Why no transparent materials with large refractive index?

[jfizzix]

I know that the refractive index is determined by a material's dielectric constant and magnetic permeability.

It's also true that we can treat the refractive index as a complex function with the imaginary part giving you an absorption spectrum.

You can then get the index of refraction from the absorption spectrum with the Kramers-Kronig relations.

My question is, what makes it that there are so few if any transparent materials with an index of refraction greater than 4?

 

[Vanadium 50]

How many materials irrespective of transparancy have an index that high?

 

[jfizzix]

Silicon at 500 nm has a refractive index of 4.3 or so. Coming up with more specific examples would be a challenge, but there's a whole field of slow light optics for narrowband light sources tuned to particular spectral lines, say of Rubidium vapor

 

[jfizzix]

Long story short, there are lots of materials that have a high index at one wavelength or another, but not that also are transparent. I don't know why you can't have both, though

 

[DrDu]

The index of refraction averaged over some frequency range is seriously restricted by sum rules. This does not preclude n to become very large near a resonance. However, near a resonance, you will also get absorption. The absorption follows a Lorentzian line shape, hence the imaginary part decays like $1/(\Delta f)^2$ with distance from the center of the line. On the other hand, the real part will decay like $1/(\Delta f)$ So for suffiently narrow absorption lines, you can get very close to the center of the line without getting appreciable absorption but a high index of refraction. In solid state this requires low temperatures to reduce spectral broadening.