Nonlinear optics: second harmonic generation

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Discussion Overview

The discussion revolves around the concept of second harmonic generation in nonlinear optics, specifically focusing on the interaction of photons within a nonlinear medium. Participants explore the theoretical and practical implications of photon interactions, including the challenges of understanding these processes in both classical and quantum frameworks.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the term "combining" in the context of second harmonic generation, questioning whether it implies a collision between photons.
  • Another participant notes that basic nonlinear optics is typically approached from a wave perspective, emphasizing the need for quantum optics to fully understand photon interactions.
  • A participant mentions that while Boyd's "Nonlinear Optics" provides valuable insights, it may not delve deeply into the photon picture, focusing instead on deriving susceptibilities.
  • One participant asserts that the photon picture simplifies to energy and momentum conservation, referencing the phase matching condition.
  • Another participant challenges this simplification, stating it does not address deeper questions about photon interactions with matter, the conversion mechanism, or the energy levels involved.
  • A participant expresses their intention to consult their professor for further clarification on the expected understanding of these concepts.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the topic, with some agreeing on the complexity of the subject while others highlight the limitations of simplified models. The discussion remains unresolved regarding the best way to conceptualize photon interactions in nonlinear optics.

Contextual Notes

Participants acknowledge the challenges in qualitatively depicting nonlinear optical phenomena and the dependence on both classical and quantum mechanical frameworks for a comprehensive understanding.

Who May Find This Useful

Students and researchers interested in nonlinear optics, photon interactions, and the theoretical underpinnings of optical phenomena may find this discussion relevant.

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"
 
Last edited:
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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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