A fisheye lens proposed over a century ago can produce perfectly focused images without using any exotic "negative refractive index" materials, a physicist in the UK has calculated.

Ulf Leonhardt of St Andrews University claims that a fisheye lens – of the type invented by the great 19th century physicist and mathematician James Clerk Maxwell – can focus beyond the troublesome diffraction limit, which precludes standard lenses from achieving a resolution finer than the wavelength of light.

Scientists thought perfect lenses were unattainable until 2000, when physicist John Pendry of Imperial College London showed that materials with a negative index of refraction – that is, those that bend light the "wrong" way – should beat the diffraction limit. But engineering such materials proved difficult, and it was only in 2005 that two groups in the US created the first "superlens" which could image features with a size just one-sixth the wavelength of light.

### 'Unlimited resolution'

Now Leonhardt has shown that Maxwell's idea, first published over 150 years ago, can give perfect images without negative refraction. "It is the waviness of light that limits the resolution of lenses," said Leonhardt in a press statement. "Apparently, nobody had tried to calculate the imaging of light waves in Maxwell's fisheye. The new research proves that the fisheye has unlimited resolution in principle, and, as it does not need negative refraction, it may also work in practice."

Maxwell's fisheye involved a refractive index profile that matches the geometry of a sphere. With this profile, light rays emitting from any direction on one point of the sphere would follow circles all the way round until they meet, perfectly, on the opposite side. Put a plane at the equator, however, and these rays would instead be mapped onto the plane's two dimensions – rather like cartographers map the globe onto a flat sheet of paper. Again, this mapped image would in principle have perfect resolution.

Could this be done in practice? The problem, as Leonhardt points out, is that distortion inherent in the mapping would require light on one side of the sphere to travel faster than the speed of light in the vacuum – a known impossibility. A way around this, he says, would be to place a mirror around the sphere's equator so that the rays give the illusion of travelling all the way round, when in fact they are reflected and are therefore travelling at subluminal speeds.

### Slab of silica

Leonhardt describes how a researcher could make a flat, two-dimensional version of the lens. In would consist of a slab of silica with tiny air holes or silicon pillars to create the refractive index profile, with a circular mirror placed on top. Unlike a superlens, in which negative refraction tends to have the unwanted side effects of high absorption and a narrow wavelength-range of operation, the fisheye lens would have high light transmission and would work across a broad part of the electromagnetic spectrum.

There could be many applications of the fisheye lens. For example, if a researcher were to place a sliver of material with an unusual structure against the lens and shine a light through it, the sliver would act as a mask, and the lens could focus an image of the structure onto a light-sensitive surface such as a photoresist. This would enable a new breed of electronics with features at atomic resolution.

### 'Work in progress'

Leonhardt told physicsworld.com that a group at Cornell University in the US is attempting to realize his design, although it is "work in progress for the time being."

The research is published in the New Journal of Physics.