Self charging phones aren't that far away
engt.co
engt.co
The way a backlit LCD works is that the backlight produces light, which goes straight into a polarizer. That polarizer absorbs 50% of the light energy - if it absorbed any less, then the light wouldn't be polarized. Then the light passes through the liquid crystal element to another polarizer, which either passes the light through or blocks it completely.
If you assume that half the screen is lit at any given time, it's physically impossible to not absorb 75% of the light in the polarizer. There are really only two ways to improve this, one is to produce polarized light directly, and the other is to return the lost energy to the device some other way (as this does).
http://en.wikipedia.org/wiki/Polarizer#Beam-splitting_polari...
The better solution is to use LEDs or OLEDs. These do not require a backlight or any blocking but just generate the necessary color of light (and only the necessary color of light) from scratch.
It's self-charging at a rate perhaps slower than the rate at which is discharges, for now, but it is effectively charging itself. The question is does it break even?