Download John Pendry - Imperial College London

Strange things happen when we simultaneously flip the sign of electrical permittivity and magnetic
permeability: we get negative refraction, and light comes to a perfect focus!
John Pendry
ELECTRICAL PERMITTIVITY, e and magnetic permeability, m ,
are concepts deeply embedded in electromagnetism and
summarise the response of an homogeneous medium to electric
and magnetic fields. These familiar quantities are usually
thought of as positive numbers, but in principle negative values
are allowed for both e and m and in practice negative values of
e are realised at optical frequencies for metals. From e and m
we can derive the refractive index,
n = em
(1)
think that whatever other weaknesses in my grasp of
electromagnetism, bending of light at a surface is something I
have got a grip on. Making the bending negative has dramatic
consequences which challenge our intuition.
Negative permittivity
If negative permittivity is required at optical frequencies we
may use a metal. Silver is a good choice because the resistivity
is very low and its permittivity almost purely negative with a
very small imaginary part. In metals the surface is of particular
which determines how light is bent on traversing from one interest because the interface between a metal and vacuum
supports electromagnetic modes, referred to as surface plasmon
material to another. e , m and n and are the
polaritons. For a flat surface the frequency
1
Negative
refractive
index
three players in our story. The theme is what
of these modes is almost independent of
happens when these quantities take negative
wavelength, except at long wavelengths
values either separately or together.
comparable to the free space wavelength at
The optical response of metals is
that frequency, typically 100nm, and except
determined their electrons which are in
at very short wavelengths comparable to the
essence a plasma of free charged particles.
spacing between electrons, typically 0.1nm,
Their finite mass means that they do not
where the modes are not defined. Between
respond instantaneously to electric fields but
these limits lies a vast range of well defined
do so 90° out of phase. Hence the negative
modes which dominate electromagnetic
values of e .
properties near the metal/vacuum interface.
Naturally occurring materials do not have A material with negative refractive index
Optical properties of metals, i.e. of
negative values of m and artificial materials bends rays of incident light to the
materials with negative permittivity, are at
‘wrong’ side of the normal. Meanwhile
with negative m appeared on the scene only the wave vector points in the opposite
their most interesting when the metal is
to the energy flow because the
recently. The trick was to produced a direction
highly structured and has lots of interfaces
group velocity is negative.
microstructured material containing coils of
with the vacuum. For example silver
wire on a scale much smaller than the
colloids such as we find in photographic
wavelength of radiation, constructed so that currents flow in plates appear black and are highly absorbing to light because
response to a magnetic field. Careful design of these structures the surface modes soak up the incident electromagnetic energy.
enables negative values of m to be achieved though so far this These surface modes also play some other tricks. Thomas
has been possible only at microwave frequencies. Figure 2 Ebbesen asked how is it possible to squeeze light through a
shows some typical values achieved in these artificial materials. small hole. His experiments showed light transmitted through
Again we see the strong dispersion with frequency which is tiny holes in a silver films, only a fraction of the wavelength in
diameter. The answer turned out to be that the light is first
required of materials with negative m .
What about negative refractive index? This I find the captured by a surface plasmon which squeezes through the hole
strangest part of our story perhaps because like most physicists I and turns back into ordinary light on the far side.
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2001
1
This surface alter ego of light
opens up optics to nanoscience.
Ordinary light with a wavelength
of several thousand nm is blind
to details of a few tens of nm. If
however we can turn light into a
short wavelength surface mode
fine details zap into focus
because the shorter wavelength
radiation responds to fine detail.
Later we shall see the ultimate
exploitation of surface modes to
construct a perfect lens.
2 Swiss rolls and magnetic materials
Doping the vacuum
At optical frequencies metals
such as silver provide a good
approximation
to
negative
permittivity, but at lower
A sheet of metal coiled into a ‘Swiss roll’ responds to a magnetic field with a current. An array of
Swiss rolls produces a material which has negative magnetic permeability over a range of
frequencies losses due to
frequencies. Improving the dielectrics used can considerably reduce the imaginary part of m and
electrical
resistance
are
increase the resonant response.
increasingly problematic and in
the microwave regime e for
compared to solid metal, about the same concentration as
dopants in a semiconductor.
metals is an almost entirely imaginary quantity.
