How does a flat wedge lens work?

Question

I've been seeing this lens in a lot of places especially microsoft:

http://www.youtube.com/watch?feature=player_detailpage&v=rJ1p5SD3sOM#t=45s

http://blog.seattlepi.com/microsoft/2010/07/08/on-tap-at-microsoft-a-3d-display-without-glasses-and-multiple-programs-at-once/?from=blog_last3

It is a flat lens that bends light at 90 degrees. This allows all sorts of neat tricks like using the screen as a camera. For the life of me I can't understand how it's being done.

Can anyone here explain?

Answer 1

The short answer is: tapered waveguides. In a regular waveguide, a ray incident at less than the acceptance angle is constrained to travel down the waveguide, because of total internal reflection. The parallel surfaces of the waveguide ensure that the ray is always reflected at the same angle, which is greater than the critical angle.

In a tapered waveguide, the surfaces are not parallel anymore, so the angle of the rays traveling down the waveguide is not constant. At a certain point, the angle becomes less than the critical angle, and so the ray exits the waveguide through the side. By controlling the angle at which the ray enters the waveguide, you control the position at which the ray exits the waveguide through the side.

At the bottom of this page there are a few papers, which explain in more detail how the phenomenon works.