Project Idea #2: A Perfect Luminaire (more explanation)

Total Internal Reflection is a phenomena that keeps light trapped within an optic fiber (and therefore a fiber bundle).  A light ray inside a medium with a higher index of refraction striking an interface will emerge at a sharper angle, and if that angle becomes so sharp that it dives back into the medium, then none of the energy in the ray will leave at all.  In general, at any interface between two media, such as glass, which has a high index of refraction, some fraction of the energy will be reflected, and some transmitted. Normal glass reflects about 4% of the light that hits it straight-on.

So the idea of the Perfect Luminair project is to figure out something simple, and very hard (at least to my knowledge.)  How do you shape a flat piece of some transparent material so that you can shine light into its side and make the light come out in an even field.  That is, in a perfect solution, you could take it outside, use a magnifying glass to focus the sun directly into the end of the fiber bundle, and the plate would magically produce a smooth, even glow.

Note that in the diagram above I have drawn two shapes, neither of which would work very well: The black shape would dump the light too quickly, and the blue shape would never dump the red ray at all!  Since their will be a certain amount of dispersion coming out of the fiber bundle, there will of course be a certain amount of light leaking almost everywhere.

We seek first a mathematical solution.  Given an input from the bundle with a given dispersion profile, what shape will maximize both the brightness and evenness of the escaping light?

Note that making light escape forward is obviously a significant problem.  You can of course back-silver the surface, though any reflection of a metallic surface will cost you about 8%.

Ideally, we would like a nice, smooth, easy to manufacture piece of glass.  However, a rugose, or bumpy, piece of glass would work as well---maybe the surface should be "rippled".

A different, but related approach would be to split the fiber bundle, and direct individual fibers to different places on the plane---but it would be better not to make any assumptions about the light entry at all.  For example, if we don't insist on a fiber bundle, then we could place a fluorescent bulb along one edge, and still produce a pleasing, diffuse light.

This problem is mathematically interesting in its own right, but could also improve light efficiency, including in developing countries, where a traditional copper-based power wiring could be completely avoided for at least some lighting situations.


If this problem has been addressed, please let me know---I'm not aware that it has even been researched.