Nonlinear optics: second harmonic generation

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SUMMARY

This discussion focuses on the concept of second harmonic generation (SHG) in nonlinear optics, specifically the interaction of photons in a nonlinear medium. It is established that two photons of frequency ω combine to produce a photon of frequency 2ω, although the term "combining" may be misleading and could be interpreted as "colliding." The conversation highlights the complexity of understanding photon interactions and suggests that while basic nonlinear optics can be approached from a wave perspective, a deeper understanding requires knowledge of quantum optics. Recommended literature includes "Fundamentals of Photonics" by Saleh and Teich, and "Nonlinear Optics" by Boyd.

PREREQUISITES
  • Basic understanding of nonlinear optics concepts
  • Familiarity with electromagnetic fields and their propagation
  • Knowledge of quantum optics principles
  • Understanding of phase matching conditions in optics
NEXT STEPS
  • Study the principles of second harmonic generation in detail
  • Explore quantum optics to understand photon interactions
  • Read "Nonlinear Optics" by Boyd for advanced insights
  • Investigate phase matching techniques in nonlinear media
USEFUL FOR

This discussion is beneficial for students and researchers in physics, particularly those focusing on nonlinear optics, quantum optics, and photonics. It is also useful for anyone seeking to deepen their understanding of photon interactions in nonlinear media.

eliotsbowe
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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"
 
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eliotsbowe said:
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.
 
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.
 
The photon picture is easy: energy in = energy out, and momentum in = momentum out (phase matching condition).
 
UltrafastPED said:
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?
 
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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