Port transmission greater than 1

I am having trouble with the Transmission result through FDTD ports. I am testing the transmission for 2 cases. 1) Through a waveguide length of 50um. 2) Through a waveguide with a ring resonator. The goal is to see the resonance show up in the Port Transmission function. (I am not trying to find the resonance of the ring resonator. That is already done in different example.)
However, when I examine the results on the port monitor transmission, I am getting values for T greater than 1. I know that the Transmission result is normalized, so I am trying to figure out what is going wrong in order to generate gain in the monitor? There are no gain or lossy elements in my simulation space. Am I having a proximity issue of the port to the PML boundary, or something to that effect?Waveguide_port_testing450nm - Copy.fsp (5.1 MB)

I am attaching the two files I am working on for reference.

Thank you

Hi @demory1,

Usually when a transmission result is greater than 1 it is due to reflections from the PML, the simulation time not being long enough, or poor material fitting leading to gain. I would:

  • increase the number of layers in the PML
  • make sure your monitors are at least half a wavelength away from the PML
  • make sure your structures extend all the way through the PML
  • increase the simulation time/decrease the autoshutoff threshold (especially for the resonator)
  • check your material fits to make sure the imaginary permittivity is close to zero

Could you please attach your other simulation file as well?

Thanks,
Kyle

The second file was too large to attach directly, so I an looking for a way to upload. I had a 10nm gap area mesh and 10nm mesh around the resonator as well to help illustrate the coupling.

Going through your bullet points.

  1. I have not done PML modifications yet for this simulation.
  2. I am making changes to this to see if it fixes some issues. I was using ports 0.5um from the edge
  3. I did notice that the resonator case did not reach auto shutoff. I remember in the FDTD resonator simulations though, that we did not reach shutoff because the energy was being trapped for many cycles.
  4. I am using the built in permittivity for Si and SiO2 at 1550nm. These should not have imaginary components.

How large does the Port monitor need to be with respect to the waveguide? I have noticed in the simple case I attached above, that it does affect the field profile in the waveguide if I resize the port.

Thank youWaveguide_port_testing450nm_with_resonator200nmgap_10nmmesh - Copy2.fsp (5.1 MB)

I was able to upload the file.

Edit- In the meantime I have been testing the base file I gave you in post 1. It seems that the Transmission is sensitive on the y-span of the port. I have shrunk the Port (1,2) y span down to 1um (y span 1um, zspan 2.35um) for a 0.22um height by 0.450um width waveguide and I am getting transmission results less than or equal to 1 instead of greater than 1. So I think this was a part of my problem. (The port monitor dimensions)
I am testing next the spacing from the Port object to the PML boundaries to determine how small I can shrink the space (to save computation time) without destroying the result integrity.

I wouldn’t recommend reducing the y span of the ports too much. They should be large enough so that they capture the majority of the fields of the waveguide modes. As long as they don’t overlap with the fields of the resonator they should be okay.

I performed some simulations using your resonator file. I moved the monitors to about 2 microns away from the PML, increased the depth of the PML to 16 layers, turned off the autoshutoff and ran with different simulation times. Here are the results at 10,000 fs and 30,000 fs:

image

Are these similar to the results you were getting? The transmission does go slightly above 1 due to the ripples in the spectrum. As you can see, increasing the simulation time decreases these ripples. This is because more light is allowed to leave the simulation so the fields are closer to zero which makes the results of the Fourier transform more accurate. I would recommend increasing the simulation time even further than 30,000 fs to get more accurate results.

It would also be a good idea to use the 2.5D FDTD solver in MODE Solutions for your initial simulations. It is much faster than 3D FDTD simulations without sacrificing too much accuracy for SOI devices. You can then use the 3D FDTD solver for your final simulations, once you are close to finalizing your design.

Let me know if you have any questions.

