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Left-Handed Materials: Super-Resolution Optics

by John G. Cramer

Alternate View Column AV-124
Keywords:  constructed, left-handed, optical, materials, negative, refractive, index, light, velocity, diffraction, limit
Published in the October-2004 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 5/4/2004 and is copyrighted ©2004 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


There has been a new development in optics, brought about by the artificial construction of new "left-handed" composite meta-materials that have "backwards" optical properties.  In this column we'll consider the development of these left-handed materials and their optical effects.

The existence of optically transparent materials is one of Nature's miracles.  Light, whether in the form of gamma rays, visible light, or radio waves, is essentially an electric field in motion.  That electric field always interacts strongly with the electrons in orbit around atoms, violently shaking and dislodging them and dumping energy in the process.  Because of this, we should naively expect all liquid and solid matter to be opaque to the passage of light, to be utterly black and absorbing.  And yet, we have transparent materials like water and glass, forms of matter through which visible light can pass almost as if the material was not there.

This amazing behavior occurs because the tightly bound outer electrons of transparent materials are vibrated in unison by the incoming light waves, so that they form a chorus line that catches and passes along the energy of light to the next line of electrons along the path.  Energy is transferred, bucket brigade fashion, by the electrons moving precisely in unison.  This process is called "coherence", and it is a very important phenomenon in optics.

One consequence of coherence in transparent materials is that the effective speed of light differs from c, the velocity of light in free space.  In water the speed of light drops to about 75% of c.  In some glass used for lenses the speed of light may be reduced to as low as 58% of c, and in diamond the speed of light goes down to 41% of c.  For historical reasons, this slow-down in light speed is represented in a rather confusing "upside down" way, using the index of refraction n, which is the speed of light in free space divided by the speed of light in the material.  The larger the value of n, the slower the speed of  light in the material.  For example, the index of refraction is n =1.33 for water, 1.75 for flint glass, and 2.42 for diamond.

Light waves in passing through the surface of a transparent material obey a rule called "Snell's Law", which requires that the index of refraction n times the sine of the angle the light makes with the direction perpendicular to the surface must be the same on both sides of the surface.  In other words, when light enters a transparent material through a surface and slows down, it bends to travel closer to the perpendicular to that surface.  Lens makers exploit this behavior by forming curved lenses that progressively tilt the surface to focus or defocus beams of light.  A lens is constructed so that the light rays passing through the lens farthest from the lens center encounter the most tilted surface and receive the strongest deflection.  This makes it possible for rays diverging from some object to be brought to a focus and to form an image of the object.

However, the wave nature of light and the limited aperture of the lens result in a limit on how sharp the image of an object can be.  This limit, called the Rayleigh criterion, is proportional to the wavelength of light divided by the lens aperture.  In part, it arises because one type of light wave, called an "evanescent" wave, is lost in passing through the glass of a lens, with a consequent loss of information and a slight spoiling of image sharpness.  This has been considered to be an unbreakable limit on the resolution of optical instruments.  However, as we will see, it appears that left-handed materials may provide an "end run" around the Rayleigh criterion, leading to improved resolution.

A light wave is formed by the simultaneous oscillations of an electric field and a magnetic field.  In transparent materials, the electric field normally has all the interactions, while its companion magnetic field essentially "goes along for the ride" and is left pretty much alone by materials it encounters.  Only when we focus on the direction of motion of the wave (or its "light pressure") does the magnetic field need to be examined.  The electric and magnetic fields are always perpendicular, and the light wave moves perpendicular to both of them.  You can use the so-called "right-hand rule" to tell which way the light wave will move.  Let the fingers of your right hand curl from the electric field direction to the magnetic field direction.  If you do this, the thumb of your right hand will be pointing in the direction that the light wave moves.

The new development is an artificially constructed left-handed material, a man-made meta-material that modifies the electric and magnetic fields of incoming light waves so that the index of refraction of the material becomes negative and the velocity of light in the material is a negative number.  At the moment, this trick is not applied to visible light, but rather to high frequency radio waves in the gigahertz region where the implementation is easier.

