# Frequency analysis, mode confusion as a function of wavelength

Dear Knowledge Exchange Community,

I am trying to simulate simple waveguide structures with regards to effective refractive index (and its derivatives) over a specific wavelength range (0.7-1um). To do so I use the “Frequency analysis” solver. I am interested in the fundamental TE-like mode. For some reason the mode seems to get confused with a more confined TM-like mode half way through the wavelength-sweep. This of course affects the effective refractive index and especially its derivatives.
Why is this occurring, and is there a way to solve this or omit the problem?

Attached is a pdf with screenshots of the “Frequency analysis” window and the Lumerical MODE file.

Best regards,
Halvor

Hello @halvorf,

Thanks for posting and welcome to the community. If you monitor the third mode in this structure as you sweep frequency, you can see that the fundamental TE and TM1 begin coupling around 850nm; switching positions in the list and producing a discontinuity in the effective index.

The FDE solver has a hard time tracking the mode during this hybridization process and when you swept you stopped tracking the fundamental TE and started tracking the TM1.

I would expect the slope to stay about the same, and the effective index to have a discontinuity at this point. I would do two sweeps up to 850nm and 850-1000nm. You can see this artifact very clearly in the n_g and dispersion.

Usually the FDE solver is capable of tracking the modes as they move up and down the list, and there may be workarounds in scripting using commands like bestoverlap. This seems to be a quirck when using anisotropic materials.

Regards,

Dear @trobertson,
Thank you for the welcome and your response.
I will look into the bestoverlap command and try to find a work around. Have you tried this yourself? If so, do you have a script to offer?
The limit approach you suggest works well in some cases. The hybridization has some bandwidth to it. Depending on the waveguide geometry the hybridization bandwidth overlaps the frequency region of interest, rendering the simulation useless.
I would therefor very much like to find a solution to the problem.

Best regards,
Halvor

Hello @halvorf,

Sorry that we missed these questions. In case another user has a similar problem, this issue is discussed in more detail in this post: