Aside from multi-layer and multi-angle discs, 3D optical matrix storage that has no moving parts save maybe a DLP to steer the beam or beams is a holy grail of the storage community.
Systems with a thereoretical density of 1TB per cm^3 have been demonstrated as far back as the 90's. Although it took an entire lab's worth of equipment to do it.
So long term, a very powerful diode, even if only in pulse mode would be desirable because you're going to be splitting up beams on X, Y, and Z axes, and probably many times after that so it can do several parallel read/writes on the dye molecules at once.
What you'd have is a little cube of transparent plastic, with something like the photo-reactive properties of those changing eyeglasses, except it only changes back only when the "erase" beam hits it instead of fading on it's own. And the lasers can scan the cube focusing at any depth to reach a dot at any row or column desired. It would be like having the data surface of hundreds of Blu-Ray discs crushed up into a little cube.