For instance, how would a "gem" made of negative refraction index material appear next to a diamond?
This question is meaningless and highly hypothetical. Where, in nature, do you get a material with a negative index of refraction? All of this type of material so far are meta-material.
I never said you would find such a material in nature. As you mention, an artificial "meta-material" can display a negative index of refraction. It may eventually be possible, if not currently feasible, to produce a structure with a substantial negative optical refractive index. My question is about how such a structure would appear versus the substance with the highest known optical index of refraction, diamond.
Er.. what do you mean by "appear"? As in what do you visually see with your eyes when you shine white light to it?
You do know that based on ALL of what we know about these meta-material, the bandwidth for the negative index of refraction to occur is extremely small, even smaller than the bandwidth of visible light. So even IF such a structure is possible in the visible range (assuming that this is what you're asking in the first place), there's a good chance that you won't notice that much of a difference in the "appearence" of the material since most of the light would not undergo any negative refraction.
Thanks, that's what I needed to understand.
Would it be much different than comparing a sphere of glass in air to a bubble of air in a block of glass?
Looking through the middle of the air bubble in glass, it should behave something like a concave lens, even though the bubble is convex.
What if it was a faceted bubble inside crystal?
it would look metallic
Such a material would look white.
A negative refractive index implies that "waves" inside such a material would have an intensity decreasing exponentially. These are called evanescent waves and occurs very often in nature. This does not mean the wave energy is absorbed in the material!
The traditional example is that of a cold electronic plasma below the plasma frequency. Such a wave impining on the plasma cannot penetrate it. It only generates an evanescent wave. Anything is reflected. So it will look white, or more precisely metallic. Indeed metals have a negative refractive index.
If there is an additional absorption mechanism, then the refractive index becomes a complex number.
I think you may be confusing refractive index with negative electrical permittivity, a negative refractive index requires both the electrical permittivity and magnetic permeability to be negative. Only meta-materials have been found to possess this property.
Currently, negative refraction is acheivable up to tens of GHz.
Here is a review paper by Costas Soukoulis' group (written in 2005) that may be of interest to all.
"Negative Index Materials: New Frontiers in Optics", Costas M. Soukoulis, Maria Kafesaki, and E. N. Economou, 2005.
A few pages down, the 'appearance' of planar negative refraction materials are discussed.
planish has the same idea as I.
Surely, a bubble in water has a negative index of refraction in the sense of the gemstone the OP mentions. More easily seen is a transparent bag or container full of air.
A bag (as simple as a baggie) full of air looks mirrored from the outside.
How about vitreous or aqueous humor gazing through the near vacuum of air?
I got to thinking about this again, and remembered that POV-Ray (free a ray-tracing program) supports refraction effects, and I speculated that it might be possible to render an object with negative values for "ior" (index of refraction) if the program would parse it.
I found a POV-Ray discussion forum thread on this very topic:
The upshot seems to be that negative ior is more of a problem of mathematics, not of physics. By default, rendered transparent objects have ior=1.0, (vacuum?). Typically you would specify some ior>1.0. You can still get interesting effects by specifying 1> ior >0. That would probably result in something similar to the bubble of air in crystal.
BTW - POV-Ray is an excellant program, if you take the time to learn the language. Totally free, for many different operating systems. - http://www.povray.org/
You are right: I had the permittivity in mind.
However, I don't see how negative permittivity and permeability leads to negative refractive index.
I assume the formula remains always the same: n = Sqrt(eps.mu).
What is the meaning then of a negative refractive index?
You may want to read this article:
Edit: John Pendry, who I believe discovered these metamaterial, should win the Nobel Prize for this.
Separate names with a comma.