The Perfect Lens
Negative refraction can be used to focus light. In fact a flat slab of material will produce two foci: one inside the medium, the other outside. This was pointed out by Victor Veselago in his seminal paper in Soviet Physics USPEKHI, 10, 509 (1968).
the focussing properties of a negative slab are rather unusual, especially for the ideal case where,
In this instance rays are drawn to an aberration-free focus, and suffer no reflection from the surfaces of the slab. Yet the focussing properties are even more remarkable than this: further investigation has shown that the slab is free from the wavelength restriction on resolution. In the ideal limit resolution increases without bounds.
In figure A an object emits electromagnetic waves of frequency w. Each wave has a wave vector, k, where,
is responsible for driving the wave from object to image, and the other two components of k define the Fourier components of the image. The larger the magnitude of the Fourier components the better the resolution. The problem is that making these transverse wave vectors too large gives an imaginary value in the formula above and the wave decays exponentially along the z-axis. These decaying components of the object field are often referred to as the ‘near field’. They are confined to the vicinity of the object and serve to lock away high-resolution information. Hence the biggest Fourier component that we can capture has magnitude,
and the wavelength restriction on resolution follows.
How does our negative slab avoid this limit? The secret it deploys is a surface resonance which is used to amplify evanescent waves and restore them to the values taken in the object plane. Given time, a resonance can build a substantial amplitude using energy drawn from the source. Absorption is the great enemy of resonances so low loss materials are essential if we are to approach the resolution offered by the new lens.
The resonances are related to the surface plasmon excitation familiar on the surfaces of metals, the condition for which is, in the short wavelength limit,
In our case,
and there are two surface excitations, one of electric the other of magnetic character.
This is a remarkable result because, in order to ‘focus’ the near field, amplification has to take place to compensate for the natural decay and furthermore the amplification has to be exactly tuned to each Fourier component of the field. Surfaces of negatively refracting materials are heavily decorated with resonant states.
Sub wavelength focusing was first realised experimentally by the Eleftheriades group at GHz frequencies where the necessary metamaterials are available.
An optical version of the lens is more difficult. Although metals such as silver have an intrinsic permittivity that is negative, magnetic responses at optical frequencies are rare and as yet we do not have a fully 3D negatively refracting optical material at least not one that is capable of sub wavelength operation. An approximation to the perfect lens can be had if all the dimensions are much less that the wavelength. Under these conditions the electric and magnetic components of the field are almost independent and we are free to concentrate on the electrical part ignoring magnetic effects. A purely electrical field is indifferent to m and therefore it should be possible to construct a ‘poor man’s lens’ of silver by tuning the frequency so that,
Losses in the silver prevent exact realisation of this condition but nevertheless a version of this lens was built by the Xiang group in Berkeley, and by the Blaikie group in Canterbury New Zealand. Both groups demonstrated sub wavelength imaging on a scale of a few tens of nanometers. Figure C below shows an image from the Zhang group. Resolution obtained is approximately l/6.
Top panel: original object
middle panel: image viewed through the silver lens
bottom panel: image without the lens
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