MIM divergance problem


I am working on this paper(MIM waveguide): Tunable Plasmonic Band-Pass Filter for regenerating its result. at first, I want to give figure 3(a).
The simulation file:rp_225.fsp (350.8 KB)

My problem: the simulation always diverged with standard pml.

when I used stabilized pml with 150 layers, the simulation was converged but the result was not similar to paper result.

I increased the alpha parameter of pml,simulation was converged but result …

I read all of information in your website but I could not find a suitable and efficient solution for MIM waveguide structure(many engineer had this problem). Can anyone tell me what is the final solution!?

General tips to solve divergence problem in metal-insulator-metal (MIM) structures


I also have same divergence problems when I simulate plasmonic structures. As far as I understand, the problems come from the reflections between metal and pml. If you put a monitor and see the electric field distribution, you will see the strong field enhancement caused by this.

Thus my solution is always to put a dielectric layer between metal and pml. Maybe there are other solutions.


Thank you @mayata
How can i set it? I do not understand what did you say
Thanks for your advise.
Could you please modify my simulation file


Can you modify my simulation file?


rp_225mayata.fsp (356.5 KB)


Thank you so much, the transmission spectra is

when I used the dielectric between pml and metal, the reflectance was occured.
Are you sure this approach is correct?


maybe you have to increase the dimension of your simulation field so that the dielectric layers do not influence the ring resonators.

Note that the feature of the ring resonators is very sensitive to the refractive index. Make sure that the refractive indices of the materials are same as those in the paper. e.g. the refractive index of the silver.


I think that this topic should be the latest topic with MIM divergence.
I want to the lumerical engineer solve this problem for many users.
@aalam @fgomez @nlui @kchow @bkhanaliloo
Thank you so much.


I increased the span of simulation and the transmission is

I am sure that the material refractive indices is true.
I think this approach is not suitable.


Hi All,

I am creating a new topic to summarize my thoughts on MIM structures, and will get back to you soon.



Dear @mostafanaseri

I think @mayata’s method will solve the divergence problem, but can create additional unexpected reflections. I wrote some general tips on how to solve the divergence problem in MIM structures here. In your case, you can obtain reasonable results by either increasing the FDTD span or using stablized PML with 256 layers. Here I provided you with the simulation file and screenshot of the results for these two cases:

Larger FDTD span with 8 layers of standard PML:

rp_225_standardPML_largerFDTD.fsp (394.6 KB)

Small FDTD span with 256 layers of stablized PML:

rp_225_stablizedPML_SmallFDTD.fsp (398.2 KB)

You can follow some of my recommendations in the original post and also perform some convergence testing to make sure that results are converged.

I hope this solves the problem, but let me know if you had any additional questions.


Thanks @bkhanaliloo
I ran the simulation file. case 1,the simulation was diverged but better than before.
I want to know,that how make this spike? because in paper was not occured.

Thank you for helps.


Dear @mostafanaseri

I spent quite a lot of time on convergence testing as below:

Originally I thought that two peaks are related to slight size mismatch of two rings as a result mesh. However, when I tried using asymmetry (for y), finer mesh and stair case, lower auto shutoff level, different BCs, increasing FDTD span, introducing a new override mesh in the gap section, I could still see the two peaks.

You can probably try using a different material fit to make sure that results are still consistent. If you are still seeing those splits, I think we need to look for a physical reason to explain what is causing it. There is a chance that in the referred paper, authors did not report the split.

Please let me know of your thoughts and I will be glad to be of a help.


I think that these spikes occures for two reason :1-pml boundary 2- material data.
I tried many cases,but these spikes always exists!


Dear @mostafanaseri

Regarding material fitting, how is that different in your simulations from the ones in the paper? (Sorry, I didn’t have access to the paper).



the pdf file: http://www.mdpi.com/1424-8220/17/3/585/pdf


Dear @m.dezyani and @mostafanaseri

Thanks for uploading the paper.

I spent quite a lot of time today modifying many things, but I think I could finally obtain the results that we were looking for.

After going over paper, material fitting seems to be identical to as what we have in simulation file. The problem, however, seemed to be due to size of the mesh.

While we were using fine mesh, it looks like it was not quite fine enough to resolve disks and the gap. Thus I modified override mesh, and used conformal variant 2. This significantly improved the results:

A few more things if you wanted to even optimize the results is to perform convergence testing. Particularly, you can use even finer mesh, increase PML layers, and use multifrequency injection.

Please go ahead with practicing them, and let me know if you had further questions,

rp_225_standardPML_largerFDTD_ver2.fsp (1.1 MB)

I hope this answered your question.


Thank you for helping us @bkhanaliloo