Nonlinear optics: second harmonic generation

[eliotsbowe]

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"

 

[kith]

Hello, I'm studying basic nonlinear optics and I would like to solve a couple doubts about (basic) photon interaction.

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.

 

[eliotsbowe]

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.

 

[UltrafastPED]

The photon picture is easy: energy in = energy out, and momentum in = momentum out (phase matching condition).

 

[kith]

The photon picture is easy: energy in = energy out, and momentum in = momentum out (phase matching condition).

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?

 

[eliotsbowe]

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