In total internal reflection light inside a dense medium reflects from the boundary to a less dense medium. Since by Snell's law there is no allowed refracted ray, all energy continues along the reflected ray. In the wave picture there is an evanescent wave decaying exponentially in the thinner medium but not transmitting any energy outward.
As noted in the answer to the previous question "Why is light energy 100% reflected in total internal reflection?" this is not exactly 100% efficient. However, there was no referenced exact answer of how efficient the reflection can be. My question is basically: given a perfect crystal slab of some material with an infinite perfect vacuum above, what is the efficiency of reflection in terms of material properties?
The most obvious limit would presumably be due to material impedance: the surface wave is moving at a certain velocity, pulling local charges back and forth in such a way that some energy is lost. Unavoidable surface imperfections may also interfere. There could also be some photon tunnelling across the interface (although that moves the analysis into the quantum realm). But are there any actual measurements or theoretical calculations of how much energy loss there is to a vacuum from the slab?
Optical fibres give some hints, although the geometry is more complex and the beam is usually parallel to the fibre rather than slanted. A length constant of $\sim 10$ km is fairly normal.
