# Talk:Nonlinear optics

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## Untitled

Should the processes under "related processes" be listed here at all? I'm not completely sure about Raman. I believe that the Raman-shifted "fluorescence" intensity is linear in excitation intensity, on the other hand it is a chi3 process. Stimulated Raman is of course a different story.

Would anyone (DrBob?) care to write a few words about phase conjugation? -- Hankwang 09:40, 4 Mar 2004 (UTC)

It's true that the "related processes" are not strictly speaking part of nonlinear optics, but they are almost always covered under that title in textbooks and courses. Perhaps just keep them as brief mentions here, and put their descriptions in seperate articles.
Phase conjugation can be achieved by both four-wave mixing and stimulated Brillouin scattering, so its kind of hard to place. I'll see if I can write a brief overview soon. -- DrBob

## Four-wave mixing

I'm having a little trouble figuring out exactly how FWM should fit into this article. As far as I know, FWM is an umbrella term which describes all of the chi(3) processes where one can distinguish, either by frequency or wavenumber, the four E-fields involved. Degenerate four-wave mixing is a term which can be applied whenever two or more of the fields have the same frequency or wavenumber. Some of the DFWM processes have their own names and some, like third harmonic generation, are almost never referred to as DFWM, even though they technically are. Is all of this correct?

I checked the Wikipedia FWM article and it seems to primarily focus on FWM in fiber optic communications. Also, it seems that FWM is re-derived in many places; at very least in this article under phase conjugation and in the Kerr effect article - and it isn't derived in the one place it should be: the four-wave mixing article.

After I found this I think that an expansion of the (E1+E2+E3)^2 can be done in the FWM article and the different classes of term related to their respective physical processes (like SPM, XPM, THG, etc.) Then articles on these processes and applications (like phase conjugation) can just link back to the FWM page. Does this sound OK? -FGS

## Brillouin and Raman nonlinear?

Rpaschotta moved Brillouin and Raman scattering from "related processes". Nonlinearity w.r.t. the light intensity suggests that the Raman- or Brillouin-shifted peak would increase disproportionally with increasing laser intensity. AFAIK that is not what happens in typical applications. I graduated on a project involving Brillouin scattering on GHz phonons and did a PhD in time-resolved spectroscopy and it is not obvious to me, so maybe it's a good idea if Rpaschotta wrote a few words about why it classifies as nonlinear spectroscopy.

Han-Kwang (talk) 14:08, 25 Oct 2004 (UTC)

Ok, here are some remarks. Of course, the Brillouin shift doesn't depend on intensity. Nevertheless, the interaction is nonlinear in the involved optical fields. Consider e.g. two beams interacting in a Raman-active medium. Now reduce both powers by a factor of ten. The result will NOT just lead to ten times lower output intensities of both beams. Instead, the interaction will become weaker. This is clearly different to the case of an electro-optic modulator, where the optical output depends linearly on the optical input (within certain bounds, of course).

RPaschotta 12:05, 30 Oct 2004 (UTC)

Hmm, I see what you mean. But along the same lines you could defend that Beer-law absorption is a nonlinear process because in a pump-probe experiment the signal depends on both the pump pulse and the probe pulse. Unless you talk about specific applications, both Brillouin and Raman spectroscopy only involve one optical field, on which the signal depends linearly.

Han-Kwang (talk) 15:58, 30 Oct 2004 (UTC)

## remark

Why do scientists use the stupid phrase "with respect to" (which they must acronymise to w.r.t. or wrt) instead of "about" or "from"? lysdexia 01:10, 21 Dec 2004 (UTC)

Wrt was not beautiful, but at least correct. Your "correction" was wrong. Han-Kwang (talk) 11:33, 26 Dec 2004 (UTC)

## Quantum explanation

Could please someone in the know add a section explaining the phenomenon from the quantum standpoint, i.e. some lower-energy photons come in, some (lower number) of higher energy photons come out. Explain the effect that produces these higher energy photons.

I am curious myself, and I believe that it would be a generally valuable addition. Thanks! =ec 195.212.29.188 (talk) 10:14, 15 February 2011 (UTC)

Interesting question. As well as I know it (maybe not very well), the usual case doesn't depend on quantum properties of photons, but does depend on quantum properties of atomic electrons. The atoms are in the electric field of the incoming light wave, which has a wavelength much larger than the atoms. The electric field, as the article notes, is comparable to the electric fields that hold the atom together. The reason that linear optics is linear (lucky us) is that at more ordinary intensities, the fields are small compared to those holding the electrons in their orbitals, and the (small) shifts are linear to a good approximation. A (classical) electric field of E0sin(ωt) comes in, a non-linear effect generates the third harmonic E1sin(3ωt). Just as classical as a mixer diode in a microwave receiver. (No second harmonic by symmetry.) This is in the limit of large numbers of photons, such that classical approximations work. Gah4 (talk) 21:20, 15 November 2016 (UTC)

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## Phase conjugate optics

I noticed the removal of a See also for lasers, which is probably right. But then I considered that one for phase conjugate optics might be included, but there is no such page! Should there be a page for phase conjugate optics? It seems to me that it is important enough to have its own page, not just a section in this page. (Not that I feel qualified to write one.) Gah4 (talk) 21:23, 15 November 2016 (UTC)

## Wrong calculation?

Hi folks, I'm not sure if the very last line of this calculation is correct:

{\displaystyle {\begin{aligned}\mathbf {P} ^{\text{NL}}=\varepsilon _{0}\chi ^{(2)}\mathbf {E} ^{2}(t)&={\frac {\varepsilon _{0}}{4}}\chi ^{(2)}{\Big [}|E_{1}|^{2}e^{-i2\omega _{1}t}+|E_{2}|^{2}e^{-i2\omega _{2}t}\\&\qquad +2E_{1}E_{2}e^{-i(\omega _{1}+\omega _{2})t}\\&\qquad +2E_{1}E_{2}^{*}e^{-i(\omega _{1}-\omega _{2})t}\\&\qquad +\left(|E_{1}|^{2}+|E_{2}|^{2}\right)e^{0}+{\text{c.c.}}{\Big ]},\end{aligned}}}

According to my calculations, there is a factor of 2 missing in front of :{\displaystyle {\begin{aligned}\left(|E_{1}|^{2}+|E_{2}|^{2}\right)e^{0}\end{aligned}}} — Preceding unsigned comment added by 92.208.178.25 (talk) 19:14, 13 December 2017 (UTC)