The basic idea of a non-imaging light concentrator is that if you just want bright light in a particular spot and don’t care about making the light form an optical image, you can just generally reflect random light into the desired place. The concentrated light then illuminates any subject in that spot from all sides, making a very bright yet diffuse light. This idea has already been used for concentrating sunlight for solar power applications, but as far as I can see nobody has applied it to photography. So, how about if I design one that will catch most of the light from my on-camera flash, and direct the bulk of it into the relatively small volume that I actually want to illuminate?
Innovations in lighting for macro photography, driven by the need to do well-lit photos of bugs. From the Backyard Arthropod, "A Field Guide to the North Side of Old Mill Hill, Atlantic Mine, MI".