2D Simulation of Bragg grating diverges


I am simulating a Bragg grating in FDTD where the change in effective refractive index is achieved by modulating the width of the waveguide. I am interested in the amount of power that is transmitted and reflected from the grating. I am also interested in the group delay experienced in the transmission and reflection, so I have profile monitors that I can calculate this from.

I’ve been having some trouble with the normalized transmitted and reflected powers being above 1 and below zero, so I started running the simulations for a longer time in order for the fields to decay completely, which instead leads to the simulations diverging after a relatively long time.
I tried to fix the problem first by decreasing Q from 0.99 to 0.9 and then to 0.5 (which made the simulations diverge faster) and then by playing around with the settings for the PML boundary. I change it to a stabilized profile and also tried a standard profile but with alpha=0.1. None of this worked so I tried changing to running the simulations with a constant refractive index for both my materials instead of dispersive materials, but this also didn’t help.

I have attached two simulation files with slightly different settings, one that diverged after some time and one that didn’t diverge but where the reflected power goes both above 1 and below 0 as shown in the plot below.

The blue line is reflected power and the green is transmitted power.

The main difference between the diverging and the stable simulation is that the modulation of amplitude of the width of the waveguide is 5 times larger in the one that diverges than in the one that is stable. Both situations are perfectly reasonable so I don’t see why one should diverge and the other not. In any case both return strange results (the diverging simulation is also a significantly longer grating, but the short ones also tend to diverge).

For reference I am using FDTD version 2020a-r6.

Finished simulation files are in this link

DivergingSimulation.log (7.0 KB) StableSimulation.log (9.5 KB)

Hello @lgutt,

To help determine the cause of the divergence, I would recommend that you try changing the y boundaries to metal instead of PML to see if the divergence problem still occurs. The results will indicate whether or not the PML is responsible for the divergence.

Regarding the transmission values above one or below zero, you are correct that this indicates that the simulation time is not long enough. Of course, the divergence problem will have to be fixed before the simulation time is increased.

With that being said, I would recommend you use the EME solver for this simulation. It is much better suited for a simulation of a Bragg grating like this, and would avoid the divergence and simulation time problems entirely. You can see an example of an EME simulation of a Bragg grating here:

Because your width modulation is continuous your simulation will require more cells, but it will still be much faster and simpler than the FDTD simulation.

Let me know if you have any questions.

Thanks! I’ll take a look at it and see if some of that helps.

Also, thanks for the suggestion but I am just simulating this relatively simple grating in order to make sure that results fit with theory. After this I want to implement chirped and apodized gratings and I assume that FDTD will better suited when the grating isn’t periodic anymore.

Hello @lgutt,

I think that even with chirped or apodized gratings the EME solver might be preferable to FDTD for a simulation with a very long propagation length like this. It may depend on the number of modes required for each section in the EME simulation, but I would expect the number of modes required to be fairly low for a device like this.

I’m basically only interested in investigate single mode wave guides, so that might be a good idea. On the other hand I want to do simulations over a range of frequencies with a large resolution in frequency, so in any case I would need to do a large sweep but that might also be worth it.