# Eigenmode Expansion Solver - Nested Periods

Hi, I’m trying to simulate some sampled Bragg gratings in Silicon waveguides using the Eigenmode expansion solver. So far I’ve been using periodic cell groups to model standard Bragg gratings, which works great. However, now I would like to add a length of waveguide before and after the grating and then make THAT entire structure periodic. Using the notation of the cell group sequence in the EME solver, I would like to get the S-parameters of a structure that looks something like:

[(1,(2,3)^20,4)^10]

Does anyone have any ideas? Thanks.

Hi Torrey,

In EME it is not possible to nest periodic structures in the way you have in mind. A good alternative in your case would be to combine EME with INTERCONNECT:

1. Simulate the Bragg grating with 20 periods and additional length of waveguide in EME and get the S -parameters.
2. Use the S-parameters to construct an optical S-parameter object that can be repeated 10 times in the INTERCONNECT simulation.

Both, the EME and INTERCONNECT simulations should be pretty fast. From INTERCONNECT you can get the S parameters for the entire device. To learn more about INTERCONNECT I suggest the following links:

Alternatively, if you want to simulate everything in EME, then you would have to draw the Bragg grating with the 20 periods and then use the periodic group definition. So you will have something like:

[(1, 2, 3, …, 21, 22)^10]

However, for a situation where the number of repeated unit cells in the “inner” structure (the unit cell of the Bragg grating repeated 20 times in your case) is larger than the number of times the inner structure itself is repeated, the EME + INTERCONNECT option is recommended.

Hope this helps!

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Thanks for your help. I tried using a S-parameter object in INTERCONNECT but found that the results were inconsistent with theory when I connected more than 1 S-parameter object in series (but a single S-parameter object gave exactly what I expected). I ended up writing a MATLAB script to calculate the reflectance of an arbitrary number of S-parameter objects and then importing the S-parameters calculated in MODE.

Hi Torrey,

I can take a look at your INTERCONNECT file and try to find the problem causing the wrong results for the series combination.