The trick is to construct a meta-material composed of a 3-dimensional array of tiny repeating clusters of small antenna bars and wires, conducting loops, and/or C-rings, so that each cluster of such elements is smaller than the wavelength of the light with which it is interacting.  For microwaves, this means that the array can have a cluster size of a few millimeters, which is well within the capabilities of modern micro-fabrication techniques.  The elements of the meta-material are designed to modify both the electric and the magnetic fields of the incoming waves so that the electric permittivity e and the magnetic permeability m are negative, and therefore are unlike the values of these constants in any known natural material.  The result is that the index of refraction n is also a negative number.  This means that the velocity the light waves in the material move in the opposite direction from the energy flow direction.  The energy goes forward but the wave crests move backwards.  The name "left-handed materials" comes from the fact that one would need to use a left-hand rule rather than a right-hand rule to determine the wave direction from the electric and magnetic fields.

For optical applications, the negative index of refraction of left-handed materials has two interesting consequences.  First, because of Snell's Law, it means that the angle that an incoming ray makes with the interface will become a negative angle on passing through the surface, so that a diverging ray becomes a converging ray.  Therefore, a simple flat surface for a left-handed material forms a converging lens.  The other consequence is that the evanescent waves generated at the interface grow in strength in passing through the left-handed material rather than dying off.  For this reason, a focus can be achieved that is independent of the aperture of the material and sharper than that predicted by the Rayleigh criterion.  In other words, super-resolution optics should be possible with lenses that are simple flat surfaces.  It's worth noting that the Doppler shift effect and Cerenkov radiation also work backwards in these materials.

Left-handed materials were first envisioned in the 1960s by the Russian physicist Victor Veslago.  At the time, it was thought that the material would have to be natural, and since no materials or crystals with negative magnetic permeability were know, it was considered a purely theoretical exercise.  But in 1996-1999, the British physicist John Pendry showed that a sub-wavelength wire and ring array should have just the properties needed to produce a left-handed medium with a negative index of refraction.

Pendry's proposal was met with great skepticism by many in the physics and electrical engineering communities, with many critics declaring that a negative index of refraction was simply impossible, and at least one critic comparing the idea to cold fusion.

However, experiments have dissipated these criticisms because it has been demonstrated that one can make three-dimensional arrays that exhibit the properties of negative index of refraction.  The Snell's law focusing was demonstrated in April, 2003 by a Harvard-MIT group for microwaves having a frequency of 10.5 GHz and a wavelength in free space of about 3 cm, with a measured index of refraction in a meta-material array of n=-0.35±0.08.  In February, 2004 a group from ITAE-Moscow demonstrated focusing and super-resolution imaging using 1.6 GHz microwaves (wavelength 19 cm).  Therefore, it is now clear that left-handed materials can be produced, at least for microwaves, and that they have the expected properties.

While these results may be important for advanced antenna design and possibly for radio astronomy, the real payoff will come if they can be extended into the region of visible light.  The issue in that region is whether functional meta-material arrays can be constructed at all, and whether the losses in such materials will be low enough to permit effective use of their optical properties.  One can think of simply scaling down the meta-material arrays from tens of millimeters to tens of nanometers.  However, conducting wires and rings at the ten nanometer scale will be chains of only a few atoms, and even if they could be fabricated by advance nano-scale fabrication techniques, their conduction properties would be determined more by quantum mechanics than by classical physics.

Thus, left-handed materials may represent the tip of a very large iceberg of technology, or they may simply become a laboratory curiosity that generates a footnote in optics textbooks.  In the next few years we should find out.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


Left Handed Material Theory

V. G. Veselago, Soviet. Phys. Usp. 10, 509 (1968)

J. B. Pendry, Phys. Rev. Letters 85, 3966 (2000).

Left Handed Material Optics Experiments

A. A. Houk, J. B. Brock, and I. L. Chuang, Phys. Rev. Letters 90, 137401 (2003).

A. N. Lagarkov and V. N. Kissel, Phys. Rev. Letters 92, 077401 (2004).

See also "Left-handed Metamaterials",

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