the second close up focus only works when the light has a certain polarization
Not entirely accurate. It would be better to say that the contacts always focus one polarization of light so you can see things close up and the other polarization normally. Normal light has both polarizations, so only one of the two will be correctly focused, the other will be incorrectly focused, causing a diffuse blur in your field of vision (in one eye.) So, 1/2 of the light in 1/2 of your eyes will be blurry. So, 1/4 of the data your brain gets will be blurry. Maybe this isn't such a problem?
Maybe you combine it with polarizing (aka polaroid) sunglasses, so that the outside world only had the correct polarization?
No, the worst case is much, much lower. The problem is that there are two different definitions of efficiency going on here. The 90-100% conversion to electricity means that 90-100% of the absorbed photons are turned into single electrons. This does *not* say that 90-100% of the energy in the original photons is converted to energy in the electrons. In fact, just as in all other solar cell devices, the photons initially create fast moving electrons, converting all of their energy. But most of that kinetic energy is lost to heat before the electrons can be extracted from the device and used to do work.
So, the take-home message is that efficiency can refer to number of converted photons, regardless of how much energy was lost to heat.
You can derive the Schwartzchild radius using newtonian physics like clone53421 is claiming, and if that was what people were basing the existence of black holes on, then clone would be right. But it is just an accident that this derivation works.
If you do the derivation properly, using general relativity, you get the same result for the Schwartzchild radius. Though there are some interesting differences in how "radius" is defined in general relativity.
So, I'm sorry that the only derivation you saw was the incorrect classical physics one (which is used to motivate the result using simple math), but the answer is still true. But honestly, if you really thought that you were the first person to realize this problem with the derivation-- that none of the thousands of physicists to learn it since it was derived had noticed this glaringly obvious problem, then you are a monumental fool.
Metamaterials don't need to be periodic. They are made up of small (compared to the wavelength of light they work with) nano-fabricated structures, but even if they are randomly distributed it will have the desired effect. Just like both periodic structures (crystals) and amorphous ones (glass) have "normal" dielectric constants, so can metamaterials.
Some people say "periodic" when they just mean "made up of small stuff". If that was your complaint, then I challenge you to find something with any index of refraction that isn't "made up of small stuff."
Experimental data speculation + crackpot plasma theory = Slashdot science?