relation between electron and light in BPM

[Dr. MohammadMahdi Ariannejad]

Dear all I was wondering which formula bpm is following for electro optic? let’s say I have a MZI silicon and it is N-type then I have light propagation as well as electrode means electron, so would anybody help me to find out what is the relation between DELTA N and DELTA n, I mean the interaction between light and electrons. many thanks

[Ravil]

Hi Mohammad,

Did try you consider Lorentz model of light-electron interaction for your task?

[Dr. MohammadMahdi Ariannejad]

Dear Ravil;
I searched alot, would you please let me know if you found some useful equation in this matter? many thanks

[Ravil]

Dear Mohammad,

I’m a little confused what kind of relations you are looking looking for… Since you are studying the application of Electro-optic effect for modulation, I’d refer you to look at Pockel’s effect phenomenon where the refractive index is changing linearly with the electric field applied. In my opinion, books Kasap “Optoelectronics and Photonics: Principles and Practices” and Agrawal “Fiber-Optic Communication Systems” are good sources for review.

[Ravil]

Can you, pls, clarify what do you exactly mean by “electrode means electron” and what is you “N” stands for: the type of semiconductor as you indicate at the beginning or group refractive index when you are talking about “DELTA N”?

[Dr. MohammadMahdi Ariannejad]

Dear Ravil;
Thanks for your nice answers I am reading and searching the books,
My task is:
we have one piece of SOI(silicon on isolator), we made a wave guide with silicon on top of SiO2, SiO2 thickness is 340nm, this silicon is N-type, then we put two electrode on the waveguide, in this case we will have drift current in silicon right?(Delta is refer to this matter), on the same time we put the light in input of waveguide, so in conclusion we have light and drift current in our silicon, what I need is to find out the intraction between the light and electron or drift current which is availabe in this piece of silicon, I refer to book of Soref, he mention about formula but it is for P-N junction, in my case we just have N-type silicon. would you please help me to find an exact relation between light and electron in the silicon? again thanks for your answers

[Ravil]

Hi Mohammad,

Yes, you are right: if you apply an electric field to any semiconductor (Si in your case) material you’ll observe a flow of weakly bounded electrons due to applied filed, i.e. drift current. Now, are you assigning delta N as a change in free carrier concentration when you are writing “Delta is refer to this matter”?

After that, when you input light into your waveguide, the guiding conditions, i.e. difference in refr. indices between your core (SiO2) and cladding (Si), and critical angle would change due to applied field. You are right here as well: the interaction b/w light and electrons will take place and will be reflected in change of refr. index of Si. This change in refr. index will be related to change in weakly bounded charges (according to well-known Sellmeier equation).

The dispersion equation which is following from mentioned above Lorentz model should work in this case, I think.

[Ravil]

Let me know about your progress or if you’ll need more elaborations about my point.

Good luck!

[Dr. MohammadMahdi Ariannejad]

Dear Ravil;
I should say fantastic, may thanks for your answers but would you please describe more? sorry I could not understand, still I cannot find a relevant formula to my matter. let go the delta never mind about delta, still I am looking for the interaction between light and electron inside the N-type Silicon. would you please help me with some more information as I can see you are so professional in this case, again many thanks for your help.

[Dr. MohammadMahdi Ariannejad]

Dear Ravil;
Regarding to Sellmeier equation, and other equation that you mention still I cannot define the interaction between the light and electron in just one piece of N-Doped silicon, would you please help me to understand more about it, now I have bunch of formula that just make me confuse, I cannot understand how to make them work. many thanks

[Ravil]

Hi Mohammad,

Sorry for my late reply due to my trips… Again, as far as I understand your research problem, my first approach would be using dispersion equation for Harmonic Oscillator from Lorentz Model. I’m attaching a paper which describes this model briefly. When you open it, take a look at eqns (6)-(9) which directly related to Lorentz Model.

I can recommend famous book E. Hecht “Optics” for more details as well.

[Ravil]

The mentioned above document is attached here. Please, let me know if I can help you more with your question.

[Dr. MohammadMahdi Ariannejad]

Dear Ravil many thanks again for your answer
I read almost 10 times the file that you attached but I could not find a suitable equation between light and electron in N-type silicon, still searching would you please let me know if you find a good equation to define the interaction between the light and electron in N-type Silicon? many thanks

[Ravil]

Hi Mohammad,

Just want to be clear: I didn’t mean that there is a direct equation for N-type Si. In our previous discussion, I was thinking about application of dispersion equation for your problem. In this equation, you need to find out the resonance frequencies for N-type Si (the doping concentration will define the number of unbounded carriers). These resonance frequencies will be defined by carrier absorption.

Do you have any data about that?

[Dr. MohammadMahdi Ariannejad]

Dear Ravil;
I seriously Have no Idea about it I just know about pockels effect and Kerr Effect,
But still I need the iteration between the light and electron in N-doped silicon in parallel way.
please help me about it 🙁

[Author]

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