Unable to reproduce literature results (adiabaticity parameters of adiabatic coupler)

Dear Lumerical support team/users,

I am trying to calculate the adiabaticity parameters of an adiabatic coupler, and the result is different with the reported result.

The reference paper is “Yung-Jr Hung, Zhong-Ying Li, Hung-Ching Chung, Fu-Chieh Liang, Ming-Yang Jung, Tzu-Hsiang Yen, and Shuo-Yen Tseng, “Mode-evolution-based silicon-on-insulator 3 dB coupler using fast quasiadiabatic dynamics,” Opt. Lett. 44 , 815-818 (2019)”.

The adiabaticity parameters is defined as

I have wrote a script to calculate the parameter accroding to definition, but I can not get the desired result. The script is attached and I will be very gratful if you can help me. Thank you very much!

adibaticity parameter.lsf (2.7 KB)

Hello @liminchang,

I do not have access to this paper, so I do know what values you are looking for. Any more information you could share would be helpful. Are you certain that these are the modes you comparing with? There is almost zero overlap between these modes, so I am not surprised that you are find a very low values for the adiabaticity parameter.

I did take a look at your script and mostly it looks pretty good; the only thing that pops out at me is the fact that the integration should only be performed over the wave guide cross section. I would suggest reducing you mesh size and the extent of the FDE region. You will still need the FDE region larger than the coupling cross-section, but you can reduce the limits of your integration appropriately. Also the numerical derivative error is about 10% the value of c? Might want to look at higher order methods if the magnetic field is changing very rapidly. Finally you should conjugate H even though the FDE is returning real field components.

I hope this helps.

Best Regards,

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Hello @trobertson,

Thank you for your kind suggestions, but I still can not fix the problem :sweat_smile:. And I would like to find further help from you.Thank you very much.

  1. I haved attched 2 pdf papers. The ol-44-4-815 is the reference paper which I am trying to reproduce. And the oe-25-12-13626 contains a more detailed definition of adiabaticity parameters. I hope they will be helpful.
    oe-25-12-13626.pdf (2.2 MB) ol-44-4-815.pdf (2.3 MB)

  2. Yes, I am comparing the first and second eigenmodes, and the adiabaticity parameter is supposed to be around 0.02.

  3. I am not very sure about that the integration should only be performed over the wave guide cross section. Should I only integrate the eigenmodes over the silicon waveguide cross section? If the answer is yes, and how should I write the script for the proposed rib waveguide?

4.I have reduced the mesh size and the extended the FDE region, and I conjugate the H. But the adiabaticity parameters are still very small.

It will be very kind if you can offer me further help. Thank you very much!

Hey @liminchang,

I too have done some experimentation with your simulation, yet I am not able to obtain the value which you quoted. From the paper I am a bit confused about how the integration area is defined and the units of E, H and c? Are they normalized to their square integral over R^2, given in SI units? Maybe there is a clue in one of the references? This might be important, and I would be interested to know the answer but it is not imperative to your results.

From my perspective the key result is not the value of the adiabaticity parameter, but it’s relationship with the propagation length. I would seek to recreate Fig 2a) in the Y .J. Hung et al paper. The biggest source of error will likely be the field derivative and you may need to experiment with higher order methods to find it.

First I would look at calculating this by sweeping over the propagation direction. The value of c does change depending on where you place the FDE region which is encouraging.

To sweep over the waveguide cross section find the mesh cell integer values that corresponds to the Si region. Then use semicolon notation to reduce the size of the integration.
Somthing like