How To Build A Maxwell's Fishpond

How To Build A Maxwell's Fishpond: One mathematical solution stuck out as being particularly special: a lens in which all rays of light follow circular arcs. In this lens, light from any point in or on the sphere is always focused to another point on the other side of the sphere...
These guys have built a two dimensional version of Maxwell's fisheye lens which works with water waves rather than electromagnetic ones. Naturally, they call their device a Maxwell's fishpond.
The device is remarkably simply--a shallow dish with a curved bottom that rises towards the middle...When filled with water, waves on the surface behave in a remarkable way. The depth of the water determines the refractive index of waves on the surface. So the trick here is to design the shape of the bottom of the dish in a way that follows Maxwell's plan.
That turns out to be pretty straightforward with the result that a circular wave pattern does not simply spread out and disperse. Instead, it always reconverges to a point on the other side of the dish, regardless of where it formed in the first place.

Light Bends by Itself

Light Bends by Itself: In the late 1970s, physicists... discovered that a so-called Airy waveform, a wave describing how quantum particles move, can sometimes bend by a small amount...

...imagine light emitted from a wide strip—perhaps a fluorescent tube or, better, a laser whose output has been expanded. By carefully controlling the initial position of the wave peaks—the phase of the waves—at every step along the strip, it is possible to make the light traveling outward interfere constructively at only points on a curve and cancel out everywhere else. The Airy function, which contains rapid but diminishing oscillations, proved an easy way to define those initial phases—except that the resultant light would bend only up to about 8°.

Now physicists Mordechai Segev and colleagues at Technion, Israel Institute of Technology, in Haifa say they have a recipe for making light self-bend through any angle, even through a complete circle. The problem with the Airy function, says Segev, is that the shape of its oscillations specify the right phases only at small angles; at angles much greater than 8°, the shape becomes a crude approximation... After laborious mathematics and guesswork, the researchers found solutions to Maxwell's equations that precisely describe the initial phases required for truly self-bending light...

Feynman's derivation of Maxwell equations and extra dimensions

[hep-ph/0106235] Feynman's derivation of Maxwell equations and extra dimensions: "It is shown that Feynman's derivation of Maxwell equations admits a generalization to the case of extra spatial dimensions. The generalization is unique and is only possible in seven dimensional space."