Hi Kyle,

The results are different. But you bring up valid points. I have not been plotting S. (How did you plot S by the way?) I have just been plotting port 2:T. When I first ran this simulation, I only used a duration time of 2000fs. I see while that may work for the simulation without the resonator, I need to increase the simulation time with the resonator. That is the first thing I will change. Attached is the Port2:T that I got when using 2000fs. “Resonance_200nmgap_10nmMesh”.

Now the width of the port. This one is really causing me problems. For simplicity, I removed the resonator and an just examining the waveguide structure. Here is the result I get with the Port (1,2) size here (yspan 1um, zspan 3um).


As soon as I increase the port(1,2) size, the results are changing. (See the red and magenta lines on the plot). The new larger port size is (yspan 3um, zspan 3um).

Now intuition here tells me that we should not have much if any loss just propagating down a strip. So I am not sure which result to trust.
Waveguide_port_testing450nm_with_resonator200nmgap_10nmmesh - Copy2.fsp (1.6 MB)

EDIT: You can disregard the part about plotting S. I did not see it in the list before. I may have glanced over it looking for T.

EDIT#2: I have tried the 2-D version of this simulation. I can see the ripples at the bottom of the plot on the order of 5%. So when you take |T|^2 or |S|^2, that value is reduced to 0.25%. This is done with 30000fs time, and the auto shut off value is 0.004 (still far from auto termination of 1e-06).
I think I have a better sense of what is going on in the with the resonator.
I am going to try the 3-D version now, with the improvements to the simulation space size, port locations, run time (fs), and PML thickness. I hope this solves my problem.

Thank you

I wouldn’t worry too much about the differences in your T results due to changing the port size. You can see in the third plot in your previous post that these differences are only around 0.1-0.3%, which is not very significant.

Yes, as you pointed out even with a 30,000 fs simulation time the simulation is still far from the autoshutoff level (by the way, T is the power transmission so you should not square it). This is most likely your main problem. It is an unfortunate fact that time domain simulations of resonator structures tend to take a long time. You should try increasing the simulation time until the ripples are reduced to an acceptable level.

Hi Kyle,

I just wanted to bring this to closure. I did the 3-D version of the structure with the resonator. I increased the PML to 16 layers, the simulation time is 30,000fs, mesh order was 1 (to test), and port sizes of (yspan 3um, zspan 3um). It appears that my port 2:T ripples are at a max of 1%. So with the higher order mesh, this may reduce further. I am a little reluctant to go beyond 30,000fs due to real world time constraints of simulation. Do you think going to 32 PML layers will have any positive effect for me in reducing the ripples, or it would have to be increasing the simulation time?

Waveguide_port_testing450nm_with_resonator200nmgap_10nmmesh - Copy3_1.fsp (2.5 MB)
I am attaching the final file for reference. In the meantime I will explore the 2D version some more just for speed increase until I nail down the final 3D values.

1 last question. Can I calculate the Q values for the resonances from this T plot directly using FWHM and wavelength data? I know with the dipole approach I could not do that as the power injected is not constant per wavelength. However, I think (correct me if I am wrong) the port is a uniform source and each resonance amplitude should be directly comparable to each other?
Thank you for the support.

No, I don’t think increasing the number of PML layers will decrease the ripples. They are caused by the fact that we obtain the transmission spectrum by performing a Fourier transform of a truncated time signal, so only using a longer simulation time will decrease them.

No, the spectrum of the signal input by the ports is not uniform over wavelength. However, the results are normalized with respect to the input spectrum so the amplitudes of the resonance peaks should be accurate provided the simulation is run long enough.

FDTD has two analysis groups for calculating Q factors, one for low Q and one for high Q resonators (the calculations used for each are discussed here). The low Q analysis group calculates the Q factors using the ratio of the resonance frequency and the FWHM. However, this is only accurate if the simulation is run until the fields decay completely. I would recommend you use the high Q factor analysis group because it seems like the fields are not completely decaying in your simulation.

I hope that helps. Let me know if you have any questions.