Is Group Velocity Dispersion Infinite for Light in Air?

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SUMMARY

The group-velocity dispersion parameter D for light in air is considered infinite due to the constant nature of group velocity, where the derivative of group velocity with respect to wave vector k is zero. This results in rapid pulse spreading, as the second derivative of the wave vector with respect to frequency is undefined. The confusion arises from misapplying the relationship between the derivatives, specifically in the context of light propagation in air.

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  • Understanding of group velocity and its mathematical representation
  • Familiarity with dispersion parameters in optics
  • Knowledge of derivatives in the context of wave propagation
  • Basic principles of light behavior in different media
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Dimani4
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Hey ppl,
I have a question for you.

For the case of light propagation in the air the the group-velocity dispersion parameter D is infinity because the derivative of the group velocity should be a zero (group velocity is constant ; w=ck and Vgroup=dw/dk). Who can explain me this? dispersion parameter is infinity meaning that the pulse will spread very fast. I never thought about that question but maybe I'm wrong. Plz clarify me that point.

formula for D parameter you can find here:
http://en.wikipedia.org/wiki/Dispersion_(optics)
 
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the question is solved. you can't not turn upside down the second derivative. i.e

a=(Dispersion parameter)=(approx) d2(k)/d2(w)\neq1/d2(w)/d2(k). here was the problem. in the case of light propagation through the air a should equal to zero.d2()-second derivative=\partial2

d2(k)/d2(w)=\partial2k/\partial2w
 
Last edited:

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