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sum frequency generation of light

Discussion in 'Electronic Design' started by Jamie, Oct 31, 2011.

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  1. Jamie

    Jamie Guest


    I'm trying to understand second harmonic generation / frequency doubling
    of coherent light in non-linear crystals, which is a specific case of
    sum frequency generation, where two phase matched input lights of
    variable frequencies, combine in matter to create a higher frequency
    output light. I am wondering about the quantum mechanics of the two
    phase matched light beams and how they create a higher frequency output
    light ie. like in this image:

    If the two input light beams with different frequencies are able to
    create an output light beam with a summed frequency, how is this
    described with quantum mechanics, or atomic/molecular electron orbitals?

  2. Martin Brown

    Martin Brown Guest



    I think you may need to be a member of IOP to read this latter link, but
    the abstract should give you keywords to use in a wider Google search.
    Might also be worth a look on ADS abstracts too...

    It is certainly not worth $33 to read it!
  3. Jamie

    Jamie Guest


    It sounds like quantum mechanics/electron orbitals aren't able to
    explain this phenomenon.

    From your explanation I guess the two input light beams are polarizing
    the matter (at three discrete frequencies f1, f2, f1+f2), and the second
    order susceptibility is the polarization that occurs at the summed
    frequency of the two beams, which creates the new higher frequency EM
    field starting with a new electric field.

    So if you have three in-phase input beams of variable frequencies, there
    would be three discrete summed frequencies (f1+f2, f1+f3, f1+f2+f3)?

  4. Jamie

    Jamie Guest


    That link makes sum frequency generation sound like a quantum process.
    Maybe there is always a classical sum frequency output, but as the
    spectroscope frequency is shifted there are peaks based on
    atomic/molecular quantum orbitals. It sounds like it is two separate

  5. Jamie

    Jamie Guest


    Does that mean that every time light passes through a crystal that there
    are material vibrations in the crystal called phonons? Or are there
    only phonons in special cases of light interacting with crystals such as
    sum frequency generation?

  6. Tim Williams

    Tim Williams Guest

    Phonons are present all the time -- they are the quantum mechanical
    vibrations of a crystal. If you imagine a crystal as a ball-and-spring
    lattice, you can imagine waves traveling through it. The quantum picture
    says these vibrations are quantized in energy levels. These vibrations
    contain energy, so this represents a bulk material property which contains
    energy, throughout the space of the crystal. If you touch a crystal to
    another, it's going to transfer this shaking, until both are shaking with
    about as much energy (note, not the same velocity or frequency, because
    that's material dependent). Starting to sound like the transfer of heat,
    right? Great!

    Phonons are also acoustic vibrations. Whereas thermal vibrations are
    randomly distributed, acoustic vibrations are coherent (or generally much
    more so). Although the frequencies are fairly low, the energy levels are
    fairly high, since the mass is a lot higher than the effective mass of a
    photon (MHz acoustic phonons might be closer in energy to ~THz optical
    photons, but you'd have to check the equations to see if that's the right
    order of magnitude).

    Last piece of the puzzle, photons can interact with phonons because
    phonons cause changes in density, and therefore permittivity, etc. This
    modulates the wavelength at least, and can lead to exchanges in energy by
    coherent or incoherent (scattering) processes.

    Finally, I'm not big on the whole acousto-optical statistical quantum
    mechanical systems thing, so I leave lots of room to be very wrong here,
    and will let others continue...

  7. Jamie

    Jamie Guest


    Thanks for all the information, I agree a difficulty in understanding
    photons/phonons is they don't qualify as material things as you say!

    Sum frequency generation is a linear process by definition, so I don't
    see how the "phonons" could be thought of as quantized for that case
    where two frequencies add up.

  8. Jamie

    Jamie Guest


    I think the two input frequencies can still create an arbitrary output
    frequency though.

  9. Jamie

    Jamie Guest


    Well I was trying to imply that if there can be an arbitrary frequency
    generated by the two input frequencies, then that would indicate that
    the intermediate phonon would not be quantized perhaps.

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