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Nonlinear optics: second harmonic generation

  1. Feb 22, 2014 #1
    Hello, I'm studying basic nonlinear optics and I would like to solve a couple doubts about (basic) photon interaction.
    Let a monocromatic (of frequency ω) electromagnetic field propagate through a nonlinear medium and let the third(and higher)-order terms in the relation between the polarization density P and the electric field E be negligible.
    I've read* that the second harmonic generation is based on two photons of frequency ω combining to produce a photon of frequency 2ω.
    I would like to understand the practical meaning of "combining" in this context: perhaps it's like "colliding"?

    May anyone help me?

    Thanks in advance.

    *Saleh, Teich - "Foundamentals of Photonics"
    Last edited: Feb 22, 2014
  2. jcsd
  3. Feb 22, 2014 #2


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    Basic nonlinear optics is done in the wave picture because it deals with coherent high-intensity radiation. Here and there, some handwaving photon illustrations are used but to really understand what goes on in the photon picture requires quantum optics.

    Boyd's "Nonlinear Optics" is a good book which goes into the quantum mechanical details but I think he too doesn't talk in-depth about the photon picture and is more concerned with things like deriving the susceptibilities from first principles, etc.
  4. Feb 22, 2014 #3
    Well, thanks for the tip, I'll check that book out. I kind of figured out that the subject is really hard to qualitatively depict.
  5. Feb 22, 2014 #4


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    The photon picture is easy: energy in = energy out, and momentum in = momentum out (phase matching condition).
  6. Feb 24, 2014 #5


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    That's the handwaving I meant. ;-) I too like this kind of reasoning, but it doesn't give you the full story.

    It doesn't answer questions like: How do the photons interact with matter? What is the mechanism of the conversion? What energy levels are involved and how to calculate them?
  7. Feb 25, 2014 #6
    Thanks for your time guys. Finally I decided to go and personally ask my professor what kind of picture he expects his students to have in mind :D
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