Diverging simulation about graphene metasurface - material fitting

Graphene-coated dielectric metasurface.fsp (248.1 KB)

Hello, I am trying to simulate dielectric metasurface loaded with graphene (λ=1.55μm) from the paper attached. First I simulate the dielectric metasurface, and a Fano resonance is shown, which is similar to the paper. But when I add the graphene which has a chemical potential of below 0.4 eV (0.5*ћω) , the simulation is diverging. Besides, if the chemical poential is tuned to above 0.5 eV, where graphene has become a dielectric-like material, the simualtion is normal. The simulation results is shown below.

This question seems similar to converging simulation about graphene plasmonic, but still I cannot fix it. Can anyone help me? My simulation file is attached.
Thanks for help.

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Dear @wuzr3

Based on the instructions on diverging simulations, I did three steps:

  • First, I changed all of the FDTD boundary conditions (BCs) to metal and saw that it is still diverging (this means that PML is not causing the problem)

  • Second, I changed the BCs back to original and changed the dt stability factor to 095, 0.9, and then 0.5. Simulation was still diverging. This means that stability is not the problem.

  • Third, and the only remaining major source of the problem was graphene material itself. I added movie monitors and I noticed that graphene behaves as gain material and drives simulations to diverge. To solve the problem, I took a look at the material properties from Material Explorer. While fit looks normal in the standard view, you can see that the real part of the conductivity gets negative for wavelength of 3-5 um:

Please note that while your source bandwidth is 1.5-1.6um, FDTD simulations actually use a pulse that includes other wavelengths too and it goes to zero at very high wavelength. A small contribution of these wavelengths that behave as gain material are the reason for divergence in your case. To solve this problem, you can either use a better fit or check the make fit passive box:

I used a chemical potential of 0.3 for the graphene. Please go ahead with the simulations and keep me updated if you had further questions.


Thank you very much. Now the problem is solved. Note that for graphene with a chemical potential of 0.2eV or 0.1 eV, the ‘make fit passive’ is not valid but use a ‘improve stability’ can avoid the diverging problem.

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Dear @wuzr3

I am glad that problem is solved, and thank you for additional information.