The fact that the wires are thin also plays a role: thin wires
However it is possible to make an artificial material with the
desired properties. To lower the frequency where negative e is have an inductance that diverges with decreasing radius and any
found we need to lower the density of the charged particles in current in the wires works against this inductance. The net
the free plasma, and to increase their mass. This can be effect is as if the electrons were much heavier than they really
achieved in a structure comprising a mesh of very thin wires. In are. In fact it has been calculated that the electrons are as heavy
one particular realisation the wires were a few tens of microns as nitrogen atoms in this structure.
Negative permeability - fooling the field
Maxwell’s equations are symmetrical in electric and magnetic
fields. So as far as Maxwell is concerned, what we can do for
electricity we can also do for magnetism: negative permeability
would be found in a free plasma of magnetic north and south
poles. Unfortunately the real world does not continue the
symmetry of the equations and has a distinct lack of free
magnetic poles: despite thorough searches not even one has
been found so far, and we need billions of them to produce
negative permeability! The only chance we have is to cheat.
Imagine a very long solenoid energised with a current:
opposite ends behave as though they were north and south
poles. Reverse the current and the poles reverse their position.
To an external observer without knowledge of the internal
workings of the solenoid and ignorant of the non-existence of
magnetic poles, it would appear as though a plasma of north and
south poles was sloshing about inside the tube containing the
solenoid. Obviously electrical currents can mimic the effect of
magnetic poles.
Next consider a stack of metal cylinders. Applying a magnetic
field parallel to their common axis induces currents flowing
around the cylinders which in turn produce a magnetic field.
The medium has magnetic properties, but is paramagnetic and
does not have negative m. Unfortunately the virtual plasma of
free poles inside the cylinders does not have positive mass! To
(a) Cross section of a high impedance surface. The structure
consists of a lattice of metal plates connected to a solid metal
fix this we need to alter that phase of the current and to do this
sheet below by vertical conducting post. Magnetic fields in the
we introduce capacitance into the system. Instead of a
plane of the surface generate currents shown in red which charge
continuous metal circumference the cylinders now comprise
the capacitance between upper and lower plates. (b) Top view of
the high impedance surface, showing a triangular lattice of
sheets of metal wound without touching in the manner of a
hexagonal metal plates.
Swiss roll as shown in figure 2. Current can only flow by
in diameter and spaced by a few mm. This reduces the density charging the capacitance between inner and outer winding. This
of electrons in the structure by about a factor of a million system now behaves like a plasma of magnetic poles with
3 A high impedance surface
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2001
positive mass and has negative permeability, at least in a
certain range of frequencies as can be seen from the panel in
figure 2.
A similar idea is deployed in the “high impedance surface”
proposed by Sievenpiper et al.. A metallic surface has as large
electrical permittivity and a magnetic permittivity of the order
of unity, and hence a low impedance. In contrast a surface with
large magnetic permeability and electrical permittivity of the
order of unity would have a high impedance to radiation. This
new material turns out to have valuable properties when used
in designing low profile antennae for mobile communications.
A cross section of the surface is shown in figure 3. Magnetic
fields parallel to the surface induce currents in the incomplete
circuit shown by charging the capacitance between the free
ends. This gives a large resonant magnetic response, and the
high impedance sought.
5 Negative refraction
Magnetic resonance imaging
Despite the high cost of MRI equipment, such is the value of
the images it is one of the most widely used imaging
techniques in medicine. A very strong quasi static magnetic
field defines the frequency of the resonance, and an RF probe
picks up the signal. Although resolution is obtained by means
of a gradient on the quasi static field, controlling and directing
the RF field is also an issue.
