Vol 438|17 November 2005|doi:10.1038/nature04242
LETTERS
Nanofabricated media with negative permeability at
visible frequencies
A. N. Grigorenko1, A. K. Geim1, H. F. Gleeson1, Y. Zhang1, A. A. Firsov1,2, I. Y. Khrushchev3 & J. Petrovic3
A great deal of attention has recently been focused on a new class submicrometre size (Fig. 1). The simplification of the resonator
of smart materials so-called left-handed media that exhibit geometry with respect to the double split-rings geometry used in
highly unusual electromagnetic properties and promise new microwaves is important for two reasons. First, this allows the use of
device applications1 6. Left-handed materials require negative current lithography techniques to fabricate metallic structures with
permeability m, an extreme condition that has so far been achieved plasmon resonances at visible-light frequencies. Second, the simple
only for frequencies in the microwave to terahertz range7 11. geometry reduces the number of resonant modes interacting with a
Extension of the approach described in ref. 7 to achieve the light field, which consequently leads to a reduction in energy losses.
necessary high-frequency magnetic response in visible optics Note that such changes in geometry also reflect the trend known
presents a formidable challenge12 15, as no material natural or from lasing techniques, where complex closed resonators used in
artificial is known to exhibit any magnetism at these frequen- masers were replaced by simple open resonators (pair of mirrors) in
cies. Here we report a nanofabricated medium consisting of lasers16,17.
electromagnetically coupled pairs of gold dots with geometry
carefully designed at a 10-nm level. The medium exhibits a strong
magnetic response at visible-light frequencies, including a band
with negative m. The magnetism arises owing to the excitation of
an antisymmetric plasmon resonance. The high-frequency per-
meability qualitatively reveals itself via optical impedance match-
ing. Our results demonstrate the feasibility of engineering
magnetism at visible frequencies and pave the way towards
magnetic and left-handed components for visible optics.
Landau and Lifshitz argued12 there is certainly no meaning in
using the magnetic susceptibility from optical frequencies onwards,
and in discussion of such phenomena we must put m ź 1 . This
statement is strongly supported by experiment: the magnetic sus-
ceptibility x of all natural materials tails off at microwave frequencies.
Still, there may be a way to overcome the fundamental limitations, as
shown by Pendry et al. who have suggested exploiting the inductive
response from structured non-magnetic materials to obtain high-
frequency magnetism7. The idea was successfully implemented by
using arrays of copper split-rings that generated a magnetic response
at frequencies up to 100 THz (refs 8 11). In this case, magnetic
properties emerge owing to collective motion of a large number of
electrons, and theoretical arguments (as, for example, in ref. 12) valid
for individual electrons and atoms no longer hold. It is tempting to
extend the approach further to visible-light frequencies, where one
can expect most applications. However, the direct scaling of
the demonstrated microwave media to visible optics is problematic.
This would require split-ring-like structures with sizes down to
100 nm and critical features9 11 controlled on the level of ,10 nm,
which is technologically difficult to achieve. More importantly, the
scaling could fail in principle because of different electromagnetic
responses of materials to visible light and microwaves (for example,
Figure 1 | Nanofabricated medium with magnetic response at optical
it was predicted that inherent losses should limit the approach
frequencies. a, Scanning electron micrograph (viewed at an angle) of an
demonstrated in refs 7 11 to frequencies well below optical9,13).
array of Au nanopillars. b, c, Numerical simulation of the distribution of
In this work, by employing a novel geometry, we make a critical
electric currents (arrows) inside a pair of such pillars for the symmetric and
step of demonstrating metamaterials with magnetic response at
antisymmetric resonant z-modes, respectively. The non-cylindrical shape of
frequencies in the visible spectrum. The design of our media follows
pillars is important to provide an efficient coupling to incident light, and was
recent theoretical suggestions14,15, and relies on antisymmetric
intentionally introduced in our design through a choice of microfabrication
plasmon resonances in a simple pair of short metal pillars of a procedures.
1 2
Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK. Institute of Microelectronics Technology, 142432 Chernogolovka, Russia.
3
Department of Electronic Engineering, Aston University, Aston Triangle, Birmingham B4 7ET, UK.
