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What causes dispersion?

  1. Sep 30, 2012 #1
    A wave travels through a (homogeneous) medium at a given velocity, the velocity depends on the frequency of the energy.... why?
     
  2. jcsd
  3. Sep 30, 2012 #2

    mfb

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    The velocity depends on the material - how elastic it is (for a mechanical wave) and similar properties. And those values can depend on the frequency (and on the amplitude, but that is a different effect). As an example, a material could be very elastic with a low frequency (it has enough time to change its shape in some way), but stiff at a high frequency.
     
  4. Sep 30, 2012 #3
    Thanks, that makes sense. How about for light waves then?
     
  5. Sep 30, 2012 #4
    For light waves, dispersion can occur in many ways. Most basically, the refractive index of a material is usually a function of the wavelength of light passing through the medium. This difference in refractive index for different wavelengths leads to a difference in angle of refraction (and velocity), causing dispersion. This is what happens in a prism.
     
  6. Sep 30, 2012 #5
    OK so why does the refractive index change for different frequencies (or wavelengths)?

    (I already know about waveguides, I'm interested in the case of homogeneous media.)
     
  7. Sep 30, 2012 #6
    The index of refraction is a property of the material in question. The structure of the medium as well as the what kind of atoms it's made from are very important parameters that decide how the index of refraction will vary with frequency.
     
  8. Sep 30, 2012 #7

    mfb

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    Same concept as mechanical waves - the polarizability depends on the frequency, this influences the electric susceptibility and therefore the speed of light. Usually, the magnetic effect is smaller.
     
  9. Sep 30, 2012 #8
    Tell me something I don't already know ...
     
  10. Sep 30, 2012 #9
    OK "polarizability" I think that is an anisotropic property. I can totally understand how a material would be anisotropic, and even, how the length scale of the anisotropic fabric would affect how anisotropic the material seemed to be to different wavelengths.

    However, in the case of sound waves, we did not need to invoke anisotropy. The material responded differently at different elastic frequencies and that was enough to explain dispersion. So I do not understand why you are bringing this polarizability into the equation and introducing it by saying "same concept as mechanical waves".

    Indeed, I can even see how anisotropy can cause dispersion. However, this would be the case of the inhomogeneous medium, which is basically dispersion caused by waveguides, and I am specifically interested in the more "intrinsic" dispersion of a homogeneous medium.

    Now I do think the concept probably is analagous for elastic and electromagnetic waves. The elastic tensor is a function of frequency, due I guess to inelastic effects dominating at certain frequencies by interesting mechanism that we have not dealt with ... (I would be interested to know more about these mechanisms if anybody can comment) ...

    So by analogy my first question would be: what is the analogy to the elastic tensor for electromagnetic waves?
     
  11. Sep 30, 2012 #10
    The "anomalous" dispersion is found in and around absorption bands.

    Basically, if an oscillator is excited by a wave whose frequency is close to the resonant frequency of the oscillator but slightly lower, the oscillator follows the forcing wave but is behind the forcing wave.

    If, however, the oscillator is excited by a wave whose frequency is close to the resonance but slightly higher, the oscillator gets ahead of the forcing wave.

    The result is that if you look at light near but slightly redward of an absorption band, you would see unusually high refractive index. If you look at light near but slightly blueward of an absorption band, you would see unusually low refractive index.

    Between absorption bands, there is "normal dispersion" - the refractive index increases blueward and does so slowly.

    Most transparent colourless substances are between two groups of absorption bands - one in ultraviolet caused by electron excitations, and the other in infrared caused by vibrations of nuclei.

    The reason substances have light speed less than in vacuum is that the electronic excitations in ultraviolet get polarized by light even at much lower frequencies, and slow down the light.

    In some substances, electrons are notably tightly held - with the result of weak refraction and also weak dispersion. Such as fluorides - the absorption of fluorides is notably far in UV, their electrons have low polarizability, the fluorides have low refractive index and also weak dispersion (big Abbe numbers).

    Is that more informative?
     
  12. Sep 30, 2012 #11

    mfb

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    It can be, but it does not have to be anisotropic.

    Electric susceptibility
     
  13. Sep 30, 2012 #12

    sophiecentaur

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    The fact is that we don't actually know what you don't know. That is not a very polite response. Try to be a bit nicer, if you can. It will elicit better responses, young man. I am correct about your gender, I think.
     
  14. Oct 1, 2012 #13
    Interesting. It seems the propagation of light through a medium involves scattering of light by the atoms in the medium. The time over which this scattering interaction occurs depends on the frequency of the light, thus you have a mechanism for dispersion.

    Does that sound OK?
     
  15. Oct 1, 2012 #14
    OK so polarizability means something different from what I thought you meant. It seems a medium can be polarised by the incoming light. I deal regularly with sound waves (I'm a seismologist) and so that is a foreign concept to me: rocks and minerals polarise sound energy, not the other way around.

    Would you agree: you can't polarise a wave in an isotropic medium.

    Thanks, I still need to consider the implications.
     
  16. Oct 1, 2012 #15
    In an isotropic medium you can have sound waves with different polarizations: longitudinal and transverse. They don't have the same speed usually. These are the S and P waves (so named in geophysics). In anisotropic media you may have more than one kind of transverse waves.
    But it's not clear what you mean by "polarization". How do the rocks and minerals "polarise sound energy"? Do you have an example?
    "Polarization" as an action (as opposite to a property: linear polarization for example) has to do with a change in the polarization state of the wave. Like when you have "unpolarized" light passing through a piece of polaroid and emerging as linearly polarized.
    I suppose it's a matter of semantics and of the same word being used in several ways.
     
  17. Oct 1, 2012 #16
    In case of a medium, "polarization" refers to the medium acquiring electric dipole momentum under influence of electric field - whether due to long-distance separation of charges (in conductors) or short distance induced electric moments.

    The mechanical analogue of "polarization" is "strain". And the analogue of "polarizability" is "compressibility".

    Note that elastic phenomena are more complex than electromagnetic. Elasticity tensor has what, 21 components? Even in completely isotropic environment, light has 1 speed, but sound has 2 (compression wave and shear wave speed).
     
  18. Oct 1, 2012 #17

    sophiecentaur

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    You are implying it is interactions with individual atoms. When EM waves travel through a medium in a coherent way, it interacts with the bulk medium. If individual atoms were involved (as with the classic interaction between a photon and a Hydrogen atom), the phase of the wave would be disrupted because the re-emitted photons would not stay in phase with each other. As it is, the wave maintains its integrity as it travels through the medium.
     
  19. Oct 1, 2012 #18
    Dispersion would manifest as a phase shift, right? So I still don't see the problem with that.
     
  20. Oct 1, 2012 #19
    Yeah I agree with everything you said ... I guess I was taliking about polarisation as an action -- the waves of course have an initial polarisation from source. An anisotropic rock can either misalign the particle motion from the ray direction for P-waves (thereby changing the polarisation in the ray frame) or propagate "fast" and "slow" polarised energy at different speeds for S-waves thereby changing linearly polarised energy into elliptically polarised energy.
     
  21. Oct 1, 2012 #20

    sophiecentaur

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    The phase shifts would all be different because there is a statistical distribution associated with absorption and emission of a photon. That's the 'problem'; the wave front would no longer have integrity and you would no longer have a 'ray'. In order to explain what goes on you need to acknowledge that the photons are interacting with the whole thing. (If you really want to consider photons in this process which is essentially a wave phenomenon).
     
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