# Bragg grating response not consistent with theory????

#1

Dear all,
I am simulating strip waveguide Bragg grating for various corrugation width. i could not correlate the simulation results (EME analysis result)

and (3D FDTD result) with the following general foumulas of Bragg grating:
a) neff is effective index without grating. this formula has nothing to do with corrugation width. but plots show that Bragg wavelength shifts teft with increase in corrugation width.
b). according to this formula bandwidth should be increased with increase in corrugation width (wider the corrugation width higher is the coupling coefficient), but in plots BW is lower at Δw = 80 nm than Δw = 60 nm than Δw = 40 nm.

formula ref: Wang, X. (2013). Silicon photonic waveguide Bragg gratings (T). University of British Columbia. Retrieved from https://open.library.ubc.ca/cIRcle/collections/24/items/1.0165738 (Original work published 2013)

EME code is here UBG_EME.lsf (4.7 KB)

another question:
how does ‘EME-analysis’ calculate s-matrix? does it use TMM; first calculate low and high effective index by FDE, then using fresnel equation calculate constituent matrices and multiply in reverse order?
(as TMM explain in book Chrostowski, Lukas, and Michael Hochberg. Silicon photonics design).
Thank you.

#2

Dear @ktwayana

I am not expert on Bragg gratings, but I will try to explain your questions:

1. This assumption is true if the effective index remains the same as waveguide, and will fail if the corrugation width is too big. If, for example, you are using a waveguide of 500 nm width, 60 nm is not a small perturbation and thus might effect the modes. This assumption will work if you expect the mode profile remains almost the same (which is probably true for ΔW< 10 nm).

2. I am not quite sure about these plots. Maybe your simulation file is not set properly and doesn’t resolve the gratins properly or simulation time was not enough? If you look at Figure 2.22 of the linked thesis, what you said should be the case.
maybe check this webinar: https://www.lumerical.com/support/video/waveguide-bragg-gratings-res.html

3. Partially right. EME calculates modes on each cell and then calculates overlap between different modes. This might be slightly different than TMM which considers only one mode. For more information please see these links:
Algorithm of EME.
https://kb.lumerical.com/en/solvers_eigenmode_expansion.html

#3

Dear @bkhanaliloo,
Thank you very much.

1. Now i understand that the CMT works well only for small perturbation.

2.Yes, there are some issues with the simulation time and set properties, but i could not understand the left shifting of central wavelength.The EME simulation of the file given here https://kb.lumerical.com/en/pic_passive_bragg_full_device_simulation_with_eme.html for different corrugation width also results left shift of central wavelength for higher corrugation width. Can we interpret this as, because of the lower average effective index for higher corrugation width? (but this interpretation is not correct if we look at the Figure 2.22 https://open.library.ubc.ca/cIRcle/collections/24/items/1.0165738 )
(i am sorry. previous post correction: in 3D FDTD plot legend for 20 and 40 should be opposite)

1. in period_sweep.lsf file here: https://kb.lumerical.com/en/pic_passive_bragg_full_device_simulation_with_eme.html calibration factor ng/neff is calculated at 1.53 microns wavelength. is there any region for calculation at this wavelength because ng/neff value depend on the wavelength that you choose?

i don’t understand why Bragg_EME.lms https://kb.lumerical.com/en/pic_passive_bragg_full_device_simulation_with_eme.html simulation not work if i extend oxide to the cladding region.

1. how can i use frequeny domain profile monitor with block boundary? file Bragg_FDTD_unit_cell.fsp here https://kb.lumerical.com/en/pic_passive_bragg_initial_design_with_fdtd.html
or is there any way to get transmission and reflection plot from block boundary simulation?

Sorry for the no of questions on a single post.
thank you

#4

Dear @ktwayana

One thing to point is that Δλ is a function of λB and your first plot shows that λB decreases with ΔW. I agree with you that this is not consistent with Figure 2.22 of the thesis (and is still a question for me too). I ran EME simulations and got similar results as yours with EME (i.e. shift in wavelength with ΔW). One possible scenario might be because the fabricated devices have rather smoothed gratings which affects the overall behaviour of the device? For example check Fig. 2.35 where the bandwidth of the fabricated device is 1/3 of the designed device.

Sorry that I do not have a clear answer for your valid questions. As I mentioned, I am not expert on Bragg gratings and I am not quite sure about all the details that might effect the final results.

Yes, the ration will depend on the wavelength, but once you picked the wavelength and calculated the calibration factor, results should be the same. The value for calibration factor should be almost the same along the gratings.

Maybe because you are not setting mesh order properly and oxide layer overrides the grating. To avoid this, change the override value of glass (rectangle object) to a value higher than 2. It is a good practice to check the injected mode before running simulation through Ports under EME to make sure that you are sending a proper mode.

There is no limitation using profile monitor, but you might need to use apodization so that you are capturing the field properly i.e. waiting long enough that the light outside the bandwidth has decayed enough. In this example, light that leaves the simulation region enters from the other side but only for wavelengths within the bandwidth. Also, since light enters the simulation region, your transmission plots (which are normalized to injected power) will be above 1.

I hope I could answer all of your questions. If you think that you following questions are not matched with the title of the post, I think it will be a good idea to create a new post.

Thanks

#5

Dear @bkhanaliloo,
Thank you very much for clarifying my confusion.
I have to look at the use of apodization. if any confusion i will create a new post.