Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Group Index dependence on refractive index

  1. Oct 23, 2014 #1
    In Ng (the group index for a range of wavelengths), there is an index of refraction n used, but if the medium is dispersive, meaning n is a function of wavelength λ, which n is used? Is it some kind of an average? Or does n not change much over this range of wavelengths? if it doesn't change much, then

    Ng = n - λ(dn/dλ)

    would be approximately

    Ng ~ n

    So, it makes sense to me that dn/dλ must not be really small, because otherwise Ng ~ n and the concept of group index is redundant with the concept of the index of refraction. but if dn/dλ is not really small, then the choice of n (the first term in Ng) becomes crucial, does it not?
    https://ssl.gstatic.com/ui/v1/icons/mail/images/cleardot.gif
     
  2. jcsd
  3. Oct 24, 2014 #2

    DrDu

    User Avatar
    Science Advisor

    ##N_g## is a function of ##\lambda## too: ##N_g(\lambda)##, so you should use the respective value ##n(\lambda)## in the formulas you gave.
    Take in mind that the group index refers to a wavepacket which is very broad, so that the spread of ##\lambda## in Fourier space is arbitrary small. If n depends strongly on ##\lambda##, the wavepacket will deform while travelling through the medium and it will be difficult to define a group velocity, or, you have to regard it as a superposition of broader wavepackets which travel with slightly different group velocities.
     
  4. Oct 24, 2014 #3
    Thanks! Makes total sense!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Group Index dependence on refractive index
  1. Index refraction (Replies: 3)

Loading...