Difference between longitudinal and transverse refractive indices

[Gobil]

hi All,

as the title suggests, I a not so clear on the difference between the two. in particular in solids, I have been looking at various approached to calculating the refractive index. But I´m not so clear on why there is two descriptions of we have a homogeneous medium.

thnks!

 

[DrDu]

Have a look at:

http://siba.unipv.it/fisica/articoli/P/PhysicsUspekhi2006_49_1029.pdf

 

[Gobil]

thanks for the article DrDu, I guess now my understanding is that we need these two descriptions because the k vector goes in a certain direction, and the dielectric function is not the same in all directions. Is this due to crystal orientations in different directions? would we need a transverse and longitudinal description for something amorphous, like glass?

 

[DrDu]

would we need a transverse and longitudinal description for something amorphous, like glass?

Yes, also in an isotropic material the dielectric constant becomes a tensor once q dependence is taken into account. The free electron gas you are especially interested in is an example.
Note that the need to make epsilon dependent on q (or k) results partially from the convention in optics to take mu=1. Compare especially sections 3.1 and 3.2 of the link I gave you.

 

[Gobil]

Yes, also in an isotropic material the dielectric constant becomes a tensor once q dependence is taken into account. The free electron gas you are especially interested in is an example.
Note that the need to make epsilon dependent on q (or k) results partially from the convention in optics to take mu=1. Compare especially sections 3.1 and 3.2 of the link I gave you.

but in an isotropic material with mu = 1 do we also need this description?

also, is this only valid for waves incident on a surface? i.e. we are going from vacuum to some material, otherwise, if we are in a infinite isotropic homogeneous medium, the direction of the k vector does not matter at all, right?

 

[DrDu]

No, you will also need this description in bulk matter ( a surface is not isotropic, is it?).
Almost all of your questions are better answered in that article than I can do it.

 

[Gobil]

I´m sorry, physically I just don't get it. In an infinite isotropic, homogeneous medium, why does the light see a different refractive index depending on what direction it is propagating??

 

[DrDu]

Indeed in an isotropic medium, light doesn't see a different refractive index depending on direction.
However it is possible that there are waves with the same frequency but different wavelength present. The most well known effect of this kind is, as I mentioned already, circular dichroism, where left and right circularly polarized light have different indices of refraction.

On the other hand, the distinction between longitudinal and transversal dielectric constant is not so much a difference of different kinds of light: As light is transversally polarized, its propagation depends only on the transversal dielectric constant. The longitudinal dielectric constant is more important in the description of the shielding of Coulomb potential or the description of plasmons.