# Discrepancy between 2.5D var FDTD and 3D FDTD

Member Posts: 4

Hi,

I am trying to simulating the transmission characteristics of a directional coupler with certain waveguide geometry. 3D FDTD is so time consuming and requires a lot of memories, so I want to use 2.5D FDTD to conduct initial optimization and then use 3D FDTD to finalize it. But one thing I notice is that, the results given by 2.5D FDTD are quite different from the ones given by 3D FDTD, and this difference seems to grow when the cross-section of the waveguide has smaller base angle (with less vertical sidewall). Does anyone come across this before? Is there a way to decrease this discrepancy?

Thank you so much!

• Posts: 751Ansys Employee

First, 3D FDTD is a full vectorial discretization of the Maxwell's equations, whereas varFDTD uses variational/reciprocity method to decompose the 3D into 1D (the slab mode) and 2D (the actual simulation). SO depending on the waveguide and mode properties, there might be some fundamental difference. Second, when there is a side wall with angle involved, 3D FDTD directly solves it but varFDTD uses the mode at the green point as reference to get the effective index for 2D simulation use. if you place the green point inside the angled sidewall, you may get different result. The detailed method for VarFDTD can be found here:

https://support.lumerical.com/hc/en-us/articles/360034917213-MODE-2-5D-varFDTD-solver-introduction-

https://support.lumerical.com/hc/en-us/articles/360045466253-Introduction-to-varFDTD-When-to-use-varFDTD

As you have noticed, 3D FDTD can be resources-consuming, and some people want to get a quick yet not so accurate result. VarFDTD is one of the simplified approximation methods, which can give reasonable accuracy. Sometimes it can give almost the same accuracy as 3D FDTD, other times it gives not very accurate result. All will depend on the fact that if the modes/structures can be accurately described by the simplified method. If you want to get more details, I encourage you to read the papers:

1. Manfred Hammer and Olena V. Ivanova, MESA Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
2. "Effective index approximation of photonic crystal slabs: a 2-to-1-D assessment", Optical and Quantum Electronics ,Volume 41, Number 4, 267-283, DOI: 10.1007/s11082-009-9349-3
3. Allan W. Snyder and John D. Love, Optical Waveguide Theory. Chapman & Hall, London, England, 1983.

To improve the accuracy of VarFDTD, you may use fine mesh. However, the final result should be verified with the full 3D FDTD.

• Posts: 18Member

Thank you so much for your comment! My understanding is that the green cross is just one specified location for the solver to calculate the effective slab mode index, and the solver will calculate the effective index throughout the structure in the same fashion, that's why solve also has test point option? My current results indicate that larger the base angle of the waveguide, **** the discrepancy between 2.5D results and 3D results.

This directional coupler model is just a test model to verify whether the results provided by 2.5D varFDTD are reliable, since the it will take approximately a week to run a full 3D vectorial FDTD simulation consuming all of the memories and it might end up not converging eventually.

• Posts: 751Ansys Employee
edited April 26

Test points are used to check the effective index at those points. You can add more and change their locations; When there is a side angle, you can place test points there to get the difference at different locations. The solvers are universal for simulations. the total simulation time depends mainly on the device size and computer performance. Sometimes it is indeed very challenge,due to different reasons. Practically not every device can be simulated by FDTD, in terms of time consumed, available computer resources and accuracy.

If the structure does not have vertical mode coupling, you may try EME.

• Posts: 18Member

Thank you! How can I check the effective indices of these test points? My structure does not have vertical mode coupling, however the mode does not propagate parallelly to either x or y axis since the structure includes ring resonator and I need to calculate the transmission at different locations, I do not see any available ports or frequency domain monitors in EME solver. Do you have any suggestion on this? Thank you again!

• Posts: 751Ansys Employee

Are you talking about VarFDTD or EME? VarFDTD is efficient for ring resonator but not EME. If you really want to use EME, there are several special steps to be applied, which is out of the scope of this thread.

In varFDTD, there is no port object; EME and 3D FDTD have port objects.

To check the effective index in varFDTD, right click "check" or choose from the down triangle:

let's focus on varFDTD, and try to see if you can get the result.

• Posts: 18Member

Thank you so much for your reply and sorry for the late response. I put the slab mode approximation green cross at almost the center of one of the waveguides, and one of the test points at the waveguide structure with the slant side and another one at the position without waveguide. The results seem to make sense except the effective index of the test point 2 is way off, since with the unetched 0.27um-thick lithium niobate, the effective index there should be approximately 1.8(the value calculated by the slab mode approximation) instead of 1.4. The results are attached in the pictures, do you have any other suggestions to make it right? Thank you!

• Posts: 751Ansys Employee

Unfortunately this might be what it is. Since this method uses the core mode profile as the reference, there is no guarantee that other places have the "correct" effective index using the reference mode profile. Please refer the principle page. If you think you can estimate the effective index by your own, you can do a 2D FDTD simulation using some data from VarFDTD, and import them into the FDTD material database.

• Posts: 18Member

What do you mean by "do a 2D FDTD simulation using some data from VarFDTD"? Do you mean using varFDTD to calculate the effective index for different structures, and subsitute the real materials with these effective materials, and run 2D FDTD simulation instead of 3D?

• Posts: 751Ansys Employee

You mentioned that the data is not expected, so you can calculate your self, and import the data, together with the effective index calculated in varFDTD that you think they are ok, then import them in the regular FDTD, and do 2D simulation. All the data has already used the 3rd dimension information so only 2D FDTD simulation is enough.

• Posts: 18Member

I see, can you give me something to refer to regarding what data I should import and how? Thank you!