335
2005 Nature Publishing Group
LETTERS NATURE|Vol 438|17 November 2005
Figure 1 shows an example of our devices and illustrates the basic the polarization of incident light was rotated by 908, the high-
idea behind the experiment. The prepared structures were large frequency, green resonance disappeared, and the reflection spectra
arrays of Au pillars fabricated by high-resolution electron-beam showed only the low-frequency, red resonance, albeit with its
lithography on a glass substrate and grouped in tightly spaced pairs position slightly shifted (Fig. 2b, d and f). The change in the
(except for reference samples consisting of similar but isolated Au reflection spectra was so marked that the colour of the samples
pillars). The structures typically covered an area of ,0.1 mm2 and viewed in white light changed (see photographs in Fig. 2). Our
contained ,106 pillars. The lattice constant, a, for periodic arrays structures looked amber for TE light, similar in colour to the media
was down to 400 nm that is, smaller than the wavelength l of visible consisting of isolated pillars. In stark contrast, for TM polarization,
light. Heights h of Au pillars (80 90 nm) and their diameters the structures look green owing to a large contribution from the
d < 100 nm were chosen through numerical simulations so that green resonance.
the plasmon resonance in the reference samples appeared at red-light The spectral positions of red and green resonance peaks did not
wavelengths, l < 670 nm. A number of different structures were depend on the lattice constant for all studied samples with pillar pairs
studied with d between 80 nm and 140 nm and the pair separation s of the same dimensions (Fig. 2c and e shows two examples with
between centres of adjacent pillars in the range 140 nm to 200 nm; a ź 400 and 600 nm). This excludes diffraction as a possible origin
that is, the gap s 2 d between the neighbouring pillars varied from for the observed resonances. This was further confirmed by making
100 nm down to almost zero. (The best results were achieved at random arrays of pillar pairs, which did not influence the spectral
s ź 200 nm, d ź 140 nm, h ź 80 nm, and s ź 140 nm, d ź 110 nm, positions of the resonance peaks. (It is worth noting that, contrary to
h ź 90 nm.) At these separations, electromagnetic interaction our case, diffraction modes play a prominent role in light reflection
between neighbouring pillars within a pair is important and plasmon from perforated metal22 or arrays of nanoparticles deposited on
resonance observed for an individual pillar splits into two resonances metallic substrates23.) Although the resonance positions did not
for a pillar pair. These resonances are referred to as symmetric and depend on a, they were strongly affected by changing separation s
antisymmetric, similar to the case of any classical or quantum system and by covering the structure with a dielectric medium, as expected
with two interacting parts and in agreement with the notation used for resonances split by electromagnetic interaction between pillars.
for plasmon resonances in nanoparticles18. As an example, Fig. 2a and b shows reflection spectra of the same
There exist three symmetric and three antisymmetric main sample as in Fig. 2c and d but covered by an optically thin (,30 nm)
resonant modes in an interacting pair with currents flowing along layer of glycerine. This resulted in a notable red-shift of the green
the x, y and z axes. Figure 1 shows the symmetric (Fig. 1b) and the resonance peak by dl < 50 nm, in agreement with red-shifts
antisymmetric (Fig. 1c) z-modes calculated for our experimental
geometry using Femlab software (Comsol Inc.). For the symmetric
resonance, electrons in neighbouring pillars move in phase and
generate overall a dipole contribution to permittivity 1, similar to
isolated or non-interacting pillars. In the antisymmetric z-mode,
however, electrons move in anti-phase so that the oscillating dipoles
cancel each other leaving only magnetodipole and quadrupole
responses19. One can see in Fig. 1c that the anti-phase movement
of electrons along the z axis effectively results in a current loop in the
z x plane (note that a pair of pillars can be thought of as a ring with
two slits at the opposite sides). This high-frequency electric current
generates a magnetic moment in the y-direction and contributes to
permeability m. Not all resonant modes are necessarily excited by
incident light. Modes coupling to light is governed by the symmetry
group of a pillar pair, which is C2v in our case. For this group, normal
incident light with the electric field along the x axis (later referred to
as TM polarization) is coupled to both the dipole symmetric x-mode
and the magnetic antisymmetric z-mode, while normal light with the
electric field along the y axis (TE polarization) excites only the dipole
symmetric y-mode, as discussed in ref. 20. The choice of the
symmetry group is important for creating magnetic response (for
example, magnetic modes are not necessarily excited in a pair of
infinite cylinders with the symmetry group C2h; ref. 21).
