loss negative-index metamaterial
superlens that is capable of resolving subwavelength features of a point source with a 0.13
resolution, which is the highest resolution achieved by a negative-index metamaterial. By separating
two point sources with a distance of /8, they were able to detect two distinct peaks on the image
plane. They also showed that the metamaterial based structure has a flat lens behavior. © 2007
American Institute of Physics. 关DOI: 10.1063/1.2750393兴
Refraction is a basic phenomenon that is widely used in
electromagnetism and optics, and forms the basis of imaging
process and lenses. Ubiquitous materials have positive re-
fractive indices; however, it is possible to obtain negative
values of refractive index by making use of the concept of
metamaterials and photonic crystals.
1,2
The possibility of
bringing the refractive index into the domain of negative
values was first discussed by Veselago
3
in which the first
steps to realize these exciting materials were taken four de-
cades later.
4
Inspired by the intriguing electromagnetic 共EM兲
properties arising from negative-index metamaterials
共NIMs兲, these types of artificially constructed structures re-
ceived burgeoning interest from the scientific community.
5–11
A perfect lens is one of the most important applications
of materials with a negative refractive index. The term, per-
fect lens, was coined by Pendry owing to the ability of such
lenses to reconstruct a perfect image by recovering the eva-
nescent components of EM waves.
12
In conventional optics,
the lenses are constructed from positive-index materials and
require curved surfaces to bring EM waves into focus.
Positive-index lenses act only on the phase of the radiation,
thus their resolution is limited to the half-wavelength. The
finer details of the image are carried by high-k components,
the so called evanescent waves, and quickly decay before
reaching the image plane. Therefore, the contribution of eva-
nescent components to the resolution of the image is absent
in conventional lenses. However, Pendry conceived that it is
possible to enhance evanescent waves by using a negative
refractive index medium. Photonic crystals
13
and
metamaterials
6–10,14,15
were experimentally demonstrated to
achieve diffraction-free imaging, in which further theoretical
studies
16–18
supported these results. In this letter, we demon-
strate an impedance-matched, low loss negative-index
metamaterial superlens that is capable of resolving subwave-
length features with a record-level 0.13 resolution, which is
the highest resolution achieved by a negative-index metama-
terial. In our study, we employed a two-dimensional 共2D兲
metamaterial based on split ring resonator 共SRR兲 and wire
geometry to achieve subwavelength resolution.
The NIM under investigation is a slab of 2D SRR-wire
arrays deposited on FR4 printed circuit boards 关Fig. 1共a兲兴,
with the parameters provided in Ref. 10. The NIM slab has
40⫻20⫻ 3 layers along the x, y, and z directions with equal
lattice constants in all directions, a
x
=a
y
=a
z
=9.3 mm. The
NIM slab has a thickness of 2.79 cm 共⬃/3兲 and a length of
38 cm 共4.8兲. Transmission and reflection measurements are
performed to characterize 2D NIM, in which the results are
plotted in Fig. 1共b兲. A well-defined transmission peak is ob-
served between 3.65 and 4.00 GHz, where the effective per-
meability and effective permittivity of NIM are simulta-
neously negative.
10
A sharp dip in the reflection spectrum is
observed at 3.78 GHz. The reflection is very low, −37 dB,
meaning that the incident EM waves nearly do not face any
reflection at the NIM surface.
The effective parameters of the NIM are retrieved by
using the calculated amplitudes and phases of transmission
and reflection by following the method in Ref. 19 The am-
biguity in the determination of the correct branch is resolved
by use of an analytic continuation procedure.
19
Dielectric
permittivity =
⬘
+i
⬙
and magnetic permeability
=
⬘
+i
⬙
are used to describe the response of materials to the
incident electromagnetic field, where
⬘
and
⬘
are the real
parts, and
⬙
and
⬙
are the imaginary parts of the corre-
sponding effective parameters. Figure 2共a兲 depicts the real
parts of 共blue line兲 and
共red line兲, and simulated reflec-
tion spectrum 共black line兲.
