Thank you very much for your warm wishes, I feel better today.
I think the divergence problem, as you might have guessed it, is due to material fit. Since the make fit passive box is unchecked, material fit returns negative imaginary part for graphene which acts like a gain for this material. This runs the simulations to diverge.
I spent quite a significant time to improve the fit, but it was not very successful. Since the imaginary part is zero, here are good links to look and see how the material fit can be improved:
A good approach would be to run multiple simulations with narrower source bandwidth (instead of one broad source) and check the material fit for each simulation.
I have also modified simulation file and used small x and y span of FDTD as geometry is periodic along these directions. You can also use finer mesh over graphene material as part of convergence testing. Here is modified simulation file for your review:
graphene_THz_metamaterial_BK.fsp (369.0 KB)
Another options would to use other material models or trying 2D graphene.