The symmetry of our pillar pairs thus implies that an array of pillar
pairs should exhibit two main plasmon resonances (z-antisymmetric
and x-symmetric) for TM light of normal incidence, one of which
(z-antisymmetric) disappears and the other (x-symmetric) changes
into y-symmetric resonance as we rotate polarization by 908, to TE
polarization. On the other hand, an array of isolated pillars should
demonstrate only one resonance for both polarizations. Our experi-
ments confirmed this. Figure 2 shows the reflection spectra measured
in normal incident light of TM and TE polarizations (green and red
Figure 2 | Experimental reflection spectra for our nanostructured
curves, respectively) for arrays made of pillar pairs of the same
media. Green and red curves are for TM and TE polarizations of normal
dimensions but different lattice constants, as well as for the reference
incident light, respectively. Micrographs of the studied samples are shown
array of isolated pillars (micrographs of the corresponding samples
on the right. For all the samples, pillars have the same separation
are shown next to their spectra.) The reference array exhibits only one
s ź 140 nm, height h ź 90 nm and average diameter d ź 110 nm. Spectra
resonance at l < 670 nm for both polarizations (Fig. 2g and h), in
a, b, are for the sample of c, d, but covered with an optically thin layer of
agreement with our symmetry and numerical analyses. On the other
glycerine; for c, d, the lattice constant a ź 400 nm; for e, f, a ź 600 nm;
hand, arrays made of the same pillars but packed in interacting pairs
g, h, are for isolated pillars with a ź 600 nm. The top photographs show
showed two distinct resonances in the TM spectra (Fig. 2a, c and e). If images of the sample a, b, in white light for two polarizations.
336
2005 Nature Publishing Group
NATURE|Vol 438|17 November 2005 LETTERS
reported for multipole resonances in nanoparticles24. Moreover, we j(q) ź j0/(1 2 iqt), where q is the angular frequency of light,
observed a significant increase (by a factor of 3) in the strength of the j0 ź 3.7 Ł 1017 s21 the conductivity of gold and t ź 2.4 Ł 10214 s
green resonance. Note that, in this case, the structure reflected as the scattering time, and the glass substrate by a dielectric with
much as 10% of light near the green resonance peak (Fig. 2a), which permittivity 1 ź 2.25. The calculations have confirmed that TM
is a significant magnitude under our experimental conditions (for green light of normal incidence with l ź 500 nm excites anti-phase
comparison, a glass substrate with 1 ź 2.25 reflects only 4% of the currents flowing mostly along the z axis (Fig. 3a), which is a
incident light). characteristic of the antisymmetric z-mode. A current loop is
The described experiments assign the green-light resonance (dis- effectively created in the z x plane, which generates strong magnetic
appearing in TE polarization) unambiguously to the antisymmetric fields Hy in the region between pillars (the red region of Fig. 3a) and
z-mode, which gives rise to m, and the red-light resonances to produces a substantial magnetic moment. On the other hand, TM
the x- and y-symmetric modes, contributing to 1 (refs 14, 15). To red light at l ź 690 nm excites mostly in-phase currents flowing
further strengthen this identification of the resonances, we compare along the x axis, which do not produce any significant magnetic
the measured spectra with theory (Fig. 3). The theoretical calcu- moment (Fig. 3b).
lations were performed with the Electromagnetic module of Femlab We have also calculated the spectral dependence of effective
software, which solves Maxwell s equations for the actual experimen- permeability and permittivity of our structures. Figure 3 shows the
tal geometry. We described pillars by Drude s conductivity absolute values and real parts for 1x and my (denoted here as 1 and m)
for the tightest pair packing (the curves were obtained by solving
Maxwell s equations for an electromagnetic wave interacting with a
periodic array on top of a glass substrate). The calculated spectral
positions of the peaks in 1 and m are in good agreement with the peak
positions found experimentally, and the theoretical reflection spectra
also agree well with the experimental data. The calculations show that
our microstructures have considerable permeability m0 ; Re(m)
ranging from 21 to 3 for the array of tightest packing (Fig. 3d).
For the sample of Fig. 2c, for example, its calculated permeability
varied between 0.5 and 1.5, and for Fig. 2a m0 varied between 20.25
and 2.1.
