Group refraction index, group velocity

AI Thread Summary
The discussion centers on the impossibility of having a group refractive index (ng) between 0 and 1, which would suggest a group velocity exceeding the speed of light (c). The user corrected their frequency-dependent refractive index expression, eliminating the problematic range where 1>ng>0. They now observe ng as imaginary in certain frequency ranges, raising questions about the physical interpretation of these values, particularly regarding evanescent waves, which do not propagate energy. The conversation also touches on the concept that while group velocity can exceed c in specific scenarios, it does not imply faster-than-light information transfer, as this would violate causality. Overall, the discussion emphasizes the complexities of refractive indices and the nature of wave propagation in different contexts.
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Can the group refractive index ng be 1>ng>0 ?
 
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This would imply a group velocity larger than c. No, this is not possible.
 
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.
 
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.
 

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