Looking for accurate result from FDE and EME solver for a waveguide coupler


I am a new user of Lumerical products. I was trying to solve a polarization rotator design using FDE and EME solvers. My simulation shows the fundamental and coupled supermodes and corresponding effective indices for those modes. Mode field distributions look similar to what we expect but the coupling length calculation from those supermodes effective indices is not matching with the published results (paper attached). The paper shows the coupling length = 134.50 um but we are getting around 128 um. I simulated the propagation with the EME solver but still got the same less accurate result. I solved the waveguide structure with our in-house FEM mode solver and the results agreeing well with the published results. I tried to increase the mesh size but the results are still not accurate. Could you please help me to rectify the problem in my program? The program and the paper are attached with the post.

Waveguide cross-section:

PR at 1.55 um_JLT paper_Barh et al.pdf (755.5 KB)


Thank you,


Hi @souvik.ghosh.1

I did some convergence testing and the results seem to converge. You can also do more by changing the mesh size and FDE simulation span. The only thing that is left is the material index. How did you obtain the material index? Were the index values or effective index of the modes reported in the paper?



Dear bkhanaliloo

Thanks for your reply. Could you please let me know how you converged and which parameter you converged? I have done some convergence test of the same structure with different mesh sizes but maximum we got the coupling length of 130 um. It never touched the value what we are getting from FEM modal solution and the value mentioned in the paper. The paper I attached they also used the time domain simulation and got the value 134 um.

Regarding the material refractive index: We took the reported data in the attached paper. Could you please guide me to get the accurate result?

Thank you.


Hi @souvik.ghosh.1

My results were close to 129um that you reported. I was hoping to push the simulations further but I was limited by the memory. My values for effective index of the TE mode of slot waveguide were 1.545008 - 1.546165 (which is different than paper).

If you have a fancier machine (more that 32 GB ram) you can use a conformal mesh and set the maximum mesh step in the y and z direction to 1nm (disable all the mesh override regions). You could also try to replicate the results in FEEM solver.

I am not sure how precise you expect the results to be, but realistically fabricating this device will be limited to fabrication errors and you expect to get a few microns difference in the coupling length due to fabrication errors.



Thanks bkhanaliloo for your help. I was worried about the computation accuracy with FDTD and I got the satisfactory result for this problem. But now I replaced the top clad air with the SiO2 of refractive index of 1.444 and used the modal solution to find out the phase matching point for coupling. image
The waveguide width (W1) we found to be 345 nm to achieve a good coupling. Then by using EME solver the complete waveguide propagation has been simulated (result screenshots are attached).
The simulated result shows no power coupling from the slot waveguide (W2) to the simple rib waveguide (W1). We have considered much higher waveguide length compared to the coupling length calculated from the FDE mode solution.

waveguide_couplers_toplayer-SiO2_temp-25C_xspan-600_gap-300.lms (326.6 KB)

The simulation model is attached here. Could you help me to find out the problem in this model? I will appreciate any help on this matter.

Thank you.


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Hi @souvik.ghosh.1

Sorry for a late reply, the case was marked as resolved and I missed to reply to your last inquiry.

I am not quite sure if the two modes that you are referring to are the even and odd modes. Here I have attached the mode 2,3 and 4 for your review:


To me, it looks like mode #3 and #4 are the even and odd modes (coupled modes). I need to learn more on how to identify the coupled modes, but the modes in the last simulation file seems different than the ones you shared in the first post.

Please correct me if I am missing anything.

SiO2 clad waveguide coupler using FDE and EME solver

[PR at 1.55 um_JLT paper_Barh et al.pdf]- Referring to Fig.3 in this paper, you will see that TE mode will be converted to TM mode when W1=460nm. This is Phase matching condition, and this paper talks about moving from one polarisation to another(TE to TM, and vice versa). In this paper Air was used as cladding material.

When I use SiO2 as clad and substrate material, I obtained similar graph as shown below:

Now if I take phase matching condition width acc to this new graph(i.e width=340nm), and try to see coupling of light from one waveguide to another(using emepropagate), I can’t see light going from one waveguide to another.
Case1: At Rib waveguide width=300nm, mode profiles,neff, and emepropagate output are shown in below fig, and coupling length will be equal to 78um

Case2: At Rib waveguide width=340nm, mode profiles,neff, and emepropagate output are shown in below fig, and coupling length will be equal to 412um


As you can see in emepropagate screenshot, light never travels from one waveguide to another,

P.S. If I use Air at top cladding material, I can see similar light moving from one waveguide to another, and theoretical value of coupling length also matches with emepropagate graph

If you put the parameters acc. to the mentioned paper in the above attached lms file, things work almost, but as I use SiO2 as clad layer, coupling from one waveguide to another never happens.