As a complementary analysis to the numerical simulations, we
have employed another approach that is routinely used in optics to
extract material parameters from reflection spectra25,26. To this end,
we noted that, neglecting mode interaction, the calculated reso-
nances in permittivity followed the standard dispersion relation25
D1(l) ź fsl2/(l2 2 l2 2 ilDls), where ls is the wavelength of the
s
symmetric resonance, Dls its half-width and fs the effective oscillator
Figure 4 | Example of fitting the experimental reflection spectra with
theory. The green curves are the measured spectra of Fig. 2; the blue curves
Figure 3 | Numerical simulations of optical response for interacting Au show the best fit based on the dispersion relations described in the main text.
pillars. a, b, Distribution of electric currents (red arrows) and magnetic The parameters of the main resonances extracted from the fitting curves are
field Hy (colour map measured in units of the magnetic field amplitude of as follows. Single pillars; ls < 665 nm, Dls < 165 nm and fs < 0.79. Pairs
the incident wave) for the pillars being illuminated by normal incident light with a ź 600 nm; ls < 690 nm, Dls < 147 nm, fs < 1.76 and la < 550 nm,
of TM polarization with wavelengths l ź 500 nm (a) and l ź 690 nm (b). Dla < 85 nm, fa < 0.06. Pairs with a ź 400 nm; ls < 685 nm,
Geometrical sizes are shown in metres at the bottom and the left of images. Dls < 147 nm, fs < 3.27 and la < 552 nm, Dla < 80 nm, fa < 0.16. Pairs
Dots in the image refer to Au nanopillars. c, d, The spectral dependence of covered with a glycerine film; ls < 710 nm, Dls < 140 nm, fs < 1.7 and
permittivity 1 and permeability m: c shows the absolute values and d the real la < 598 nm, Dla < 80 nm, fa < 0.32. The spectrum of the sample covered
parts. e, f, Calculated reflection spectra corresponding to the experimental with a glycerine film is offset for clarity. The insets show micrographs of the
situation in Fig. 2. corresponding samples.
337
2005 Nature Publishing Group
LETTERS NATURE|Vol 438|17 November 2005
7. Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from
strength. The spectral dependence of calculated permeability is
conductors and enhanced nonlinear phenomena. IEEE Trans. Microwave Theory
also described well by the Pendry-type expression7,10 ml ź
Tech. 47, 2075 (1999).
-2084
1 f l2=l2 2 l2 2 ilDla, where la, Dla and fa are the same
a
a a
8. Wiltshire, M. C. K. et al. Microstructured magnetic materials for RF flux guides
notations as above but for the antisymmetric resonance (see Sup-
in magnetic resonance imaging. Science 291, 849 -851 (2001).
plementary Information for details). The combination of these 9. Pendry, J. B. & O Brien, S. Magnetic activity at infrared frequencies in
structured photonic crystals. J. Phys. Condens. Matter 14, 6383 -6394 (2002).
dispersion relations with the Fresnel s reflection coefficients for a
10. Yen, T. J. et al. Terahertz magnetic response from artificial materials. Science
thin anisotropic film placed on a glass substrate25,26 leads to relatively
303, 1494 -1496 (2004).
simple expressions that can be used to fit the experimental spectra
11. Linden, S. et al. Magnetic response of metamaterials at 100 terahertz. Science
and find 1 and m. For example, in the case of Fig. 2c, the best fit to its
306, 1351 (2004).
-1353
spectra yields x0 < 20.5 (m0 < 0.5) near l ź 470 nm and corrobo- 12. Landau, L. D. & Lifshitz, E. M. Electrodynamics of Continuous Media Section 60
(Oxford, Pergamon, 1960).
rates the results of the Femlab calculations (see Fig. 4). Similarly, the
13. Dimmock, J. O. Losses in left-handed materials. Opt. Express 11, 2397 -2402
spectra for the samples covered with a glycerine film and showing an
(2003).
increased strength in the antisymmetric resonance yielded a signifi-
14. Panina, L. V., Grigorenko, A. N. & Makhnovskiy, D. P. Metal-dielectric medium
cant increase in jxj, such that negative values of m0 were achieved
with conducting nanoelements. Phys. Rev. B 66, 155411 (2002).
almost routinely. For example, x0 was about 21.3 at the green 15. Podolskiy, V. A., Sarychev, A. K. & Shalaev, V. M. Plasmon modes in metal
nanowires and left-handed materials. J. Nonlinear Opt. Phys. Mater. 11, 65
-74
resonance in Fig. 2a (that is, m0 < 20.3). Although our structures
(2002).
exhibited both negative m0 and negative 10 within the same range of l
16. Prokhorov, A. M. Molecular amplifier and generator for submillimeter waves.
(for example, 10 < 20.7 and m0 < 20.3 at the green resonance in Fig.