⬘
and
⬘
possess negative values
between 3.63 and 3.93 GHz. The minimum reflection in the
simulations occurs at 3.74 GHz, where
⬘
=
⬘
=−1.8 共dashed
orange line兲. The real and imaginary parts of the index of
refraction n
⬘
共blue line兲 and n
⬙
共green line兲 and the real part
of impedance Z
⬘
共red line兲 are plotted in Fig. 2共b兲. The im-
a兲
Electronic mail: aydin@fen.bilkent.edu.tr
FIG. 1. 共Color online兲共a兲 Photograph of NIM slab with three unit cells
along the z direction. 共b兲 Measured transmission 共blue兲 and reflection 共red兲
spectra for a NIM slab.
APPLIED PHYSICS LETTERS 90, 254102 共2007兲
0003-6951/2007/90共25兲/254102/3/$23.00 © 2007 American Institute of Physics90, 254102-1
pedance is defined as Z=
冑
⬘
/
⬘
; therefore impedance
matching is obtained when
⬘
=
⬘
. Expectedly, the imped-
ance of NIM is matched to that of free space at 3.74 GHz,
where Z
⬘
=1.
The imaging measurements presented here are per-
formed at 3.78 GHz, where the reflection is considerably low
and the losses due to reflection are negligible. The NIM has
a refractive index of n
eff
=−2.07± 0.22 at 3.78 GHz, which is
measured by using a wedge-shaped 2D NIM.
10
The refrac-
tive index obtained from the retrieval procedure is n
eff
=
−1.81. Figure of merit is defined as the ratio of n
⬘
to n
⬙
and
used to characterize the performance of NIMs.
20–22
In our
simulations, we found n
⬘
=−1.81 and n
⬙
=−0.15 at 3.74 GHz.
Therefore, the figure of merit is 12, the highest value ever
reported. The NIM structure has low absorption losses, and
therefore can be used to achieve subwavelength resolution.
In the imaging experiments, we employed monopole an-
tennae to imitate the point source. The exposed center con-
ductor acts as the transmitter and receiver and has a length of
4cm共⬃ /2兲. Firstly, we measured the beam profile in free
space that is plotted in Fig. 3共a兲 with a red dashed line. The
full width at half maximum of the beam is 8.2 cm 共1.03兲.
Then, we inserted NIM superlens and measured the spot size
of the beam as 0.13, which is well below the diffraction
limit. The source is located d
s
=1.2 cm away from first
boundary and the image forms d
i
=0.8 cm away from second
boundary of the superlens. The intensity of the electric field
at the image plane is scanned by the receiver monopole an-
tenna with ⌬x = 2 mm steps. The field intensity is normalized
with respect to the maximum intensity in figure.
However, this focusing behavior could have been due to
a channeling effect. The SRR-wire boards are separated with
9.3 mm and the field may propagate on these channels. To
ensure that the subwavelength imaging is due to the effective
response of NIM and not that of individual channels, we
moved the point source along the source plane to check the
flat lens behavior.
23
The resulting intensity distributions are
plotted in Fig. 3共b兲 for different source locations, namely, x
=0 cm 共black line兲, 0.5 cm 共red line兲, and −1.3 cm 共gray
line兲. In all the cases, the images were formed exactly at the
same x distance with the source. It is noteworthy that the
distances are not the multiples of the lattice constant, i.e., the
sources are not located on the axes of SRR-wire boards.
We used two point sources separated by distances
smaller than a wavelength to obtain subwavelength resolu-
tion. The sources are driven by two independent signal gen-
erators and the power distribution is detected by using a mi-
crowave spectrum analyzer. The frequencies of the sources
differ by 1 MHz to ensure that the sources are entirely inco-
herent. The reason behind using incoherent sources is to pre-
vent the contribution of interference effects to the imaging
resolution measurements.
