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Guilin Sun
Ansys Employee

 “updating slab modes” is just a reminder message. No worry about it.

"Gamma-X sweep from 0-1 " it sould be from 0 to 0.5 since it is folded.

I would suggest you to continue using 3D FDTD as 2D varFDTD might not be that accurate.

I guess there are some unwanted frequency points on the "bands". Usually it means the simulation time needs to be a little bit long. But it cannot be too long to reach autsohutoff min default value of 1e-5. Otherwise the bands will have some missing points.

You may need to use symmetry-type of BCs to separate TE/TM modes if the structure has some symmetry: https://optics.ansys.com/hc/en-us/articles/360034382694-Symmetric-and-anti-symmetric-BCs-in-FDTD-and-MODE 

Other factors please read this post: 

Ansys Insight: Why my simulation result is different from published paper or experiment?