# varFDTD vs EME

I am trying to decide which solver on MODE solution can be suitable for my 3D structure since simulations using 3D FDTD aren’t time efficient. I just can’t understand this sentence from the knowledge base

“For planar geometries where there is negligible coupling between vertical modes, varFDTD can achieve accuracy comparable to 3D FDTD with computation times comparable to 2D FDTD. For 3D geometries where there is coupling between vertical modes, EME is a frequency domain method that offers a good alternative to 3D FDTD because its computational requirements scale exceptionally well with distance.”

What is meant by vertical modes?

Many SOI based planar structures without vertical mode coupling are able to make use of varFDTD, such as a ring resonator, and there is a white paper. However, there are certainly some types of structures that varFDTD is not the best candidate. Here is some description from the solver physics of varFDTD solver:

The varFDTD solver is based on collapsing a 3D geometry into a 2D set of effective indices that can be solved with 2D FDTD. This works best with waveguides made from planar structures, as the main assumption of this method is that there is little coupling between different supported slab modes. For many devices, such as SOI based slab waveguide structures, that only support 2 vertical modes with different polarization, this is an excellent assumption.

Vertical modes coupling
varFDTD is designed for planar structure where there is no vertical coupling between slab modes. When the structure is collapsed into a 2D set of effective material, the modes calculated by the solvers are the slabs modes supported by the slab waveguide. If there are coupling between the vertical slab modes, this assumption is not valid any more. This spot size converter is an example where there are vertical coupling during mode propagation. The screenshot below shows the vertical mode profiles of the input smaller si waveguide and output larger polymer waveguide. The xz field profile shows how light is converted from a smaller to a larger spot size.

Thus, varFDTD should not be used and this is an example that EME is recommended.

Polarization conversion
In the varFDTD solver setting, you will need to choose what polarization for the simulation. In other words, when TE is chosen, only TE modes are considered. If there are conversion between TE and TM modes, for example this polarization converter, we should use EME instead since varFDTD is not designed to handle polarization conversion.

non-planar structure
If your structure is non-planar, then EME or FDE maybe be a better option, such as a fiber. There is also a post related to this scenario.

There is a post that has a little more general info on when to use what solvers.

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Therefore, how can you use this software to check whether there is any vertical modes coupling or polarization conversion occurring?

I guess the logic is that you already have some idea whether your device has vertical couple or not. Usually, the structure itself tells you some information. For example, a planar structure should typically have no vertical coupling. Then, users can decide on varFDTD vs EME.

If your goal is to know whether your device has vertical couple by running a simulation, one way is to run a FDTD simulation. Depending on the type of device, there might be other ways to get more information.

@kchow As I understand from above discussion, varfdtd cannot be used at all to simulate focusing grating coupler with single mode fiber above. As in this case we have coupling from the grating to the fiber. Is this right?

like you said it definitely has vertical coupling, therefore varFDTD is not recommended. You should use FDTD for this part.

However, varFDTD may be used to simulation the taper region, like this example.
https://kb.lumerical.com/en/index.html?pic_passive_tapers_soi.html

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@kchow I have a similar problem. I am simulating a 1x2 tapered MMI acting as a 3dB power splitter, and i have really diferent results depending on which solver i use.
In my case, for varFDTD, the optimum length is about 26.2 um, while the EME solver gives me a length of 30um.

How can i decide which solver is better?
Thanks

Looks like the results returned by the two solvers are not widely different, at least not an order of magnitude off. Don’t forget that these are two different methods so the results should never be exactly the same. That said, I think it is possible to bring the results closer by making sure you follow the best simulation practices, and minimize simulation errors by testing the convergence. You can either upload the files to here so we can take a look at it, or/and take a look at these pages for tips on convergence tests.
https://kb.lumerical.com/en/index.html?layout_analysis_test_convergence.html