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1854 – Maxwell’s Fish-Eye Lens

1854 – Maxwell’s Fish-Eye Lens

In 1854, James Clerk Maxwell conceived of a perfect spherical lens while pondering the eye of a kipper (fish) that was served for breakfast. When light moves from one medium (like air) to another (like glass or water) it is bent as its speed changes. The degree to which it is bent is called the “index of refraction”. In some substances, the refractive index can change on a gradient as the substance changes. In Maxwells theoretical lens, the index of refraction would change as a function of the radius of the sphere. This would make it capable of converging all of the light reflected from an object into a perfect image of the object.

A mathematical problem arises with this theory when the limit of resolution is reached. In 1873, Abbe described this as a “diffraction limit” where the ability of a lens to resolve detail is limited as the size of the object approaches the size of the wavelength of the light being used.

For some time, it was assumed this limit would only be circumvented by using theoretical metamaterials with a negative refractive index. Metamaterials were first described in 1967 and a superlens based on them was described by John Pendry in 2000.

Perfect imaging

As a student at Trinity College in Cambridge, Maxwell wrote down the formula for a lens that reminded him of the eyes of fish (legend has it that he dreamed up his lens by musing over the eyes of a kipper at breakfast). In Maxwell’s “fish eye” [6] light rays from any point faithfully meet at a corresponding image point, all light rays from the object make it to the image. If light would consist of particles that follow the ray trajectories it would form a perfect image. But light is also a wave; and we know from Abbe that it is the waviness of light that limits the resolution of lenses. It was assumed that in reality the resolution would again be about half the wavelength. In 2009 we predicted [7] that this is not so: Maxwell’s fish eye should image waves with perfect resolution. This contradicted the accepted wisdom of subwavelength imaging [1] and created controversy [8]. Now there is strong experimental evidence [9] that it works. To understand why it works we need a bit of Einstein.

Maxwell’s Fishpond – [arxiv.org]

We have shown how an exotic phenomenon from trans-formation optics – the Maxwell’s Fisheye lens – can
be converted into simple water waves in a tabletop
“Maxwell’s Fishpond”.

0085 – Ptolemy
0965 – Alhazen
0984 – Ibn Sahl “On Burning Mirrors and Lenses” describes the law of refraction
1602 – Harriot discovers Snell’s law but does not publish
1621 – Snell’s (Snellius) law describes refraction
1637 – Descartes “Discourse on Method”
1662 – Fermat‘s Principle
1678 – Huygens-Fresnel principle
1608 – telescope
1642 – Newton – bio

1831 – Maxwell – bio
1851 – Helmholtz invents the opthalmoscope
1973 – Abbe diffraction limit
1874 – Abbe designs the refractometer

1944 – Luneburg spherical lens
1967 – Veselago describes metamaterials
2000 – Pendry proposes superlens made from metamaterial.

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