Thanks, waiting for your response


Hi @sunny.chugh

I am still puzzled to solve the mystery. The paper that you are mentioning is not attached. Also. I downloaded the file and set the top layer to air but could not reproduce the plot in your previous post. Can you please share the working simulation file with me?

I cannot see the coupling when slot mode is selected in the bottom waveguides. However, when the fundamental TM mode is selected in the top waveguide, I can see the coupling:


As you can see, the mode is coupled from top waveguide to bottom waveguides but it is not the slot mode. There should be something that we are missing here.

Please let me know of your thoughts.


HI @bkhanaliloo. Thanks very much for your reply. First, I am attaching the paper I was talking about.
PR at 1.55 um_JLT paper_Barh et al.pdf (755.5 KB)

When I use Air as clad material, I obtained similar graph(to Fig.3 in the attached paper) as shown below:

Now I am attaching 3 lms file corresponding to 3 different values of TM rib waveguide width(i.e 440, 450,460nm). Also I am attaching screenshots of graphs I obtained. In all three you will see, light is travelling from TE slot waveguide to TM rib waveguide.

  1. TMwidth=440nm

waveguide_couplers_toplayer-Air_temp-25C_xspan-600_gap-500-TMwidth-440.lms (314.1 KB)

  1. TMwidth=450nm

waveguide_couplers_toplayer-Air_temp-25C_xspan-600_gap-500-TMwidth-450.lms (314.1 KB)

  1. TMwidth=460nm

waveguide_couplers_toplayer-Air_temp-25C_xspan-600_gap-500-TMwidth-460.lms (314.1 KB)

Now, I am providing you graph when I use SiO2 as clad material, again I obtained similar graph(to Fig.3 in the attached paper) as shown below:

Now I am attaching lms file corresponding to TM rib waveguide width of 340nm. Also I am attaching screenshots of graphs I obtained. Now, when I am using SiO2 as clad in this case, you will see light is not travelling from TE slot waveguide to TM rib waveguide.

waveguide_couplers_toplayer-SiO2_temp-25C_xspan-600_gap-300-TMwidth-340.lms (314.1 KB)

Please let me know if I have made myself clear to explain it to you.
@bkhanaliloo Waiting for your response.


Hi @sunny.chugh

Thank you very much for sharing the files and a detailed explanation.

I spent a few hours to resolve the mystery today. I think the results that you are seeing, i.e. no coupling for the top glass layer, is correct and we need to explain why.

When I check the modes in two cases, I realized that the third mode in the two cases, i.e. top air vs top clad, are quite different:

For both simulation files, I changed the number of cell groups to 2 to include propagation before the double waveguide region and study the coupling between different modes:

When I checked the internal s matrix from EME results, the results were quite different and more importantly, the S13 that shows the coupling between the 1st mode of first cell and 3rd mode of second cell was almost zero for the top clad case. This value is ~7% with the top air case. For your review I have include these plots below.

As a result you are not seeing any coupling between the waveguides when the top layer is glass. I think to have a polarization rotation, you need to break symmetry which in this case is done by having different top and bottom layers. I will discuss it further with some senior colleagues and will keep you updated if I found anything new.

Top air


Top glass:


Please keep me updated with your thoughts.


@bkhanaliloo Thanks very much for your reply.
I think ideally it should work with SiO2 as clad layer because it is working when I am taking Air as clad and I have tried with having SU8 as clad material. Its working for both cases, so it should work with SiO2 as well.

I will wait for your further response.


Hi @sunny.chugh

I discussed your case further with my colleague and my previous response seems to be valid. While the TE- in the slot waveguide and TM-mode in the strip waveguide are phase matched, the TE-mode in the slot waveguide is not coupled to TM- supermode. As a result the power coupling from slot waveguide to strip waveguide is zero as the second and third modes are required for power coupling.

I checked the paper and did not find much discussion about symmetry of the geometry. Authors mention that a low index material can be used in the slot region to achieve similar results, but they did not talk much about replacing top air layer with a cladding and there might be a reason why did not do this…

You can also repeat simulations in FDTD starting with a shorter length like 50um. If there was any coupling, please let me know and I will be glad to take another look.