Is there a theoretical maximum for refractive index?

Question

May there be materials yet to be discovered which may have a higher refractive index than today's known materials (for wavelengths within the visible range)?

Is there a theoretical limit for the refractive index of a material?

Answer 1

Theoretically, there is no limit to the refractive index. The reason is that, if you go by the definition, $n= c/v$, the more you can slow down light (short of stopping it completely), the higher you refractive index will be. And, mathermatically, we are looking at the following,

$$ n = \lim_{v \to 0^{+}} \frac{c}{v} = \infty $$

and is undefined at 0, which is why the limit is coming from the left.

For example, using a cloud of cold atoms (laser cooled), light can be slowed down light to less that 10 mph. See link.

http://www.nature.com/news/1999/990225/full/news990225-5.html

Practically, there is a limit to refraction imposed by the nature of the refractive medium itself and the nature of the condensed state. In terms of materials, there are advances using metal arrays to increase the refractive index even more. See link.

http://physicsworld.com/cws/article/news/2011/feb/16/metamaterial-breaks-refraction-record

Answer 2

Since the refractive index is given by $\displaystyle{n_{12}=\frac{\sin \theta_1}{\sin \theta_2}}$, theoretically there is no limit at all on the value of refractive index. You could say that it must be positive, but then check this out: http://en.wikipedia.org/wiki/Negative_refraction