Top: the sample and the microwave absorber were placed between
A recent paper in Science explored the possible application
top and bottom parallel aluminum plates spaced 1.2 cm apart. The
of the magnetic Swiss rolls to directing the RF fields. We have
thick red arrows represent the microwave beam. The detector was
argued that these coils behave as though they contained a
rotated around the circumference of the circle in 15° steps and the
transmitted power spectrum was measured as a function of angle, q,
magnetic plasma of free north and south poles. In other words
from the interface normal.
near the resonant frequency they are like magnetic wires
Bottom: transmitted power at 10.5 GHz as a function of refraction
conducting flux to where it might be needed. Another crucial
angle for both a Teflon sample (dashed curve) and a negative
property is that, being constructed entirely of non magnetic
refractive index sample (solid curve). For the Teflon sample, the
refracted power peak was measured to be 27° corresponding to n
ingredients, their response to the quasi static fields is zero. This
= +1.4. For the LHM sample, the peak was at 61° from which we
guarantees that the imaging process remains undisturbed.
deduce the index of refraction to be n = -2.7.
Wiltshire et al. were able to demonstrate that a bundle of
First, as was discussed in an earlier Physics World article, he
Swiss rolls conducts the RF field from a patient’s hand (for
example) and gives a strong signal in the receiving coil. Without showed that a slab of such a medium would focus light. He also
pointed out that the energy flow in an electromagnetic wave
the Swiss rolls no image can be seen.
would be in the opposite direction to the wave vector (see
4 Swiss rolls and magnetic resonance imaging
figure 1), which led him to christen these materials ‘left
handed’. Other surprising consequences were a reversed
Doppler effect and Cerenkov radiation that emerges in the
opposite direction to the direction of the incident particle.
However after a few more papers, in the face of the complete
unavailability of any material with negative permeability,
interest in the subject died out and the paper was forgotten. It
was only the design of artificial materials with negative
permeability that prompted Smith and Schultz to revive the idea
and to construct the first negative refractive index material.
More recently, Shelby Smith and Schultz published an
exciting paper in Science demonstrating that a prism of the new
material bends light in a negative direction. Figure 5 shows their
A small 37 mm diameter coil acts as the receiver, and a thumb is
experiment and the data they obtained. The work of Smith and
the object to be imaged. The 200-mm space between the phantom
Schultz showed that it was not impossible to realise these
and the thumb is filled either with an inert plastic block (centre)
strange materials and brought a renewed interest to the field
when only the phantom is visible, or with Swiss rolls (right). Now
stimulating a further injection of ideas
the image of the thumb can clearly be seen.
A blast from the past
Some years ago, in 1968, a remarkable paper was published by
V.G. Veselago which speculated as to the consequences of
making both e and m negative. He came to some remarkable
conclusions.
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The challenge of the near field - a perfect lens
Central to the immense field of optics is the ability to control
and particularly to focus light. one of the earliest applications of
optics was the microscope which revealed details of the natural
world previously hidden from us. Soon it was realised that there
is a natural limitation to the power of the microscope set by the
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wavelength of light. Nothing smaller than this can be resolved.
As science has advanced to study the world of nanotechnology
the optical microscope has become increasingly redundant as a
tool of investigation. Yet it is a mistake to suppose that there is
no electrical or magnetic activity on very short length scales. For
example if we could map the electric fields close to a set of
atomic dipoles emitting visible light they would reveal where
the atoms were. The problem is that these fields are largely
electric fields lacking the magnetic component needed to escape
from the vicinity of the dipole. Far from the dipole these ‘near
fields’ fall of as 1 r 2 in contrast to the radiative field with its
1 r decay. The former contains all the fine detail but decays
rapidly and has so far eluded capture, the latter is subject to the
wavelength restriction in resolution but propagates freely and
can easily be captured and focussed into an image. Because the
near field components are missing this image will not resolve
details of the atomic dipoles
Until recently that has been the end of the story, but last year I
asked myself if negative refractive index materials could change
this situation. We already new that a slab of negative refractive
material can focus light from objects placed on one side to an
image of the far side. I thought that I had better check whether
the near fields are left out of the image just as they are
abandoned by a conventional lens.
It seemed a silly question because to focus the near fields we
need to amplify them to compensate for their rapid decay.
Surely this violates energy conservation? But not so because
there is a get-out clause: energy is transported away from an
object entirely by the far field and the near field being static
does not need a flow of energy to sustain it. In fact a rigorous
Satisfying Maxwell is all very well, but what is happening
inside the material, and how can a passive substance behave like
an amplifier? It turns out that the interior of our negative
material is acting in some ways like a photographic process with
negative and positive images. The key to understanding lies in
recognising that equation (2) is the condition for surface
plasmon states to exist on the surface of the material. These
states can be thought of as highly localised excitations which
once excited do not propage parallel to the surface. As a first
step the weak incident near field excites surface plasmons on
the first surface of the slab. Think of this as a sort of
photographic negative - it is certainly not a focussed image.
