Group refraction index, group velocity

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Discussion Overview

The discussion revolves around the concept of group refractive index (ng) and its implications on group velocity, particularly in the context of frequency-dependent refractive indices and the interpretation of imaginary values of ng. Participants explore theoretical limits and physical interpretations related to wave behavior.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the group refractive index can be greater than 0 but less than 1 (1>ng>0).
  • Another participant asserts that this would imply a group velocity greater than the speed of light (c), which they claim is not possible.
  • A participant shares their experience with a complex, frequency-dependent expression for refractive index, noting that they no longer obtain values for ng within the range of 1>ng>0, but instead find ng to be greater than 1 in some ranges and imaginary in others.
  • This participant seeks clarification on the physical interpretation of imaginary ng, asking if it relates to evanescent waves and what such waves physically represent.
  • Another participant explains that evanescent waves are non-traveling and decay exponentially, suggesting they do not carry energy directly.
  • There is a mention of exotic cases where group velocity can exceed c, but it is noted that in such cases, the group velocity may not correspond to information transfer, which cannot exceed c without violating causality.

Areas of Agreement / Disagreement

Participants express differing views on the implications of group refractive index and group velocity, particularly regarding the possibility of ng being imaginary and the physical nature of such waves. The discussion remains unresolved with multiple competing interpretations present.

Contextual Notes

The discussion includes complex mathematical expressions and assumptions regarding the behavior of refractive indices across different frequencies, which may not be fully resolved or defined.

carlos-carlos
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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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