I took the time to recreate the coloring effects my phone screen has when the screen is off and viewed at an angle. When I rotate my phone once the color shifts from dark-gold-ish to dark-aqua back to dark-gold-ish.
There are two effects that are too difficult to create in vanilla cycles (without plugins):
- Because of the pixels there is a slight interference pattern (hence the discoloring). I'd have to get the thickness of pixels, the IOR of pixels and calculate the color that is cancelled out through interference (the result is a wavelength that I would have to convert to RGB). Besides it doesn't really come out IRL either.
- Because the screen is made of pixels that act like little reflectors, it'll look like a caleidoscope when you reflect a light source off of it. It would require a rediculously detailed normal map and a lot of processing power, so I neglected that as well.
Anyways, if you want to "turn on the screen", then run whatever you want to display through an emission (I'd say 0.9 strength is a good value) shader and that into the empty socket on the dark-aqua 'Add Shader' node. I find the result to be very close to real life.