Spatial distribution of the eigenmodes from the dipole cloud analysis

… continuing discussion from this post

I need to determine the spatial distribution of the eigenmode (resonant mode of the current ring resonator)
in a 3D volume. For that I used dipole cloud sources instead of the current mode source but I have some problem removing some of the source discontinuities.
What I currently am doing is finding the field from the dipole cloud analysis at the resonance wavelength and later subtracting the scattered fields of the dipoles within that volume to obtain only the eigenmode distribution.
Your feedback on that would be appreciated.

Hadisehring_res_Lumerical.fsp (672.5 KB)

Hi @hadiseh.alaeian

Can you confirm that you have attached the correct simulation file as I am not seeing dipole cloud in the attached file?Also, can you please clarify what you mean by subtracting the scattered fields of the dipoles?

I guess this will be a good example to get some intuition on how you can simulate the modes of a ring resonator in FDTD. You can also check any other KB example on cavities and resonators section.



Please find the .fsp file here!
Using the mode source I was able to fine tune the structure parameters to get a resonance at about 795nm (the wavelength I need). However using the dipole cloud and a bunch of time monitors I am not able to properly get that resonance.
Do you have any idea what the problem could be?

Thank you,
HadisehRR_EigenMode_Lumerical.fsp (297.1 KB)

Hi @hadiseh.alaeian

I guess there is a better way to locate the source and monitors. Since we are looking for ring modes and light propagates inside the ring, we need to have source and monitors inside the ring. This way we are exciting the modes of interest and also collecting them efficiently. Please refer to this page for a similar case about microdisks:

Also, I would expect that we need to use Time appodization in monitors so that we wait for a while and then start recording. This way we can remove the field coming from sources and only capture the rings modes:

Please go ahead and use the disk case for starting point. This is the first time I am running the simulations and with your help we should be able to find the resonances very soon.


Thank you for the response and referring me to the proper example!
I followed your suggestion of putting both the source and monitors inside the ring and properly apodized frequency domain monitors to get rid of dipole source singularities and transient behavior.
Also I increased the simulation time of 5000 fs. However the results are still problematic. Would you mind kindly check the new .fsp file and results?

Thank youRR_EigenMode_Lumerical.fsp|attachment (309.7 KB)

Dear @hadiseh.alaeian

I noticed that some of dipole sources/monitors are located outside the ring. Also, since the ring that you were working with was large (radius~30um) and simulation were taking a long time, I tried to focus on a simpler case of a ring with radius of 2um. Ultimately my goal is to simulate your case, but since this is my first time simulating a ring resonator I thought it will be easier to start with a simpler case. Also, I removed the waveguide to study only the ring resonator (external waveguide might effect the quality factor and frequency of resonant modes but not the physics and our strategy).

I have my simulation file attached with the screenshots of first resonance:

RingResonatorRadius2um.fsp (300.9 KB)

Please note that the strength of the peak depends on the location of dipoles and monitors (here I located them all in the fist quarter as I was planning to use symmetry later on but you can randomly locate them at any point on the ring resonator).

Please go ahead and modify your simulation file. I am working on your case but it might take a while for me to get back to you as optimizing your devices for larger ring might take a while.

Also, do you have a reference for your simulations? It should give us intuition on how we can optimize the dipoles and monitors to capture the modes properly.


Thank you for the response!
I’ll try to modify the simulation according to yours and would update yon on the outcome.
I don’t have any reference since this my my design for a specific device to fabricate. Also just to clarify the radius is 12.7um.

Thank you again!

Dear @bkhanaliloo
I just finished sets of different numerical simulations following your instructions and features in your sample file. To reduce the simulation time I used symmetric boundary conditions as well. Removing the waveguide to retain the 4-fold symmetry I ran couple of simulations for symmetric Y and (A)symmetric for X. Attached please find the spectrum of the point monitor for each case as well as a modified .fsp file. Thought the results seems to be OK-sih regarding the resonance wavelength the field profile still seems to be the superposition of more than one mode since it is not rotationally symmetric as an eigen-mode in such geometry is expected to be. Any feedback on that?