Next the surface plasmons excited on the first surface begin a
resonant interaction with the surface plasmons on the second
surface and because the resonance is very strong the image is
transferred to the second surface in a hugely amplified form. In
fact it is still out of focus because the various components have
been deliberately over-amplified so that the field escaping from
the far side of the slab decays by just the right amount to bring
all the components to exactly the right amplitude in the image
plane. So now we can understand how it is possible to amplify
the near field: resonances are the key and it is well known how a
very weak source can stimulate a large resonant amplitude.
But is it any use?
This is a new field, or at least a recently revived one, and so far
most of the activity has concentrated on understanding these
very strange materials and trying to make practical realisations.
To make an enduring contribution we must find applications. No
problems about that if a perfect material were easily available.
Who wants DVDs that can store 100 times more data than they
do now because the optics are 100 times better?
6 Focussing the near field
Who wants to do optical lithography on silicon
with a resolution 10 times better than at present?
What hospital would refuse an MRI machine an
order of magnitude cheaper than the present
generation? All these things might be possible
given perfect realisation of the materials. It all
turns on what can be done in practice so the next
stage of the game is to see what we can get away
with in terms of less than ideal materials, and by
optimising their design. There are some hopeful
signs: pure silver might be a good candidate for an
near field optical lens and in the microwave region
artificial structures are being designed that give
moderately good approximations to the ideal. The
problem is that very weak near fields need very
The near-field component of an object needs to be amplified before it can make
its contribution to an image. This can be done by forming a ‘negative image’ in the
strong amplification and this places severe
surface plasmons on the left hand surface of the slab which in turn couple to and
constraints on material properties.
resonantly excite surface plasmons on the right hand surface. Thus amplification
So wide are the potential applications for these
is seen to be due to resonant enhancement of a field. The condition n = -1
materials that even if we fail to reach some of our
ensures existence of surface plasmon modes at the operating frequency.
more ambitious goals, it would be surprising if
solution of Maxwell’s equations leads to the remarkable
some of the applications were not realised. The outlook is very
conclusion that the near fields can be focussed by a negative
positive for negative materials.
refractive index material with only one proviso: that the
condition,
e = -1, m = -1
(2)
is exactly fulfilled. The requirement that negative materials are
dispersive tells us that this can happen only at a single
frequency. For the first time Maxwell’s equations give us a
prescription for the perfect lens and that was the title of a
Physical Review Letter which appeared in October of last year.
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Further reading
T. W. Ebbesen et al. 1998 Extraordinary optical transmission through
sub-wavelength hole arrays Nature (London) 391 667
J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart 1999
Magnetism from Conductors and Enhanced Non-Linear Phenomena
IEEE Transactions on Microwave Theory and Techniques, 47, 2075
J.B. Pendry 2000 Negative Refraction Makes a Perfect Lens Phys. Rev.
Lett. 85, 3966
D.F. Sievenpiper, L. Zhang, R.F. Jimenez Broas, N.G. Alexopolous, E.
Yablonovitch 1999 High-Impedance Magnetic Surfaces with a
Forbidden Frequency Band IEEE Transactions on Microwave Theory
and Techniques, 47, 2059
R.A. Shelby, D.R. Smith, S. Schultz 2001 Experimental Verification of a
Negative Index of Refraction Science, 292, 77
D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz
2000 Composite Medium with Simultaneously Negative Permeability
and Permittivity Phys. Rev. Lett. 84, 4184
V.G. Veselago 1968 The Electrodynamics of Substances with
Simultaneous Negative Values of e and m Soviet Physics USPEKHI, 10,
509
M C K Wiltshire, J B Pendry, I R Young, D J Larkman, D J Gilderdale
and J V Hajnal 2001 Microstructured Magnetic Materials for RF Flux
Guides in Magnetic Resonance Imaging (MRI) Science 291 848
John Pendry is in The Blackett Laboratory, Imperial College, London,
SW7 2BZ, UK
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