Is Group Velocity Dispersion Infinite for Light in Air?

AI Thread Summary
The discussion centers on the group-velocity dispersion parameter (D) for light in air, which is argued to be infinite due to the constancy of group velocity. This implies that the pulse of light spreads rapidly. The confusion arises from the mathematical treatment of the dispersion parameter, particularly regarding the second derivative of wave vector (k) with respect to frequency (w). The participants clarify that the correct interpretation of the derivatives is crucial, as it affects the understanding of dispersion in this context. Ultimately, the discussion resolves around the nuances of the mathematical definitions and their implications for light propagation in air.
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
 
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