# Nonlinear optics: second harmonic generation

• eliotsbowe
In summary, the author discusses how nonlinear optics is done in the wave picture and how quantum mechanics is necessary to understand the full picture. He goes on to say that it is hard to qualitatively depict the subject and that one needs to understand the energy in and energy out terms as well as the momentum in and momentum out.
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?

*Saleh, Teich - "Foundamentals of Photonics"

Last edited:
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

## 1. What is second harmonic generation (SHG)?

Second harmonic generation is a nonlinear optical process in which two photons with the same frequency interact with a nonlinear material, resulting in the generation of a new photon with twice the frequency and half the wavelength of the original photons.

## 2. How does SHG work?

In SHG, the incoming photons interact with the electrons within the nonlinear material, causing them to oscillate at twice the frequency of the incoming photons. This results in the emission of a new photon with a frequency twice that of the original photons.

## 3. What is the importance of SHG in scientific research?

SHG is an important tool in studying the properties of materials, as it can provide information about the symmetry and structure of a material. It is also used in various applications, such as in laser technology, telecommunications, and biomedical imaging.

## 4. Can SHG occur in all materials?

No, SHG only occurs in materials that possess certain nonlinear properties, such as crystals and some polymers. These materials must also have a non-centrosymmetric crystal structure for SHG to occur.

## 5. What are some challenges in using SHG for research?

One of the main challenges in using SHG is finding suitable nonlinear materials that can efficiently convert incoming photons into the desired output. Another challenge is controlling the polarization and phase of the incoming photons to optimize the SHG process.

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