Edge coupler with inverse waveguide taper coupling efficiency


I am trying to find the coupling efficiency from a fiber to an inverse taper waveguide in Lumerical MODE EME . For that I am trying put two 2D EME monitors to get field profiles (E, H): one at the fiber and another at the waveguide (output section). I want to calculate the poynting vectors, and from there, power at that two monitors. I would like to see how much power is coupled finally, from fiber to the output waveguide and what percentage of input power that is. I also used two sets of data: 1) From the two EME monitors 2) The field profile at the port. My questions are:

Q1. I wrote code based on script given in Working with the Poynting Vector . Does this same method/code works for MODE EME monitors/ports?

Q2. When I change the inverse taper length ( or propagation distance) in EME analysis window (‘group spans’ in cell group definition), does the monitor at the waveguide shifts too according to the propagation length? Because I did not get any difference in the power calculated for two different length (10 um, 1000 um). I expect the power at the output waveguide to be less since there will be loss if the inverse taper size is smaller. In that case, Can you please take a brief look if I am writing the code correctly (pls see the attached lsf code file)?

Q3. Lastly, I also tried the same thing with Field profile from port 1 (input) and 2 (output). To my surprise, I got the power at two monitor to be same, even output waveguide have slightly higher power (ratio = 1.0019 something). Do you think the port method should be used or the monitor method?

I am sorry for the long post and I really appreciate your help. Thanks in advance.

poynting vector _EME field monitor method.lsf (975 Bytes) Poyting_vector_EME_ports method.lsf (944 Bytes)

Hello @sh72,

This approach you are using should work, as discussed on this post:

The monitors can be used to calculate the total power moving through the waveguide, but not the power coupled into individual modes. The power coupled into the output mode is calculated by the EME solver automatically, and can be determined from the S parameter results. For example, if only one mode is selected at the input and output, then |S_{21}|^2 will give the power coupling efficiency. This result should be less than or equal to the power calculated by the monitors.

Yes, if you change the group spans (and click “eme propagate” again) the monitors should take this change into account. I don’t see any mistakes with your script, the results should be calculated properly. Do the S parameter results change when you increase the taper length?

These field profiles are the calculate mode profiles, they are not the actual electric field transmission through the ports. These mode profiles are normalized, so you will receive the same result if you calculate the power in each of them.

I hope this helps, let me know if you have any questions.

Hi @kjohnson,

Thanks for your reply and it is getting more clear to me now. However, I do have some followup question:

Q4. How can I find the mode overlap between fundamental mode at the output waveguide and all other mode combined in the output waveguide? Basically, I want to find the coupling of fundamental mode into the output waveguide (maybe as percentage of all modes). Can you help me write a script for that using EME field profile monitor or ports? (see the previous attached file for geometry of output waveguide )

Q5. Does |S21|^2, you mentioned above, take into account the mode overlap at the fiber - taper waveguide tip interface ? or it just calculates mode conversion efficiency at the taper section? Or it can be assumed as product of two (overlap x mode conversion efficiency)?

Q6. In FDE mode overlap analysis between fiber mode and taper tip mode, if I click optimize position with tick in box " shift d-card center" (fiber fundamental mode in global deck), do I need to manually shift the fiber position according to x/y/z shift result before running EME analysis? or it will take care of it automatically?

Thanks for your time. I really appreciate your help.

You can select multiple output modes in the port of the output waveguide. All of the selected modes will be included in the user S-matrix result returned by the EME solver. You can use these S parameter results to see how much the input fiber mode is coupled into each of the selected output modes (see this page for a description of the S matrix mapping).

This result is the fraction of the power in the input fiber mode that is coupled into the selected output mode in the output waveguide. It takes into account the power coupling of all the modes in each cell, so it will take into account both the mode overlap and the mode conversion efficiency in each cell along the taper.

You will have to manually shift the fiber once the overlap analysis obtains the optimized position, it will not be moved automatically.

Hi @kjohnson,

Thank you for the reply. I have one last question and I really appreciate you helping me a lot.

According to your reply, my understanding is that |S21|^2 gives overall coupling efficiency between fiber and taper waveguide which include mode overlap and taper mode conversion efficiency. However, in FDE analysis, I found 62.7% overlap between fundamental mode at taper tip- fiber interface which is between cell 1 and 2 in EME. In EME analysis, after ‘eme propagation’, when i look ‘overlap 1_2’ (from EME::cells::cell 1), it shows 69% overlap. And similarly S 1_2 shows value 1. (see attached image)

Also overall |S21|^2 after propagation length sweep shows ~ 99% coupling efficiency which doesnt seem to be right to me.

My confusion is that how come |S21|^2 is ~99% while the FDE overlap is 62.7% or 69 % (from cell)? Am I making any mistake in the simulation or missing some points?

I have attached the simulation file for convenience and images.Final Edge Coupler_ SiN_visible_145 nm width_top cladding equal box_No input seg_10 modes.lms (441.0 KB)

T vs taper length

Hello @sh72,

Note that the FDE overlap calculation only involves those two modes. However, not all of the light propagating into the fiber will be in that taper mode. As this is the end of the taper, it is likely that there will be light propagating in other modes or in the cladding that will also be coupling into the fiber. I would assume that this extra light is what is making up the rest of the 99%.

Let me know if you have any questions about this.

Thanks. Now I got it

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