group refraction index, group velocity

carlos-carlos

Can the group refractive index ng be 1>ng>0 ?

mfb

This would imply a group velocity larger than c. No, this is not possible.

carlos-carlos

Thank you for your answer!
I have a very complicated expression for my refractive index which is frequency dependent. I fixed the mistake and now I do not have 1>ng>0 for any frequency.
ng>1 in some frequency ranges, but now I get ng imaginary like ng=A*i in other frequency ranges. Besides, at a particular frequnecy I have A -> infinitive.
How can I interpret ng imaginary?
Are they evenescent waves ?
What are physically such a waves ?
And such a divergence?
Is that damping?
or what?
Thanks for any comments.

chrisbaird

Evanescent waves are non-traveling, spatially exponentially decaying waves. They are real, but do not carry energy directly. Think of wiggling a rope trying to get a wave to go down it but the rope is so heavy that you never succeed in getting a wave to travel down, you only get a fixed wiggle shape at the front.

Group velocity can in certain exotic cases be greater than c, but in those cases the group velocity either does not correspond to anything (you can only have a group velocity if there is a group), or the group velocity no longer corresponds to the rate at which information is traveling, which can never be greater than c or causality would be violated.