Zh. Eksp. Teor. Fiz. 34, 1658 (1958).
-1659
2a), m had a rather large imaginary component (m00 ; Im(m) < 1i at
17. Schawlow, A. L. & Townes, C. H. Infrared and optical masers. Phys. Rev. 112,
the resonance), which so far has not allowed the observation of
1940 -1949 (1958).
18. Aizpurua, J. et al. Optical properties of gold nanorings. Phys. Rev. Lett. 90,
negative refraction.
057401 (2003).
We have however observed another effect optical impedance
19. Jin, R. et al. Controlling anisotropic nanoparticle growth through plasmon
matching that is more tolerant to dissipation but also exclusive to
excitation. Nature 425, 487 -490 (2003).
materials with a finite permeability. The effect of impedance match-
20. Barron, L. D. Molecular Light Scattering and Optical Activity (Cambridge Univ.
ing is characterized by the total suppression of reflection from an
Press, Cambridge, UK, 1982).
21. Kottmann, J. P. & Martin, O. J. F. Plasmon resonant coupling in metallic
interface between two media with different refraction indices,
nanowires. Opt. Express 8, 655 (2001).
-663
n ź (1m)1/2, but the same impedance values, Z ź (1/m)1/2. This
22. Ebbesen, T. W., Lezec, H. J., Ghaemi, H. F., Thio, T. & Wolff, P. A.
impedance matching is well known for electrical and microwave
Plasmon-assisted transmission of entangled photons. Nature 391, 667
-669
circuits but was never observed for conventional optics, because it
(1998).
requires m 1 (except for singular cases of optical waveguides27),
23. Felidj, N. et al. Enhanced substrate-induced coupling in two-dimensional gold
which has been unachievable until now. In our case, this phenom- nanoparticle arrays. Phys. Rev. B 66, 245407 (2002).
24. Mock, J. J., Smith, D. R. & Schultz, S. Local refractive index dependence of
enon resulted in a total invisibility of our structured films at green-
plasmon resonance spectra from individual nanoparticles. Nano Lett. 3,
resonance frequencies for TM polarization of incident light, while
485 -491 (2003).
the films could still be seen by using phase contrast imaging or
25. Born, M. & Wolf, E. Principles of Optics Section 2.3 (Cambridge Univ. Press,
TE polarization. For brevity, the experiments are described in
Cambridge, UK, 1980).
Supplementary Information. 26. Abeles, F. in Physics of Thin Films Vol. 6 (eds Francombe, M. H. & Hoffman,
R. W.) Ch. V -VII (Academic, New York, 1971).
Received 19 May; accepted 19 September 2005. 27. Gademann, A., Durkan, C. & Shvets, I. V. Optical impedance matching with
near-field optical microscopy. J. Phys. D 36, 2193 (2003).
-2197
1. Veselago, V. G. The electrodynamics of substances with simultaneously negative
values of permittivity and permeability. Sov. Phys. Usp. 10, 509 (1968).
-514
Supplementary Information is linked to the online version of the paper at
2. Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85,
www.nature.com/nature.
3966 -3969 (2000).
3. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative Acknowledgements This research was supported by EPSRC (UK). We thank
index of refraction. Science 292, 77 -79 (2001). L. Panina and D. Makhnovskiy for discussions, and N. Roberts for collaboration
4. Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C. & Schultz, S. in experiments. A.A.F. acknowledges support from INTAS.
Composite medium with simultaneously negative permeability and
Author Information Reprints and permissions information is available at
permittivity. Phys. Rev. Lett. 84, 4184 -4187 (2000).
npg.nature.com/reprintsandpermissions. The authors declare no competing
5. Pendry, J. B. Positively negative. Nature 423, 22 (2003).
-23
financial interests. Correspondence and requests for materials should be
6. Houck, A. A., Brock, J. B. & Chuang, I. L. Experimental observations of a
left-handed material that obeys Snell s law. Phys. Rev. Lett. 90, 137401 (2003). addressed to A.N.G. (sasha@man.ac.uk).
338
2005 Nature Publishing Group
Wyszukiwarka
Podobne podstrony:
335 3382005 12 442005 05 444434blue nature126@7 pol ed02 200506 2005 5 099Laszlo, Ervin The Convergence of Science and Spirituality (2005)2005 09 38więcej podobnych podstron