Group refraction index, group velocity

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SUMMARY

The discussion centers on the properties of the group refractive index (ng) and its implications on group velocity. It is established that ng cannot be greater than 1 or less than 0, as this would suggest a group velocity exceeding the speed of light (c), which is impossible. The conversation also explores the occurrence of imaginary values for ng, indicating the presence of evanescent waves, which are non-traveling and decay exponentially. The relationship between group velocity and information transfer is clarified, emphasizing that while group velocity can exceed c in exotic scenarios, it does not equate to the transmission of information.

PREREQUISITES
  • Understanding of group refractive index (ng) and its significance in optics
  • Familiarity with the concept of group velocity and its limitations
  • Knowledge of evanescent waves and their physical properties
  • Basic principles of wave propagation and energy transfer in physics
NEXT STEPS
  • Research the mathematical formulation of group refractive index in frequency-dependent media
  • Explore the implications of imaginary refractive indices in wave physics
  • Study the characteristics and applications of evanescent waves in optical systems
  • Investigate scenarios where group velocity exceeds the speed of light and their theoretical implications
USEFUL FOR

Physicists, optical engineers, and researchers in wave mechanics who are examining the properties of light propagation and the implications of refractive indices in various media.

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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