RR_EigenMode_Lumerical.fsp (306.4 KB)

As a follow up I am uploading the results of a much longer simulation 9ps since I was thinking that too much power is still in the region by the end of simulation. Attached please find the response of one of time monitors. Though I apodized the monitors around 8000 for just 100fs I still am not able to get a proper resonance mode profile.

Dear @hadiseh.alaeian

I think that you should not be worry about the auto shutoff level. As you might have noticed, the level drops to ~0.5 after a while and remains at the same value for almost the entire simulation. This means that the majority of the injected source is propagated by the ring. This is not very surprising: theoretically you have a very low material and radiation loss, and a big ring like this (you are right, 12.7 um in radius :slight_smile: ) should have many resonances and thus supporting many wavelengths.

I added the number of sources (and making sure that we will excite both TE and TM modes of the ring resonator), and removed the symmetry for now. Please note that you might loose some of the modes when you apply the symmetric boundary conditions (BCs) if your mode does not have the defined symmetry. I changed the apodization type to start (because we want to capture the propagated mode until the end) and modified the simulation time. I also used a slightly broadband mode (0.7 – 0.8). Modes seem to be more rotationally symmetric:

For the next steps can you please do followings:

  1. Use finer mesh and make sure that your results converge.

  2. Study how the results vary with FDTD simulation time and monitor apodization settings (mainly apodization center (fs))

  3. Apply symmetry to study modes of interest (for faster and final simulations)

Here is my modified file:

RR_EigenMode_Modified.fsp (320.1 KB)

Please keep me updated with your new findings and I am happy to be of any help.


Dear @bkhanaliloo

Many thanks for the invaluable help and insightful comments!
I followed the instructions and was working on various combination of apodization, mesh refinement, excitation signal bandwidth, etc. However as you can see in the attached figure the field profile is not still uniform which makes me believe it is still lacking some sort of convergence.

It’s surprising since the same methodology would properly extract and separate the eigen modes of a smaller ring, as you nicely showed in your case, but going to a larger size as my case it fails to work properly.
Any comment on that?

Thank you for your extremely helpful comments!

Dear @hadiseh.alaeian

Thank you for updating me and doing all the extra work.

In small rings, due to radiation loss, modes that are not supported by the ring will escape the ring quickly. Also in larger rings light requires more time to finish a round path. The other difference is that FSR is inversly proportional with ring radius, thus modes are quite close in larger rings and you might need higher resolution for monitors.

Can you please clarify if you checked other wavelengths too and what wavelength was this? I noticed that the modes that are not supported by the ring will look a bit asymmetric. In the figure that I provided on earlier post, I picked a wavelength with E magnitude to be maximum, which indicates the mode is supported by the ring.


You’re absolutely right! The fields are indeed asymmetric and kind of aphysical as a mode when it’s slightly off resonance. I’d checked it and it was fine right at the resonance. However one major issue is locating the resonance. The resonance peaks are very dependent on the mesh accuracy (I currently am using 5) and also the dipole source bandwidth (780,800)nm currently in my case. Since these changes are drastic in the scale of cavity FSR then it certainly is possible that I miss the resonance mode in the field profile monitor when I change the simulation parameters.
Do you think this change in resonance is really a convergence issue or after all the best accuracy that I can get with FDTD?

Dear @hadiseh.alaeian

I expect that this is convergence problem.

One more check: can you please add time monitors inside the ring, use same apodization that you use for other monitors, and look at the spectrum (right click on the monitor and select spectrum) after simulations finished? Since the spectrum will be a direct Fourier transform of data inside the ring, they should reveal resonances more precisely. Please tun for different mesh sizes and let me know if results still vary with mesh size.


Thank you @bkhanaliloo!
I was trying to investigate the effect of different things like apodization, mesh size, and bandwidth and now I guess I have a good estimate of the eigenmodes. They still vary slightly but I’m afraid that is not avoidable due to the discretization.

Thank you again for the valuable help and guidance!

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Dear @hadiseh.alaeian

I guess I am in the same page as you, though it is more intuitive why the resonances vary with mesh sizes. I hope that variations are not too big, otherwise we can investigate them again in more details.

Anyhow, I am glad that we had a good progress and hopefully the results were convincing enough.