"high non-linearity" of what?

Read at least Wikipedia (here, https://en.wikipedia.org/wiki/Chalcogen) and study the basics of the Mendeleevian table of chemical elements, before posing such a question.

PS: No wonder that Toyota experiences certain flaws, if its Technological Institute cannot answer such an elementary question ;-)

Thank you for your answer. What I meant was the third order nonlinear

optic susceptibility of tellurite and chalcogenide glasses.

Dear Harutaka, 

Though experts can easily guess your “nonlinearity” is concerning optical properties, I advise you to make questions to be specific. Moreover, I strongly recommend you to put your own idea in your questions. It helps you to prove that you are not simply looking for instant solution.

Many of "common knowledge" in field of science and technology are actually "no one knows why". If you do well, you may trigger fruitful discussions among experts.

Here, I occasionally found an article, which may answer your question (see introduction).

http://www.nature.com/articles/srep39234

However, I have a little doubt whether this explanation is appropriate or not. Though I am not expert of this area, we may discus about this later.

Harutaka, I proud of you, you have a strong spirit to seek deep understanding of the universe. I believe your future is bright.

Dear Harutaka,

the question is highly non-trivial. And therefore, I disagree strongly with Peter Enders. The answer does not lie in Wikipedia, in fact, there is no simple answer to your question at all and I believe that even the experts in non-linear optics can not just calculate in before-hand what material mix they should use for which nonlinear optical application.

As far as chalcogenide glasses are concerned (As,Te,S,Se as major glass forming elements/ingredients), it might be that the large nonlinear polarisation could have something to do with the "softness" of the glassy lattice, but you will have to search the original literature on the subject.

A good friend of mine and a real expert on chalcogenide glasses in general and on their optical properties in particular, might be able give you some suggestions. Contact him with reference to me. His name is Ladislav Tichy , professor at Pardubice University, Czech Republic.

Interesting question, good luck in your search for the answer.

With best regards

Petr

Dear Petr and Harutaka,

According to the article in Nature, which I post last time, “Chalcogenide glasses are reported to get higher nonlinear optical properties than oxide glasses due to low vibrational energies of bonds induced by heavy chalcogen atoms.” However, the frequency of visible light is far above that of atomic vibrations (phonon). This is why I wonder this explanation.

Instead of that, I suggest following explanation; the potentials binding valence electrons of heavy chalcogen atoms are “shallow” comparing with that of oxygen atoms due to the larger atomic number. Consequently, the wave function of the valence electrons is more “flexible” for inputs of external electric fields. Do you think this explanation make sense?  

P.S. Recently I learned one thing that we must take caution with effect of alcohol when we post something through internet. Spelling dozen of destructive comments into whole world, criticizing people as lazy based on own prejudice. Then own reputation is totally gone... The most miserable thing, after that, is the comments remain forever. If you were drunken, it’s better not to access SNS including ResearchGate. (I myself am the one who must take this caution seriously?)

Dear Yoshiki and Harutaka,

I must admit that your argument about atomic vibrations being too slow to account for optical non-linearities  in the visible range of the el.mag. spectrum is a quite valid one. 

As a consequence, the non-linear polarisation processes must be electronic. Although I would still maintain that the lattice non-linearity (non-harmonicity) might be involved, I agree again that a model involving only electrons might be the most adequate, at least at this stage. It even might be that your proposal is a good starting point. But here I would focus on the strength of bonding of chalcogen valence electrons to its neighbours and in particular on the effective one-particle potential and it's non-linearity.

My first question would be : In materials with strong optical non-linearity, is the linear term also much larger than in the other materials ? I myself have no answer, but it might be that if the electronic polarisation is large in these materials, it could point towards the final model/explanation. As far as I know from AgAsS2 system studies, the optical dielectric constant is not much larger than in other semiconductors (it is ~9-10 as compared to Si 11.8, but be aware of an unexplained contribution below 1 GHz !). So, my first reaction would be therefore that the large electronic polarisation and large non-linearity in dielectric constant are not correlated. 

As far as your P.S.: is concerned, I fully agree with you. And you definitely need not apply this caution to yourself. Your tone is sober and gentle (and friendly!), something that does not surprise me now.  I have just returned from Japan and this has been my experience, peoples are friendly, helpful and very considered.

With best regards

Petr

Dear Petr and Harutaka,

Thank you for your heart-warming message.

I think we must consider the band gaps too. Optical non-linearity means the materials are transparent; it means the band gaps are higher than the energy of the light; Si is out of our consideration. So far, most of transparent materials are oxides and a few of nitrides. So, we can consider comparisons only with oxides.

Your concern is right; the “flexibility” of wave function is firstly results high dielectric constants. I think the high non-linearity can be attributed to the weak bindings of electrons; the shallow “depth” of the potentials---more precisely, lower limit of the parabolic approximation of the potential. And it may results weak bindings of atoms---poor mechanical strength, because the strength is also linearity limit of the elastic property. There is an interesting discussion in this ResearchGate:

https://www.researchgate.net/post/How_can_we_correlate_melting_point_dielectric_constant_and_Youngs_modulus_of_a_material_with_its_band_gap

I agree with the conclusion that there is no universal physical relationship, because there are too many factors to be considered, but, it is also obvious that there is a strong correlation. I’d never think of that before. This is quite interesting.

Dear Yoshiki and Harutaka,

I can see that there is something that I did not really know, namely (as you point out) that the non-linearity (optical) takes place for the photon energies below the band gap energies - very interesting. 

I agree also with your other points , but have nothing useful to add to our discussion as yet. I will look at your reference first.

With best regards

Petr

Dear Petr and Harutaka,

The requirement the photon energies below the band gap is not the condition for the non-linearily but simply the condition for optical transparency. If the photon energy was more than the band gap, thematerial absorb the photon thus any of optical phenomenon can be observed.

Thank you for your reply.

Dear Yoshidi and Harutaka,

I understand now and I agree. Not knowing how the optical non-linear devices look like, it is not unreasonable to assume that near band gap light would not be absorbed too much. Also , even metallic layers, if sufficiently thin, are "transparent".

I have just read your link and at least for the time being , I have no innovative ideas, where to search for the more general model, apart from our discussion so far.

still very interesting problem and if I come-up with something worth discussing, I will let you know. This goes though other way round also, so please let me know if you find something.

My e-mail address is :

[email protected] 

Can I have yours ?

with best regards

Petr

Dear Petr, 

Thank you for your invitation. I do this answering here as my self training, and so far, I'm not willing to extend this activity to outside of RG. Later, we may see each other on answering for someone's question again.

Thank you again for your nice responses.