Confusion with negative permittivity

[Vinc0110]

Negative permittivity values apparently cause problems in the simulation, as explained in the FAQ:
https://meep.readthedocs.io/en/latest/FAQ/#why-does-my-simulation-diverge-if-the-permittivity-is-less-than-0

I'm now wondering why the predefined perfect electric conductor (PEC) material is then using epsilon=-inf instead of epsilon=+inf:

meep/meep.i, line 1780:

perfect_electric_conductor = Medium(epsilon=-inf)

If I attempt to model an imperfect electric conductor replacing the PEC, say a copper sheet with a frequency-dependent complex epsilon using a LorentzianSusceptibility with a magnitude of around 1e6 to 1e7, the Eigenmode decomposition with MPB for the EigenModeSource does not work anymore and the fields seem to blow up.

However, If I flip the sign for a negative permittivity, MPB does work again, the simulation finishes and I'm getting correct results. The only problem is a RuntimeWarning and a lot of confusion, because this seems to contradict the statements in the FAQ.

RuntimeWarning: Epsilon < 1 may require adjusting the Courant parameter. See the 'Numerical Stability' entry under the 'Materials' section of the documentation

It would be nice if someone could clarify what's going on here and give a hint how to properly model a lossy metal that works with EigenModeSources. After all, the examples in meep/materials.py are also using positive permittivity values.

[stevengj]

What is actually used in the FDTD algorithm is 1/ε. So, it doesn't matter for perfect metals if ε=±∞, since in either case you get 1/ε = 0.

[stevengj]

properly model a lossy metal

You need to use dispersive materials.

that works with EigenModeSources

These use MPB, which only supports non-dispersive materials with ε > 0. See also #1319 for how we might improve this in the future.

[Vinc0110]

Thanks for the explanations.

These use MPB, which only supports non-dispersive materials with ε > 0. See also #1319 for how we might improve this in the future.

Does this also mean that it's not currently possible to simulate complex scattering parameters when dispersive materials are involved (i.e. any realistic materials), because Meep's mode decomposition feature also relies on MPB?

[Vinc0110]

In the documentation for the EigenModeSource, I just read that any dispersion will be ignored by MPB during mode calculations. Is it ignoring the entire material, or just the resulting imaginary part of the permittivity?
In the latter case, the result should still be close enough and the EigenModeSource profile and the mode decomposition for calculating scattering parameters should work. This is however not the case for my simulations.

[stevengj]

@smartalecH enabled some support for dispersive materials in #919, so the documentation should be updated to reflect that. It ignores the imaginary part of the permittivity, however.

Nevertheless, it still won't support negative permittivity, since MPB requires ε and μ to be positive-definite.