Questions about FDTD simulation of a waveguide bragg grating

Hi, everyone.
I want to calculate the reflection coefficient of a waveguide bragg grating like this

where w=1.2 μm, t=0.9 μm, d=250 nm, Gamma=292 nm. The length of grating region is 203 μm, i.e. 700 periods. Each period of the grating has 9 grids.
Due to the fine grid in the grating region, the simulation is quite time-consuming. So I am trying to find a appropriate simulation time. I have used 5000fs and 10000fs, however, the simulation results seem to be different:

As can be seen in the figure, there are ripples in the high reflectivity band and the maximum of reflection coefficient exceeds 1 which are abnormal.
My questions are:

  1. How can I get the correct result?

  2. Should I increase the simulation time and to what value the simulation time should be increased?

Attached is my project file:Grating_700period_longtime.fsp (4.2 MB)
Thanks a lot!

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Hi @jialin_jiang

I had a few comments regarding your simulation file that might explain why you see a reflection greater than 1. Please make sure that your geometry exceed your simulation region such as on the left, right, and bottom of your simulation region. For example, if silicon is the bottom layer, expand it as in your current setup your devices are sitting on the air. Also expand the Mode source so that it is wide enough to cover the injected filed completely. The other concern is about the Mesh: choose dx as a multiple integer of your grating so that you have enough meshing inside the devices and it overlaps with the devices on the boundaries.

I tried to run the simulation and I find out that your simulation stops before you reach the auto shutoff level. This is because you need even longer simulation time. If you are looking for a faster and more optimised solution to the problem, consider using EME. You can set the simulation for arbitrary number of periods (100 here). Another option would be to use Bloch boundary conditions which gives you information about the center wavelength and bandwidth of the grating. You can read more about it here.

I hope this was helpful.


Hi, bkhanaliloo
Thanks for the reply.
The bottom of the simulation region is air because the structure is suspended. I will modify the file as you suggested.
I might have another question, how can I know whether the simulation stops due to auto shutoff? I usually run the simulation at night and see the results the next morning.

Hi @jialin_jiang

I guess I understood your geometry now, so the etched layer was SiO2. I hope you can get reasonable results using FDTD.

I started a new topic here that will answer your question.

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Hi, bkhanaliloo
I try to increase the simulation time to 30000fs which is 3 times of the original value. I also have adjusted the simulation file as you suggested, whereas the simulation is divergent. The result of time monitor is shown as below

Could you please tell me how to address this problem?

Dear @jialin_jiang

The source of divergence problem that you are seeing might be have different reasons and requires to do some converging testing. The first step for you would be to set all the boundary conditions to metal and run the simulations to see if the problem is from PML or stability factor. Then you will need to adjust the PML boundary condition (for eg. to profile->stablized one or changing the number of layers). A movie monitor that records the data on the simulation region and inside PML will be a great source of help to understand where the divergence occurs.

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Hi bkhanaliloo. I have another question:
Can the varFDTD solver be used to simulate the grating in order to reduce the simulation time?

Dear @jialin_jiang

VarFDTD works best if the thickness of the structure remains constant throughout the geometry. However, you might get reasonable results for this structure as long as the thin section of waveguide is not etched all the way down to the substrate. Please keep me updated of the results as I have not done this simulation.