13
The measured power distribution
of sources, separated by / 8, is plotted by the black line 共쎲兲
in Fig. 4. As seen in the figure, the peaks of two sources are
clearly resolved. The resolution becomes better for / 5 sepa-
ration between the sources 共red line, 䉲兲. Finally, when the
sources are /3 apart 共blue line, 䊏兲, two peaks are entirely
resolved. In order to avoid any possible channeling effects,
the sources are intentionally not placed at the line of SRR-
wire boards. Besides, the distances between the sources in all
three experiments are carefully chosen such that they are not
multiples of the lattice constant. The lattice constant is on the
order of / 8.5; therefore the NIM structure behaves as an
effective medium. The periodicity has a significant effect on
the resolution of the superlens by limiting the recovery of
evanescent components.
17
Following the analysis by Smith et al. where they dis-
cussed the effect of deviation from the ideal parameters on
subwavelength resolution, one may argue that superlens with
=
=−1.8 may not provide / 8 resolution. We think that
FIG. 2. 共Color online兲共a兲 Real parts of retrieved effec-
tive permittivity 共blue兲 and permeability 共red兲, and re-
flection spectrum 共black兲. 共b兲 Real parts of a retrieved
refractive index 共blue兲, impedance 共red兲, and imaginary
part of the refractive index 共green兲.
FIG. 3. 共Color online兲 The measured power distributions at the image plane
共a兲 with 共blue兲 and without 共dashed red line兲 NIM superlens. Normalized
intensity in free space is multiplied with 0.4 in the figure. 共b兲 The field
profiles from single sources placed at three different locations along the x
direction that are x=0 cm 共black line, 쎲兲, 0.5 cm 共red line, 䉲兲 and −1.3 cm
共gray line, 䊏兲.
254102-2 Aydin, Bulu, and Ozbay Appl. Phys. Lett. 90, 254102 共2007兲
anisotropic effects take place in our superlens and the ob-
served high resolution may be attributed to inherent aniso-
tropy of our structure. The effect of anisotropy on imaging
performance is discussed by Lagarkov et al.
7
In the near-field regime, the electrostatic and magneto-
static limits apply, and therefore, the electric and magnetic
responses of materials can be treated as decoupled.
12
This in
turn brings the possibility of constructing superlenses from
materials with negative permittivity
9,14
or negative
permeability.
15
Recently, Wiltshire et al.
15
reported /64
resolution that is obtained from a magnetostatic superlens
operating at radio frequencies with an effective permeability
value of
eff
=−1. The advantage of using negative-index
lenses over negative-permittivity or negative-permeability
lenses is that the subwavelength resolution can be obtained
for both transverse-electric and transverse-magnetic polariza-
tions of EM waves. However, single-negative lenses can
only focus EM waves with one particular polarization.
Superlenses can be used in several applications such as
imaging, sensing, and subwavelength nanolithography. Here,
we verified that it is possible to obtain subdiffraction resolu-
tion from a microwave superlens with an effective negative
refractive index. Since the NIMs are gearing toward optical
frequencies,
20–22
we believe that subwavelength resolution
can be achieved at visible wavelengths by employing thin
NIM superlenses. However, meticulous designs are needed
to achieve low loss, impedance-matched superlenses at opti-
cal frequencies, since the amount of absorption losses
is relatively large compared to the losses at microwave
frequencies.
This work is supported by the European Union under
the projects EU-NoE-METAMORPHOSE, EU-NoE-
PHOREMOST, and TUBITAK under Projects Nos.
104E090, 105E066, 105A005, and 106A017. One of the au-
thors 共E.O.兲 also acknowledges partial support from the
Turkish Academy of Sciences.
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FIG. 4. 共Color online兲 The measured power distributions for two point
sources separated with distances of /8 共black line兲, /5 共red line兲, and /3
共blue line兲. The normalized intensity in free space is shown with a green
dashed-dotted line and multiplied with 0.2 in the figure.
254102-3 Aydin, Bulu, and Ozbay Appl. Phys. Lett. 90, 254102 共2007兲
